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  • 1970-1974  (751)
  • 1971  (751)
  • Organic Chemistry  (689)
  • Engineering General  (62)
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  • 1
    Electronic Resource
    Electronic Resource
    Editorial (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 3-3 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030103
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  • 2
    Electronic Resource
    Electronic Resource
    The numerical solution of non-linear consolidation problems (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 5-11 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It has long been recognized that permeability, compressibility and viscosity vary during the consolidation of soil. However, the introduction of these variations into consolidation theory leads to formidable difficulties due to their rendering the equations highly non-linear. Numerical methods are given herein which enable the governing equation to be solved for a variety of different non-linear laws.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030104
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  • 3
    Electronic Resource
    Electronic Resource
    Application of the simultaneous iteration method to undamped vibration problems (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 13-24 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems. This method is of significance when a few of the dominant eigenvalues and eigenvectors are required from a large matrix, and hence is particularly suitable for vibration problems involving a large number of degrees of freedom. It is shown that advantage may be taken of both the symmetry and the band form of the mass and stiffness matrices, thus making it feasible to process on a computer larger order vibration problems than can be processed using transformation methods. A method of allowing for body freedom is given and some numerical tests are discussed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030105
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  • 4
    Electronic Resource
    Electronic Resource
    An economical method for determining the smallest eigenvalues of large linear systems (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 25-33 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The general eigenvalue problem Ax = λBx as arising from vibration problems tackled by the finite element method is often solved by the economization method in which the two matrices are reduced to a more manageable size and approximate answers are obtained.This paper analyses the method in a more mathematical way than previous accounts and leads to a definition of the optimum set of variables to be retained during the reduction. An extension to the method is suggested which allows the approximate eigenvalue to be improved and bounds are obtained on the eigenvalues of the full problem before reduction.An estimate is made of the calculation involved in the method and it is concluded, by reference to examples, that the extended method leads to a more efficient algorithm.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030106
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  • 5
    Electronic Resource
    Electronic Resource
    Solution of the compressible flow equations (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 35-43 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique is described for solving the compressible flow equations in subsonic flow. The general quasi-linear equation ∇.g∇v = 0 is considered with g a function of ∇v. ∇v, and iterations of the form ∇.gn∇vn+1 = 0 are analysed, where g0 is suitably chosen and gn defined from vn for n≥1. This approach is applied to the compressible flow equations in terms of a velocity potential ø: monotonic convergence is predicted and at each iteration the error is multiplied by a factor less than the square of the greatest Mach number in the solution.Reliable convergence has been obtained in practice solving the linear equation for øn+1 by a finite difference method. The alternative of working in terms of the stream function ψ is discussed, and also discretization by the finite element method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030107
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  • 6
    Electronic Resource
    Electronic Resource
    Dynamic analysis of structures using the rank force method (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 103-117 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the finite element rank force method for the dynamic analysis of redundant structures is presented. The applied loading consists of discrete and distributed loads. Both forced and free vibrations are considered, the latter yielding latent vectors corresponding to dynamic redundancies.It is shown that the dynamic properties of an element are given by a static flexibility matrix, an inverse mass matrix, a damping parameter and a displacement vector representing the effect of the applied distributed loading.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030112
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  • 7
    Electronic Resource
    Electronic Resource
    An annular segment finite element for plate bending (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 119-129 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A stiffness matrix for a finite element having the planform of an annular segment is derived using the displacement approach. Numerical problems involved in the derivation are discussed and rapid convergence to exact solutions is demonstrated on three sample problems. It is concluded that the new element will be of great value to engineers concerned with the analysis of slabs of bridge decks curved in plan.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030113
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  • 8
    Electronic Resource
    Electronic Resource
    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030201
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  • 9
    Electronic Resource
    Electronic Resource
    Process analysis by statistical methods, D. M. Himmelblau, Wiley, New York, 1968. No. of pages: 460. Price: £8·75; $19.95 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 151-151 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030117
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  • 10
    Electronic Resource
    Electronic Resource
    Editorial notice (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 154-154 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030202
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  • 11
    Electronic Resource
    Electronic Resource
    The finite difference and localized Ritz methods (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 155-160 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The conventional central finite difference equations for the plane stress extension of flat plates are derived as a localized Ritz process. A dual differential-variational discretization of this type enables common classification of the finite difference and finite element methods. Also, it provides alternative methods of establishing sufficiency conditions and relative rates of convergence for discrete systems derived from a localized Ritz process, and the existence of solution bounds for discrete systems derived using difference procedures.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030203
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  • 12
    Electronic Resource
    Electronic Resource
    Finite element formulation of general electrothermoelasticity problems (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 161-179 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the development of consistent discrete models, via the concept of finite elements, of linear and non-linear electrothermomechanical behaviour of continuous bodies. In the development, general energy balances are utilized to derive equations governing electromagnetic fields over an element and coupled equations of motion and heat conduction of a typical element of the continuum. These equations make it possible to study a general class of field problems involving arbitrary geometries and boundary conditions. Sample problems are included.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030204
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  • 13
    Electronic Resource
    Electronic Resource
    Axial wave propagation in membrane shells of revolution (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 181-198 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic finite element technique, which is referred to in the literature as ‘computer-analysis’, is applied to wave propagation problems occurring in finite and semi-infinite linearly elastic membranes of revolution. Both semi-infinite and finite versions of cylindrical and conical membranes are considered, and a finite membrane having a meridional curve which is parabolic is solved. The source of excitation is generally a constant velocity motion of one end of the membranes, but the results for a stress-pulse input at one end of a semi-infinite cylindrical membrane are also given. The results for the finite membranes are new, and the results for the semi-infinite problems are discussed with respect to previously published results. The two-dimensional state of stress in the membrane requires careful ordering of the calculations, and the boundary conditions for finite membranes are shown to follow logically from this ordering of the calculations. The difference in the solutions resulting from prescribing an axial or a tangential velocity excitation at the end of a conical membrane is presented, and the mesh size necessary for convergence to the solution is indicated. The graphs of the results clearly indicate regions in space and time where the membrane model should be replaced by the shell formulation to represent a realistic structure. The technique is shown to be self-contained and independent of any formal method such as the method of characteristics.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030205
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  • 14
    Electronic Resource
    Electronic Resource
    Dynamic programming and the solution of the biharmonic equation (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 199-213 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of the biharmonic equation in a rectangular domain is presented in the context of continuous dynamic programming techniques. The equations are specialized to the solution of elastic rectangular plates. A suitable approximate expression of a certain functional equation containing derivatives only in one direction is used to derive equations for the stiffness and flexibility matrices of the plate. It is shown that those matrices satisfy matrix Riccati equations subject to suitable initial conditions. It is also shown that the condition of optimality in the Hamilton-Jacobi-Bellman equation directly expresses a classical variational principle, i.e. the principle of complementary energy. Some numerical examples are finally presented.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030206
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  • 15
    Electronic Resource
    Electronic Resource
    Quadrature rules for brick based finite elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 293-294 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030213
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  • 16
    Electronic Resource
    Electronic Resource
    A note on accuracy and convergence of finite element approximations (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 291-292 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030212
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  • 17
    Electronic Resource
    Electronic Resource
    Reduced integration technique in general analysis of plates and shells (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 275-290 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of plate and shell problems by an independent specification of slopes and middle surface displacements is attractive due to its simplicity and ability of reproducing shear deformation. Unfortunately elements of this type are much too stiff when thickness is reduced.In an earlier paper a derivation of such an element was presented1 which proved very successful in ‘thick’ situations. Here a very simple extension is made which allows the element to be economically used in all situations.The improved flexibility is achieved simply by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties. The process is of very wide applicability in improvement of element properties.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030211
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  • 18
    Electronic Resource
    Electronic Resource
    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030301
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  • 19
    Electronic Resource
    Electronic Resource
    A powerful hybrid method in finite element analysis (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 389-403 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An important limitation of finite element analysis, namely, the need for a large number of small elements in regions of finite or infinite stress concentrations and the difficulties of convergence in such cases, is well known. Rao1 suggested a possibility of overcoming this by developing hybrid techniques combining continuum and finite element concepts. In such techniques, each region of stress concentration is covered by one large ‘primary element’ whose description includes term(s) identifying the type and order of concentration, while the remaining structure is split into a few ‘secondary elements’ which are conventional finite elements. In this paper a procedure incorporating this concept is developed and its effectiveness is clearly demonstrated by successful application to two important examples, one of them with stress singularities. The concept, in fact, can be applied equally well to other two- and three-dimensional problems of continua with discontinuities and concentrations.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030308
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  • 20
    Electronic Resource
    Electronic Resource
    Discussion of paperSuryanarayan Patnaik and Pasala Dayaratnam, ‘Behaviour and design of pin connected structures’, Int. J. num. Meth. Engng, 2, 579-595 (1970). by Suryanarayan Patnaik and Pasala Dayaratnam (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 443-444 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030312
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  • 21
    Electronic Resource
    Electronic Resource
    Recent advances in matrix methods of structural analysis and design, edited by R. H. Gallagher, J. T. Oden and Y. Yamada, University of Alabama Press, Alabama, 1971. No. of pages: 904. Price: $32.50 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 446-446 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030315
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  • 22
    Electronic Resource
    Electronic Resource
    Discussion of paperR. S. Barsoum and R. H. Gallagher, ‘Finite element analysis of torsional and torsional-flexural stability problems’, Int. J. num. Meth. Engng, 2, 335-352 (1970). by R. S. Barsoum and R. H. Gallagher (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 444-445 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030313
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  • 23
    Electronic Resource
    Electronic Resource
    Announcements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 447-448 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030316
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  • 24
    Electronic Resource
    Electronic Resource
    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030401
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  • 25
    Electronic Resource
    Electronic Resource
    The elasto-plastic indentation of a half-space by a rigid sphere (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 451-462 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Using the finite element method, a detailed study of the deformations and stresses produced in an elastic-perfectly plastic half-space indented by a rigid sphere was done. The analysis covers the transition region from the maximum elastic contact load to a state where this load has been increased one hundredfold. Experimental results available in the literature are in good agreement with the analysis. In solving repeatedly the large number of linear equations involved in the solution of the problem, it was found profitable, in order to save computer time, to modify the direct elimination method. This technique is described in some details in the paper.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030402
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  • 26
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    Electronic Resource
    Non-linear structural analysis by dynamic relaxation (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 463-483 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Dynamic relaxation, an iterative method for use with digital computers, is described and is shown to be suitable for the solution of a system of linear equations and in particular for such problems derived from structural frame analysis. It is further shown that the method may be modified to include non-linear equations relating to these problems.Some specific examples of linear and non-linear solutions are given and comparisons are made with another computer method which performs the same tasks.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030403
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  • 27
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    Electronic Resource
    A note on convergence of finite element solutions (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 485-493 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence of nodal displacements obtained by the finite element method is investigated for special element patterns in plane elasticity with the aid of the differential equation derived from the equilibrium condition at each node. The convergence of strains is also discussed. It is shown that averaging is an effective tool for obtaining approximations to strain for some kinds of mesh arrangement. It is also shown that the approach becomes inaccurate along force boundaries.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030404
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  • 28
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    Stress and deformation analysis of fibrous composite materials by point matching (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 89-101 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The point matching numerical method and its generalization, the method of boundary point least squares, have been successfully applied to numerous boundary value and eigenvalue problems. The present paper demonstrates the application of these techniques to problems in the micromechanics of fibrous composite materials, i.e. determination of elastic moduli and stress concentrations for parallel-fibre materials which are loaded transversely with respect to the fibres. The solution technique utilizes exact solutions of the governing equations of plane elasticity for each component fibre and its surrounding matrix material in a typical repeating section of the composite material. The continuity conditions for stresses and displacements between fibre and matrix and the repeatability conditions at the boundary of the repeating section are satisfied approximately in a pointwise manner. Some special numerical techniques which were found to be particularly useful in applying the point matching method to these problems are delineated. The method is demonstrated for composite materials having circular, elliptical and square fibres in regular, staggered arrays. Numerical results are given which show the accuracy of the method as well as stress concentration and composite elastic moduli data.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030111
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  • 29
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    Concave programming and piece-wise linear programming (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 131-144 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the mathematical foundations of a technique that has been used extensively in structural optimization.1-6 Two basic problems are considered. The first of these is the concave programming problem which consists of finding the global minimum of ‘piece-wise concave functions’ on ‘piece-wise concave sets’. Since any function can be approximated by a piece-wise concave function, this method could in principle be used to find the global minimum in non-convex optimization problems. The second one is the piece-wise linear programming problem in which the objective function is convex and piece-wise linear. The iterative method outlined for handling this problem is shown to be much more efficient than the standard simplex method of linear programming.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030114
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  • 30
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    Generation of two- and three-dimensional finite elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 327-347 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many of the known finite elements are based on a variational procedure in a functional basis of monomials. The present paper attempts to formulate completely a finite element procedure which is non-variational on a functional basis which is left to the choice of the user.
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    URL: http://dx.doi.org/10.1002/nme.1620030304
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    An equation solver of very large capacity (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 379-388 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A very simple equation solver of very large capacity is developed. The method described here does not require a very large in-core memory; however, a fast random access device like a magnetic disk drive is required.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030307
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    A numerical solution of axisymmetric problems in elastodynamicsThis research was supported by the Research Foundation of the State University of New York. (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 361-377 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The equations governing the axisymmetric dynamic deformation of an elastic solid are considered as a symmetric hyperbolic system of linear first-order partial differential equations. The characteristic properties of the system are determined and a numerical method for obtaining the solution of mixed initial and boundary value problems in elastodynamics is presented. Two examples are considered.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030306
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    The solution of structural equilibrium equations by the conjugate gradient method with particular reference to plane stress analysis (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 349-360 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer program is described for the analysis of plates in extension using the equivalent plane-framework idealization. The conjugate gradient method is adopted to solve the resulting large number of simultaneous equations. Performance figures are quoted for the program when used on an ICL KDF9 machine with a restriction of 18K on the available core store. The method is generally shown to provide a satisfactory solution to a heavy computational task and thus permits the solution of very large structural systems on a small computer.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030305
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    Improved numerical integration of thick shell finite elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 575-586 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quadratic thick shell element derived from a three-dimensional isoparametric element was first introduced by Ahmad and co-workers in 1968. This element was noted, however, to be relatively inefficient in representing bending deformations in thin shell or thin plate applications. The present paper outlines a selective integration scheme for evaluating the stiffness matrix of the element, in which each component of the strain energy is evaluated separately using a different Gaussian integration grid for each contribution. By this procedure, the excessive bending stiffness of the element, which results from the use of me quadratic interpolation functions, is avoided.The improved performance of this element, as compared with the original thick shell element, is demonstrated by analyses of a variety of thin and thick shell problems. Editors' note: A similar development was outlined by O. C. Zienkiewicz and co-workers in lnt. J. num. Meth. Engng, 3, 275-290 (1971). Some important details differ between the two papers which are thus complementary.
    Additional Material: 14 Ill.
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    Incremental displacement in non-linear analysis (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 587-588 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030412
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    An introduction to APL, W. Prager, Allyn and Bacon, Boston, 1971. No. of pages: 134 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 591-591 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030414
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    Letters to the editor (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 588-591 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030413
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    An introduction to applied probability and random processes, J. B. Thomas, Wiley, New York, 1971. No. of pages: 350. Price: £6·15 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 591-592 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030415
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  • 39
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    Masthead (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030101
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  • 40
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    Erratum (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 1-2 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030102
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  • 41
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    The piecewise-linear analysis of two connecting structures including the effect of clearance at the connections (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 45-51 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of analysis is presented for two structures which have connections with clearance. It is assumed that the behaviour of the structures is described, by the movement of discrete nodes and that as the load on the structure changes, clearances open or close between corresponding nodes on the structures; each time this occurs the stiffness of the combined structure changes because its configuration has changed. Between these changes, the structure will behave linearly and the overall behaviour can be described as piecewise linear. Applications include diesel engine crankshafts with bearing clearances and the wrap-around problem in pin-and-eye connections.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030108
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    Finite element method applied to the problem of stability of a non-conservative system (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 63-87 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is applied to the stability analysis of structural systems subject to non-conservative forces. The development of the method is general, but the specific application considered here is the stability of thin-walled members subject to follower forces. The method predicts the type of instability, whether it be buckling or flutter. Example problems, for which exact solutions are known, illustrate the accuracy and convergence characteristic of the finite element formulation.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030110
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    Non-axial-symmetric thermal stresses in circular discs or cylinders (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 53-61 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A solution is presented for the computation of the transient thermoelastic stresses in a hollow cylinder with temperature boundary conditions given as a circumferential variation of surface heat transfer coefficient. The temperature distribution is solved explicitly. The problem is set up using the Airy stress function which leads to the biharmonic equation. This approach requires the satisfaction of three Michell integrals at the inner boundary in order to ensure single-valued displacements and rotation. An iterative method is described in which these integrals are all simultaneously satisfied and thus provide the necessary non-zero boundary conditions for the solution of the biharmonic equation which is rapidly solved by Gaussian elimination. Results are presented for the general case where the temperature is a function of r and θ. The computer program is checked by assuming a constant value of the surface heat transfer coefficients. In this case a closed form solution is obtained.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030109
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    Non-linear programming for the plastic analysis of local deformations in shell structures (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 215-232 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents an analysis of the response of plastic spherical and cylindrical shells subjected to loads applied through a rigid boss. Special emphasis is placed on following the load-deflection behaviour of these structures after the application of the yield-point load in order to predict the appearance of any snapping action.The method of analysis assumes that upper bound calculations are applicable and that the associated velocity fields can be represented by a series of piecewise continuous polynomials. The internal dissipation of energy for the structures are then written in terms of the coefficients of these polynomials and the values appropriate to the solution are found by using a non-linear programming routine.The results of this analysis are correlated with a non-dimensional boss size parameter p and compared with the results of experimental investigations. Mention is also made of the possible effects of initial imperfections.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030207
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    Trigonometric function representations for rectangular plate bending elements (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 261-273 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A study of bending of plates for small deformations by applying the finite element method is presented in this paper.A new class of displacement functions has been developed for rectangular bending elements. For the first time a method is proposed for the derivation of displacement functions in which trigonometric expressions that had apparently failed to yield satisfactory results in earlier attempts can be used along with polynomial terms.The derivation leads to conforming type of displacement functions which satisfy the convergence criterion. The approach also demonstrates how many more new displacement functions can be found.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030210
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  • 46
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    A steepest gradient method for optimum structural design (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 249-259 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a search procedure for finding the unconstrained maximum or minimum of a function of many independent variables. If this function represents the volume, cost, stiffness, etc. of a structure and each of the independent variables is associated with a parameter governing the geometry of the structure then designs of optimum geometry may be made in certain cases with the assistance of this search procedure. The procedure consists of steepest gradient calculations used in conjunction with a reverse Fibonacci location process. A ridge-following technique is included to speed convergence in addition to localized exploration in the region of an optimum.The search procedure has been programmed for computer use and an outline of its structural design applications is presented together with an example of its efficiency in a specific case.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030209
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  • 47
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    Vibration analysis of rotating cantilever plates (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 233-248 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc. The plane of the plate is assumed to make any arbitrary angle with the plane of rotation of the disc. The distributed centrifugal force is resolved into two components - one acting in the plane of the plate and the other normal to the plate. The stresses produced in the middle surface of the plate due to the in-plane forces are first determined. The increase in the bending stiffness of the plate elements due to these in-plane stresses is obtained in a manner similar to that used in the stability analysis of plates. The component of the distributed centrifugal force normal to the plate surface is added to the inertia force.From the results of computations carried out for various values of the aspect ratio, the speed of rotation, the disc radius and the setting angle, empirical formulae are derived giving the effect of these parameters on the natural frequencies. These empirical formulae are observed to be in agreement with the corresponding known formulae for rotating cantilever beams, when the aspect ratio is high.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030208
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    On the calculation of consistent stress distributions in finite element approximations (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 317-325 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory of conjugate approximations1 is used to obtain consistent approximations of stress fields in finite element approximations based on displacement assumptions. These consistent stresses are continuous across interelement boundaries and involve less mean error than those computed by the conventional approach.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030303
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    Network-topological formulation of analysis and design of rigid-plastic framed structures (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 425-441 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified network-topological approach to the formulation and solution of the analysis and minimum weight design of rigid-plastic structural systems is presented. It is shown that both analysis and design can be formulated using network concepts, but that, in contrast to elastic networks, the formulation results in a mathematical programming problem. Formulations based both on the static and kinematic theorems of plasticity are presented, and it is shown that duality guarantees that the two types of formulation yield identical results. The problem is first formulated on the basis of a simple definition of yielding, and is then generalized to the case where yielding is defined in terms of a yield surface.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030311
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    Numerical control, olesten, Wiley-Interscience, New York, 1970. No. of pages: 645. Price: £9.50 (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 445-446 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030314
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    A refined curved element for thin shells of revolution (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 495-508 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A refined axisymmetric curved finite element for the analysis of thin elastic-plastic shells of revolution is described in the paper. The improved element is obtained by employing cubic polynomials in terms of local Cartesian co-ordinates for the assumed in-plane and out-of-plane displacements. This introduces into the solution two internal degrees of freedom in the cord direction of each element. These internal degrees of freedom are removed by static condensation before assembling the individual element stiffness matrices, and are subsequently recovered after the nodal displacements are obtained. On comparison with the previous formulation, this procedure greatly improves the accuracy of the solution especially with regards to in-plane stress-resultants at discontinuities in the meridional curvature and interelement equilibrium of forces. The latter fact makes it possible to analyse shells with a discontinuous meridional slope. In using this element, improvement in the convergence of the elastic-plastic solutions has also been observed.Several examples illustrate the quality of solutions. The reported study is limited to axisymmetric loadings cum boundary conditions.
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    URL: http://dx.doi.org/10.1002/nme.1620030405
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    Numerical methods for evaluation of equilibrium composition of ideal gases (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 509-517 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper considers methods of solution of the relevant equations based on the Newton-Raphson process. Expressions are derived for calculation with both good and very poor initial guesses and for calculation of pressure, volume and temperature during an equilibrium process. A method of programming the calculations is outlined. Variations and modifications to suit specific situations are discussed.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620030406
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    A frontal solution program for finite element analysisB. M. Irons, ‘A frontal solution program for finite element analysis’, Int. J. num. Meth. Engng, 2, 5-32 (1970). (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 149-149 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030116
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    Note on dynamic relaxation (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 145-147 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Dynamic Relaxation (DR) method of solving a set of simultaneous linear equations requires an estimate of the spectral radius of the matrix. Dividing each equation by the corresponding row sum of moduli of the elements of the matrix gives a convenient upper bound of unity to this. This note shows that the DR method then gives a faster asymptotic rate of the convergence than the degenerate Chebyshev method which it closely resembles.
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    URL: http://dx.doi.org/10.1002/nme.1620030115
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    Discussion of paperS. Gallof and B. Kaplan, ‘Numerical solution and utilization of Green's functions,’ Int. J. num. Meth. Engng, 1, 169-175 (1969). by S. Gallof and B. Kaplan (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 295-296 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030214
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    A static and dynamic finite element shell analysis with experimental verification (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 299-315 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A system of finite element shell analysis codes, called SABOR/DRASTIC, is used to analyse a complex two-layered shell of revolution under static and dynamic asymmetric loads. The dynamic analysis is compared with experimentally measured response. In this linear elastic analysis, emphasis is placed on the inherent flexibility of the finite element method in modelling the complex structural geometry of a given test specimen. Static studies, which involve variations in important shell parameters, and dynamic studies, which provide a successful correlation with experiment, are used to illustrate both the detail and the generality with which shell analyses may now be performed with confidence.
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    Linear programming methods of displacement analysis in elastic-plastic frames (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 415-423 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The analysis is aimed at determination of displacements in elastic-perfectly plastic frames, in the case of monotonically increasing loads. Spread of partial plasticity from hinges and change of geometry on the conditions of equilibrium are not included. Extremum energy principles and linear programming methods are employed to solve the problem. Both the kinematic and the static formulations of the problem are presented. The mathematical models of the formulations constitute a dual pair of linear programming problems.
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    URL: http://dx.doi.org/10.1002/nme.1620030310
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    Use of optimization methods to solve heat convection problems with unknown wall boundary conditions (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 405-413 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In convection heat transfer problems, it is convenient to solve the governing differential equations by using straightforward marching techniques for numerical integration. However, the boundary layer equations in these heat transfer problems are not of the initial value type even though they are parabolic equations. Consequently marching techniques are not successful until correct initial values are known. A means of determining these initial values is presented herein. Selected optimization methods are utilized in conjunction with marching integration techniques to solve third- and fourth-order ordinary differential equations which have three unknown initial boundary conditions. Two optimization methods, one deterministic and the other non-deterministic in nature, are used both independently and in combination as determined by the particular circumstances. Two applications are used to demonstrate the technique and comparison is made with existing solutions.
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    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030309
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    An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co-ordinates (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 519-528 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer orientated method is presented which generates meshes of triangular elements in plane and curved surfaces. Depending on geometrical and material variations, the region to be discretized is divided into a number of four sided zones. By using curvi-linear co-ordinate systems, nodes within and on the boundary of each zone are automatically positioned and referenced to a global Cartesian co-ordinate system. Elements are automatically assembled from these nodes. Input data is required to specify the positions and material properties of each zone and how they are connected. Examples are given which illustrate the range of meshes that can be generated. Extension of the method to generate three-dimensional tetrahedral elements is indicated.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030407
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    A finite-deflection analysis of shallow arches by the discrete element methodThis paper is Crown copyright and is reproduced here with the permission of the Controller, Her Majesty's Stationery Office. (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 529-552 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discrete element displacement method is used to analyse the finite-deflection behaviour of shallow arches. The arches are idealized as assemblies of shallow curved elements and the necessary properties of the displacement patterns in these elements are discussed. Numerical solutions of the geometrically non-linear problem are obtained by directly minimizing the total potential energy of the system.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030408
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    Global-local finite element (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 565-574 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element procedures usually require more degrees of freedom for a specified accuracy than does a classical Ritz procedure if suitable coordinate functions are available. This paper develops a combined global and local dependent variable representation which couples the conventional and finite element Ritz methods. This hybrid method preserves much of the flexibility of the finite element method while increasing the solution accuracy for a specified system order. The method is illustrated by examination of a beam and a plate vibration problem.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030410
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    A simple algorithm for the stiffness matrix of triangular plate bending elementsThe authors are indebted to the referees for many comments and suggestions. (1971)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 3 (1971), S. 553-563 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For a hierarchy of polynomials on the triangle there is derived an algorithm for computing the stiffness matrix of the plate bending element. The algorithm is easy to program and means a considerable saving of the computing time. The same approach can be used for any elliptic equation with constant coefficients.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620030409
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  • 63
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    Struktur-Reaktivitätsuntersuchungen mit heterosubstituierten Nitrilen. IV. Kinetik und Mechanismus der gekoppelten Additionen von N-Methylanilin und Phenolen an Arylcyanate (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 58-68 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Bei der gemeinsamen Einwirkung von Phenolen und N-Methylanilin auf Arylcyanate katalysieren die Phenole die N-Methylanilin-Addition zu Isoharnstoffen und N-Methylanilin die Phenol-Addition zu Kohlensäure-diesterimiden. Die Reaktionen verlaufen über sechsgliedrige übergangszustände und sind durch stark negative Aktivierungsentropien (≈ -43 cal/Mol · grd) gekennzeichnet. Substituenteneffekte wirken sich unterschiedlich aus. Bei substituierten Arylcyanaten ist die Elektrophilie der OCN-Gruppe, bei substituierten Phenolen die Stärke der Assoziate maßgebend für die Reaktionsgeschwindigkeit. In den letzteren Fällen lassen sich daher die Additionsgeschwindigkeiten durch lineare Beziehungen der Form lg k = a · Δ\documentclass{article}\pagestyle{empty}\begin{document}$ \widetilde{v} $\end{document}OH - b beschreiben.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/prac.19713130107
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    Zum sterischen Verlauf asymmetrischer Induktionen. I. Beziehungen der Konstitution und Konfiguration zwischen rac. α-Alkylamino-propiophenonen und ihren Reduktionsprodukten (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1-16 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Nach bisherigen Ergebnissen entstehen aus Mono- und Dialkylaminopropiophenonen durch Reduktion entsprechende α-Aminoalkohole der erythro-Konfiguration. Aus vergleichenden Untersuchungen an Modellketonen mit verzweigten Alkylresten am Stickstoffatom geht der Zusammenhang zwischen diesen Strukturelementen am Asymmetriezentrum mit der sterischen Richtung der asymmetrischen Induktion und den Modellen vom Reaktionsmechanismus hervor. Die Diskussion führt zu folgender Voraussage: α-Dialkylamino-pro-piophenone mit normalen oder einfach verzweigten Alkylresten (z.B. Isopropylrest) werden zu erythro-Epimeren reduziert. Wenn am dialkylierten Stickstoffatom ein Alkylrest mit einem tertiären Kohlenstoffatom (z.B. tert.-Butylrest) gebunden ist, erhält man Reduktionsprodukte der threo-Konfiguration.
    Additional Material: 10 Tab.
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    URL: http://dx.doi.org/10.1002/prac.19713130102
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    Kinetische Untersuchung der bei den Umsetzungen von Phenolen mit Phosphoroxidchlorid ablaufenden konkurrierenden Folgereaktionen (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 69-82 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Kinetik der Umsetzungen von Phenolen mit Phosphoroxidchlorid bzw. den entsprechenden Phosphorsäure-arylesterchloriden wurde durch volumetrische Verfolgung des freigesetzten Chlorwasserstoffes untersucht. Die Geschwindigkeitskonstanten wurden mit Hilfe digitaler Rechenprogramme bzw. durch Simulierung des Reaktionsystems auf einem Analogrechner bestimmt.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/prac.19713130108
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  • 66
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    Zur Kinetik der Spaltung der Phosphor-Kohlenstoff-Bindung in Aroyl-Phosphonsäurediäthylestern (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 83-98 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Kinetik der zu Benzoat-Ionen und Phosphorigsäurediäthylester führenden Spaltung der Phosphor-Kohlenstoff-Bindung von Aroylphosphonsäurediäthylestern läßt sich in Dioxan-Phosphatpuffer-Lösungen mittels einer spektralphotometrischen Meßmethodik verfolgen. Für p-Methylbenzoyl-, Benzoyl- und p-Chlorbenzoyl-phosphonsäurediäthylester 2a-c werden die Geschwindigkeitskonstanten und Aktivierungsparameter der P-C-Bindungsspaltung für unterschiedliche Mischungsverhältnisse des Lösungsmittelsystems im pH-Bereich 5 bis 8 bei Temperaturen zwischen 20° und 40° angegeben. Die pH- und Lösungsmittelabhängigkeit der Spaltungsgeschwindigkeit, der durch die HAMMETT-Beziehung beschreibbare Substituenteneinfluß auf die Geschwindigkeitskonstante, die Korrelation der k-Werte mit den polarographischen Halbstufenpotentialen der Reduktion von 2a-c sowie die UV-Spektren dieser Substrate werden diskutiert. Auf Grund des experimentellen Nachweises der allgemeinen Basenkatalyse in SÖRENSEN-Phosphatpuffer-Lösungen wird als geschwindigkeitsbestimmender Schritt der Spaltung die Lösung der P—C-Bindung, die die Deprotonierung eines Substrat-Wasser-Adduktes einschließt, vorgeschlagen.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/prac.19713130109
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    Heterocyclic azo dyes. III. Azo Dyes Containing the Benzo-1,2,3-thiadiazole Nucleus (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 129-136 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The synthesis, some dyeing and fastness properties of several new dispersed and acid dyes derived from 5-amino-benzo-1,2,3-thiadiazole are described. Comparison between the dyeing properties of some synthesised dyes and other similar dyes is also given.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/prac.19713130113
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    Zum Mechanismus der Oxydation mit Permanganat in alkalischer Lösung. II Oxydation tertiärer C—H-Bindungen (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 153-160 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Als Modellreaktionen zur Aufklärung der Kinetik und des Mechanismus der Oxydation tertiärer C—H-Bindungen durch Permanganat in alkalischen Lösungen wurde die Oxydation von Diphenylessigsäure untersucht. Es wurde gezeigt, daß bis zu Laugenkonzentrationen von etwa 1 m ein Mechanismus unter direktem oxydativen Angriff des Permanganats auf die tertiäre C—H-Bindung überwiegt und im geschwindigkeitsbestimmenden Schritt eine H—übertragung erfolgt. Die Geschwindigkeitskonstante beträgt 3,3 · 10-3 1 mol-1 s-1 bei 20°C und der kinetische Deuteriumisotopieeffekt 7,8.Mit steigender Laugenkonzentration wird in zunehmendem Maße ein radikalischer Mechanismus unter Beteiligung von OH-Radikalen wirksam. Dies drückt sich in einer charakteristischen Zunahme der Geschwindigkeitskonstanten mit steigender Laugenkonzentration sowie in einer Abnahme des kinetischen Isotopieeffektes aus.Es wird eine Variante zur kinetischen Analyse der beiden Mechanismen angegeben und die Geschwindigkeitskonstante für die Reaktion der OH-Radikale mit der tertiären C—H-Bindung zu 1,4 · 107 1 mol-1 s-1 bei 20°C bestimmt.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130116
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    Alkoholysis Reactions of Hexaalkoxy Dititanium Alkylene-bis(acetoacetates) (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 174-178 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130119
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    Co-ordination Complexes of Tungsten-oxy-dichloride Dialkoxides, molybdenum-oxy-dichloride dialkoxides and molybdenum tri-chloride dialkoxides with 1,10-phenanthroline (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 187-192 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130121
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    Masthead (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971) 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130201
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    Nitrovinylverbindungen. I. Dinitroalkadiene als thermische Abbauprodukte von MANNICH-Basen-dihydrochloriden (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 205-210 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Durch Aminomethylierung von α,ω-Dinitroalkanen entstehen symmetrische Bis-MANNICH-Basen, die nach Überführung in ihre Dihydrochloride zu Dinitroalkadienen thermolysiert werden. Zur Struktursicherung dienen NMR-Spektren und die Addition von p-Toluidin.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/prac.19713130203
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    Dehydrierung 1-substituierter Pyrazolidone-(3) in Gegenwart von Formaldehyd und sekundären Aminen (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 236-246 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Dehydrierung der N-MANNICH-Derivate 2 1-substituierter Pyrazolidone-(3) ergibt C-MANNICH-Derivate 5 1-substituierter 3-Hydroxy-pyrazole. Die Ausbeute an 5 ist quantitativ, wenn der 1-Substituent Aryl ist und nimmt mit zunehmender Zahl der α-H-Atome im 1-Substituenten ab. Als Nebenprodukte entstehen 1-Alkyliden- bzw. 1-Aralkyliden-pyrazolidon-(3)-N1⊕,N2⊖-betaine (Azomethinimine) 6. 5 erhält man auch direkt aus 1-substituierten Pyrazolidonen-(3), Formaldehyd, sekundären Aminen und Jod. NMR-, IR-Spektren und Reaktionsmechanismen werden diskutiert. 1-Cyclohexylpyrazolidon-(3) 1 b wird von Jod zu 3-Hydroxy-1-cyclohexylpyrazol 3c und dem Azomethinimin 6c dehydriert, mit Brom entsteht außerdem 4-Brom-3-hydroxy-pyrazol 4c.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130207
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    α-Substituierte Phosphonate. XII. Zur Reaktivität von Acetalen des Formylphosphonsäureesters (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 265-276 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Alkyl- und Arylacetale 1 des Formylphosphonsäurediäthylesters wurden in wäßrigem bzw. nichtwäßrigem Medium mit HCl order HBr umgesetzt, wobei je nach eingesetztem 1 Spaltung der P-C-Bindung bzw. Entalkylierung der Phosphonsäureestergruppen beobachtet wurde. Glatte P — C-Spaltung trat auch beim Erwärmen des Diäthylacetals 1a mit Brenzcatechin ein. - Durch Umsetzung von 1a, b bzw. 1 d mit Na-Äthylat wurden die Na-Salze der entsprechenden Monoester von 1 erhalten, die sich zu gemischten Diestern 12 alkylieren bzw. mit Säure in die Phosphonsäuremonoester 5 überführen ließen. Aus den Arylderivaten 5b und 5c wurden die Säurechloride 14b und c gewonnen. 14b gab mit Phenylmagnesiumbromid das Phosphinsäurederivat 17c. - Mit PCl5 reagierten die Ester-acetale 1 nicht unter Bildung der Phosphonsäuredichloride, sondern wiederum unter Spaltung der P—C-Bindung.
    Additional Material: 2 Tab.
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    URL: http://dx.doi.org/10.1002/prac.19713130211
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    The STOBBE Condensation, Part IX. The cyclisation of (E)-3-Methoxycarbonyl-4-(5′-methyl-2′-thienyl)-but-3-enoic acidi.e., COOCH3 group and thiophen ring in trans-position. The nomenclature of cis/trans isomers used herein follows the IUPAC 1968 Tentative Rules, Section E, Fundamental Stereochemistry, J. org. Chemistry 35, 2849 (1970). See also: J. E. BLACKWOOD, C. L. GLADYS, K. L. LOENING, A. E. PETRARCA, and J. E. RUSH, J. Amer. chem. Soc. 90, 510 (1968); Introduction to Subject Index of Chem. Abstr. 66 (1963)., and α,β-bis-(5-methyl thenylidene)-succinic anhydride, to benzothiophen derivatives (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 247-253 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The condensation of 5-methyl-thiophen-2-aldehyde with dimethyl succinate in the presence of potassium t-butoxide or sodium hydride gave predominantly (E)-3-methoxy-carbonyl-4-(5′-methyl-2′-thienyl)-but-3-enoic acid 1a, whose configuration is proved by cyclisation with sodium acetate in acetic anhydride to the corresponding benzothiophen derivatives 2. Alcoholysis of the derived (E)-carboxy-4-(5′-methyl-2′-thienyl)-but-3-enoic anhydride 3 gives the half-ester 1c which is isomeric with the half-ester 1a. Condensation also gave the α,β-bis-(5-methyl thenylidene)-succinic acid 4a in small amounts. The derived anhydride 5 yields on pyrolysis 4-(5′methyl-2′-thienyl)-2-methyl-benzothiophen-5,6-dicarboxylic anhydride 6.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130208
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    Der elektronenstoßinduzierte Abbau von Tetraalkoxysilanen (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 357-370 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Zerfallsreaktionen der Tetraalkoxysilane Si[—O—(CH2)nCH3]4 (n = 0-4) und Si[—O—(CH2)nCH(CH3)2]4 (n = 0, 1, 2) bei Elektronenstoß in der Ionenquelle des Massenspektrometers werden wiedergegeben. Sie bestehen im Abbau der primär durch Fragmentierung aus dem Molekülionen gebildeten Ionen (Alkyl-O-)3Si+ und (Alkyl-O-)3Si—OCH2+. Diese Abbaureaktionen sind Folgen von Wasserstoffumlagerungen, in deren Verlauf Aldehyd- und Olefinabspaltungen miteinander konkurrieren. Im allgemeinen überwiegt die Olefinabspaltung. Die Besonderheiten dieser Reaktionen bei der Fragmentierung der verschiedenen Tetraalkoxysilane werden diskutiert.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130221
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    Masthead (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971) 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130401
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    Beitrag zur katalytischen Veresterung von Carbonsäuresalzen mit Alkylhalogeniden (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 561-568 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Herstellung von Estern aus Alkalisalzen verschiedener Carbonsäuren mit Alkylhalogeniden in Gegenwart von tertiären Aminen oder quartären Ammoniumsalzen wird am Modellbeispiel Natriumbenzoat/Benzylchlorid/Triäthylamin untersucht und die Abhängigkeit der Reaktion von verschiedenen Parametern bestimmt. Die Ergebnisse sind durch die Annahme einer zusätzlichen Reaktionsphase an der Festkörperoberfläche erklärbar. Als Katalysator wirkt das quartäre Ammoniumion, tertiäre Amine sind nur als Vorstufe anzusehen.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/prac.19713130402
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    Reactivity of the exocyclic double bond in 4-arylidene-2-phenyl-2-imidazolin-5-ones toward organomagnesium compounds. II (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 594-601 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 4-Arylidene-2-phenyl-2-imidazolin-5-ones 1 react with Grignard reagents in a boiling ether-benzene mixture to yield 4-diarylmethyl derivatives 2 together with their oxidation products 3 and 4. The exocyclic double bond in 5 also undergoes addition reaction with the same reagents to yield 4-triarylmethyl derivatives 6. Alkylation of 2 affords the 4-alkylimidazolones 7 and 8.
    Additional Material: 3 Tab.
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    URL: http://dx.doi.org/10.1002/prac.19713130406
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    Spektrale Eigenschaften einiger Glucopyranoside und 2-Desoxyribofuranoside tautomeriefähiger π-Mangel-Heteroaromaten (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 614-625 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Titelverbindungen wurden NMR-, UV- und CD-spektroskopisch untersucht. An Hand der chemischen Verschiebung der Protonen des Zuckerrestes wurde für alle untersuchten N-β-D-Glucopyranoside eine anti-Konformation nachgewiesen. Das Vorzeichen der Cotton-Effekte der Glucopyranoside und Desoxyribofuranoside hängt außer von der Konfiguration wesentlich von der Struktur des Aglykons ab. Veränderungen in unmittelbarer Nähe des glykosidischen Stickstoffatoms (6-Azathymin- und Pyridazon-(3)-Derivate) führen zu einer Umkehr des Vorzeichens der Cotton-Effekte.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130409
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  • 81
    Electronic Resource
    Electronic Resource
    Fragmentierung von N-Chlor-azocarbonamiden (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 642-645 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Phenylazocarbonamide liefern nach N-Chlorierung mit tert.-Butylhypochlorit in Chloroform in einer Fragmentierungsreaktion kristallines Phenyldiazoniumchlorid 4 in hoher Ausbeute. Auch N-Chlor-cyclohexyl-azocarbonamid ist fragmentierbar.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130412
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  • 82
    Electronic Resource
    Electronic Resource
    Zur Alkylierung des Ammoniaks und einiger seiner Derivate durch o-Xylylendihalogenide (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 686-698 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Umsetzung von o-Xylylendihalogeniden mit Ammoniak und einigen seiner Derivate (Benzylamin, N,N-Diphenylhydrazin, Carbonsäurehydrazide, Harnstoff, Cyanamid) liefert Isoindolin 2, 2-substituierte Isoindolin- und o-Xylylendiaminderivate.Eine neue Methode zur Darstellung von 2 aus o-Xylylendihalogeniden und Cyanamid wird beschrieben.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130416
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  • 83
    Electronic Resource
    Electronic Resource
    Reactions with 2-thiazolin-5-ones. III. The behaviour of 4-Arylazo-2-alkoxy-2-thiazolin-5-ones toward amines and Grignard reagents (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 706-714 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Treatment of 4-arylazo-2-alkoxy-2-thiazolin-5-ones 4a-f with glycine or phenylhydrazine effects their conversion into 1-aryl-5-alkoxy-1 H-1,2,4-triazole-3-carboxylic acid derivatives 5a-j, with the loss of hydrogen sulfide. On the other hand, the reaction of the 2-ethoxy (4a-c) and the 2-isopropyloxy (4g-i) derivatives with strong basic amines involves the loss of an alkyl mercaptan to yield the N-substituted amines 7d-j of 1-aryl-Δ2-1,2,4-triazolin-5-one-3-carboxylic acids. The 2-benzyloxy derivatives 4d-f react with the same reagents to give the N-substituted amides 2a-g of 1-aryl-Δ2-1,2,4-triazolin-5-thione-3-carboxylic acids, with the loss of benzyl alcohol.Hetero-ring opening of 4, followed by recyclisation, occurs upon treatment with ethyl or phenyl magnesium halides to yield the triazolinethione derivatives 13 a-c.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130418
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  • 84
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    Kationische Farbstoffe und Vorstufen. VI. Versuche zur Cyclisierung von S-Ketomethylen-sowie o-Hydroxyphenyl-thiolester-Derivaten zu 1,3-Oxathiolium- bzw. 1,3-Dithiolium-Salzen (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 722-729 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Es wird über Versuche zur Synthese von 1,3-Oxathiolium-Salzen aus S-Ketomethylen sowie o-Hydroxyphenyl-thiolester-Derivaten berichtet. Die Salze bilden sich nur bei der Einwirkung von starken Mineralsäuren (HClO4) auf o-Hydroxyphenyl-thiolester bzw. auf ihre zugehörigen Ausgangsverbindungen, während unter gleichen Bedingungen die entsprechenden S-Ketomethylenderivate nicht reagieren. Diese cyclisieren dafür aber in Gegenwart überschüssiger Thiosäuren zu 1,3-Dithiolium-Salzen, deren Struktur, ebenso wie die der 1,3-Oxathiolium-Salze, an Hand analytischer und spektroskopischer Daten gesichert wurde.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130420
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  • 85
    Electronic Resource
    Electronic Resource
    Synthese und Reaktivität von 6-Fluor-thymin (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 602-606 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ausgehend von 2,4,6-Trichlor-5-methyl-pyrimidin läßt sich über 2,4,6-Trifluor-5-methyl-pyrimidin und 5-Methyl-2,4-dibenzyloxy-6-fluor-pyrimidin durch nachfolgende Abhydrierung der Benzylgruppen 6-Fluor-thymin in guter Ausbeute gewinnen. Die Verbindung ist im Gegensatz zu 6-Fluor-uracil in wäßriger Lösung stabil und daher als biologisch aktive Substanz einsetzbar. Mit NH3 oder Benzylamin reagiert 6-Fluor-thymin leicht zu 6-Amino- bzw. 6-Benzylamino-thymin.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130407
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  • 86
    Electronic Resource
    Electronic Resource
    Kationische Farbstoffe und Vorstufen. VIII. Synthese von Kondensierten 1,3-Oxathiolium-Salzen durch Umsetzung von Chinonen mit aromatischen Thioamiden (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 737-744 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Durch Umsetzung von Chinonen mit N,N-disubstituierten Aryl-thioamiden in Gegenwart saurer Kondensationsmittel wird ein neuer Typ farbiger heterocyclischer Verbindungen mit kondensiertem 1,3-Oxathiolium-System erhalten. Es wird über die optimalen Herstellungsbedingungen sowie über einige charakteristische Spektraldaten dieser Verbindungsklasse berichtet.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130422
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  • 87
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    Electronic Resource
    Steroide. XXIX. Addition von N-Chlorurethan und N, N-Dichlorurethan an Steroidolefine sowie Umsetzung der Additionsprodukte zu Äthoxycarbonylaziridinen und Aziridinen (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 811-816 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Durch radikalische Addition von N-Chlorurethan und N,N-Dichlorurethan an Cholesten-(2), Cholesterylacetat und Androstenolonacetat erhält man die entsprechenden vicinalen Chlorurethane, die mit Alkali zu Carbäthoxyaziridinen und Aziridinen umgesetzt werden.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130505
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  • 88
    Electronic Resource
    Electronic Resource
    Preparation and Electronic Spectra of Mercaptoacetamides (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 849-854 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new method for preparing 2-mercaptoacetamide and N-alkyl-2-mercaptoacetamides has been described. Electronic spectra of sixteen N-alkyl and N-aryl-2-mercaptoacetamides have been compared with corresponding substituted acetamides and discussed. The results reveal the possibility of an intra-molecular hydrogen-bonding between —NH hydrogen and sulphur of —SH group.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130509
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  • 89
    Electronic Resource
    Electronic Resource
    Die Synthese von 1-Amino-4-aryl-1,2,3-triazolen aus α-Brom-und α,α-Dibromcarbonylverbindungen (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 882-888 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Sowohl durch Umsetzung von α-Brommethyl- als auch von α,α-Dibrommethyl-aryl-ketonen mit Hydrazin lassen sich 1-Amino-4-aryl-1,2,3-triazole darstellen, deren reduktive Desaminierung 1-H-4-Aryl-1,2,3-triazole liefert.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130513
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  • 90
    Electronic Resource
    Electronic Resource
    Zur Kenntnis der Infrarotspektren einiger ArsonsäurenMitteilung Nr. 212 aus dem Forschungsinstitut für Aufbereitung Freiberg/Sa. (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 889-898 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Infrarotspektren von Butan-, Hexan,- Heptan-, Octan- und Decanarsonsäure sowie von Phenyl-, o-Methylphenyl-, p-Methylphenyl-, p-Äthylphenyl- und p-Diphenyl-arsonsäure werden im Bereich von 400-3500 cm-1 mitgeteilt und die Frequenzen zugeordnet. In den Spektren der Alkanarsonsäuren können im üblichen Erwartungsbereich keine As—C-Valenzschwingungen nachgewiesen werden. Die Bindung eines Phenylringes an den Arsonsäurerest macht die Spektren im Gebiet der AsO-Valenzfrequenzen unübersichtlich. Die Unterscheidung dieser Banden von den CH-out-of-plane-Schwingungen ist unsicher.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130514
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  • 91
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    Electronic Resource
    Beitrag zur Ermittlung der absoluten Konfiguration der Sulfinyl-Gruppe bei Sulfoxiden von S-alkylierten L-Cystein-DerivatenVerwendete Abkürzungen: S—Me-Cys(O): S-Methyl-L-cysteinsulfoxid, N∊—Ac—Tlys(O): N8-Acetyl-L-thialysinsulfoxid.Herrn Prof. Dr. Horst Hanson zum 60. Geburtstag gewidmet (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1092-1100 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Konfigurationszuordnung für die Sulfinylgruppe von Sulfoxiden S-alkylierter L-Cystein-Derivate kann, da in dieser Reihe ein Standard existiert, durch Vergleich der ORD- und CD-Spektren, aber auch durch Vergleich enzymkinetischer Daten erfolgen. Das Verhalten bei Ionenaustausch und Chromatographie läßt ebenfalls Schlüsse auf die Absolutkonfiguration am asymmetrischen Schwefelatom zu.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130613
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  • 92
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    Electronic Resource
    Kationische Farbstoffe und Vorstufen. XV. Synthese von 2-Dialkylamino-thiapyryliumsalzen durch Reaktion von β-Chlorvinyl-methin-immoniumsalzen mit substituierten Thioacetamiden (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1113-1117 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Durch Umsetzung von β-Chlorvinyl-methin-immoniumsalzen mit N, N-disubstituierten Thioacetamiden in Essigsäureanhydrid entstehen die neuartigen 2-Dialkylamino-thiapyryliumsalze 10. Diese reagieren mit CH-aciden Verbindungen zu substituierten 2-Methylen-2H-thiapyranen 11. Die UV-S-Absorptionen der Verbindungen 10 und 11 werden mitgeteilt.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130616
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  • 93
    Electronic Resource
    Electronic Resource
    Reactions of 4-Benzylidene-3-methyl-5-oxopyrazoline, pyrazole blue, and rubazoic acid with GRIGNARD reagents (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1143-1147 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: While 4-benzylidene-3-methyl-5-oxopyrazoline 1 and pyrazole blue 2 with GRIGNARD reagents gave 1,4-addition, rubazoic acid 3 gave 1, 2-addition on both sides with ethylmagnesium bromide.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130621
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  • 94
    Electronic Resource
    Electronic Resource
    Isothiocyanate. XXV. Umsetzungen von Benzoylisothiocyanat mit Amino-N-heterocyclen (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1148-1154 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Benzoylisothiocyanat reagiert mit Amino-N-heterocyclen zu N-heterocyclisch-, N′-benzoyl-substituierten Thioharnstoffen 1a-j. In einigen Fällen entstehen zugleich die Benzoylderivate der Amino-heterocyclen 2a, b sowie azakondensierte 2-Thion-1,3,5-triazine 3a, b. Geeignete heterocyclische Thioharnstoffe 4b, f, h lassen sich durch Brom zu 1,2,4-thiadiazolo-anellierten Heterocyclen 5a-c cyclisieren.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130622
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  • 95
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    Electronic Resource
    A study of Magnetic Behaviour of Certain Liquid Mixtures of Cyclohexane (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1178-1180 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130625
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  • 96
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    Electronic Resource
    Zur quantenchemischen Berechnung von NMR-Parametern auf der Basis des CNDO/2-Verfahrens (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1070-1080 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Am Beispiel einfacher Methylverbindungen CH3X wurden aus Eigenvektoren und Eigenwerten von Allvalenzelektronenrechnungen in CNDO/2-Näherung Größen berechnet, die der 13C—H-, der geminalen H—H-Kopplungskonstante bzw. der 13C-chemischen Verschiebung der Methylgruppen proportional sein sollen. Die theoretischen Größen werden mit den entsprechenden experimentellen Werten verglichen. Güte und Grenzen der Näherungsverfahren werden diskutiert.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130611
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  • 97
    Electronic Resource
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    Quantenchemische Untersuchungen an Farbstoffaggregaten. I. Allvalenzelektronen-SCF-Berechnungen am Trimethincyanin und Doppelmolekülmodellen (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1101-1109 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Mit einem Allvalenzelektronen-SCF-Verfahren - der INDO-Methode - wird die Elektronenstruktur des Tri- und Pentamethincyanins untersucht. An ausgewählten Modellen wird für die möglichen geometrischen Anordnungen der Trimethincyanin-Einzelmoleküle in Doppelmolekülen die relative energetische Stabilität abgeschätzt. Die Berechnungen bestätigen die schon früher festgestellte starke Ladungsalternation und einen weitestgehenden Bindungsausgleich entlang der Polymethinkette. Die Elektronendichteverteilung wird duch die Zusammenlagerung von Trimethincyaninmolekülen zu Doppelmolekülen wenig verändert. Das Modell mit einer „mauerwerkartigen“ Anordnung erweist sich als das stabilste.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130614
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  • 98
    Electronic Resource
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    Die Synthese von 3(5)-Hydroxy-pyrazol sowie von 5-Hydroxy-1-methyl- und 5-Hydroxy-1-cyclohexyl-pyrazol (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1118-1124 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Eine auf Acrylnitril und Hydrazin basierende Synthese von 3(5)-Hydroxy-pyrazol 5a durch Sulfinateliminierung aus 1-(p-Toluolsulfonyl)-pyrazolidon-(3) in nicht-wäßrigem Milieu wird beschrieben. Die Methylierung von 5a liefert Gemische von 5-Hydroxy-1-methyl-pyrazol 5b und 1,2-Dimethyl-pyrazolon-(3) 7. 5b wird chemisch eindeutig durch Sulfinateliminierung aus 2-Methyl-1-(p-toluolsulfonyl)-pyrazolidon-(3), 5-Hydroxy-1-cyclohexyl-pyrazol durch Dehydrieren von 2-Cyclohexyl-pyrazolidon-(3) gewonnen. Die Methylierung von 5a mit 2 Mol p-Toluolsulfonsäure-methylester in DMF liefert in guter Ausbeute 7, analog ergibt 3(5)-Hydroxy-5(3)-methyl-pyrazol 1,2,5-Trimethyl-pyrazolon-(3).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130617
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  • 99
    Electronic Resource
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    Umsetzungen mit RhodanaminHerrn Prof. Dr. Dr. h. c. Alfred Rieche zum 70. Geburtstag in Verehrung gewidmet (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1125-1130 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Phenol und Anilin werden durch Rhodanamin 1 in para-Stellung rhodaniert, p-Toluidin in ortho-Stellung. Acetophenon ergibt unter Verbrauch von zwei Mol 1 2-Amino-4-phenyl-5-rhodano-thiazol 6. Von β-Dicarbonylverbindungen abgeleitete Enamine 7 a, b, c werden zu Rhodan-enaminen 8 a, b, c rhodaniert, aus denen leicht Amino-thiazole, das Dithiin 10 und das Thiazolon 11 erhalten werden können.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130618
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  • 100
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    Relation between chemical Structure and Absorption Spectra of Monoazo Dyes containing the benzo(b)thiophene nucleus and its derivatives (1971)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 313 (1971), S. 1131-1138 
    Details
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The ultraviolet and visible absorption spectra of some azo dyes containing the benzo(b)-thiophene, benzo(b)thiophene-1,1-dioxide and 2,3-dihydrobenzo(b)thiophene-1,1-dioxide moieties are investigated in correlation to their molecular structure. It was found that the position of absorption bands depends upon the type of moieties attached to the azo centre.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19713130619
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