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  • 1975-1979  (1,627)
  • 1965-1969
  • 1890-1899
  • 1880-1889
  • 1975  (1,627)
  • General Chemistry  (809)
  • Organic Chemistry  (659)
  • Engineering General  (84)
  • Ultrastructure  (75)
Material
Years
  • 1975-1979  (1,627)
  • 1965-1969
  • 1890-1899
  • 1880-1889
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  • 101
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 169-185 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A theoretical formulation and the analysis of heat conducting fibre-reinforced structures are shown herein. Viscoelastoplastic behaviour at infinitesimal strain is considered in the context of non-equilibrium irreversible thermodynamics. To demonstrate the theory, a fibre-reinforced cylindrical rod subjected to a dynamic axial load is solved via the finite elements. Strain hardening of both fibres and matrix media is incorporated in the analysis. The results clarify the relationships of energy dissipation resulting from viscoelasticity, plasticity, or the combined effects with respect to orientation of the fibres.
    Additional Material: 6 Ill.
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  • 102
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 219-233 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The over-relaxation technique has been used in conjunction with the finite element method in a regional time-dependent simulation of the subsidence of Venice. One year of computer experiments have shown that in basins with a ratio h/R ≤ 10-2 between the vertical and the horizontal dimension, the over-relaxation technique can lead to unsatisfactory results. In single precision and for relatively large time steps, the solution of the final linear system can be inaccurate if the optimum over-relaxation factor ω is not correctly assessed. In transient analyses, instability can also occur. The latter may be avoided by properly reducing the time step or by switching to double precision. Steady state simulations can also require double precision to provide accurate results even when the best ω is used. Instability and inaccuracy disappear in basins for which h/R ≥ 10-1. In addition the processor time diminishes significantly as in this case the number of iterations necessary to obtain a good solution is considerably smaller than the order of the matrix.
    Additional Material: 16 Ill.
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  • 103
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 252-252 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 104
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 235-238 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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  • 105
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 250-252 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
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  • 106
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 337-351 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of moments is a semidiscrete numerical method for solving partial differential equations. The method approximates the solution of a partial differential equation by a finite sum of products of two functions. One function in the product is an unknown function of a single variable and the other function (moment function) is a prescribed function in the remaining variables. Using variational technique we obtain a finite system of boundary value problems of ordinary differential equations for the unknown functions.The main goal of this paper is the study of the theoretical background and numerical effectiveness of the method of moments for solving linear partial differential equations on rectangular-like domains.The mathematical formulation of the method together with error estimates and the theory of optimal moment functions are given. If for the one-dimensional moment functions piecewise polynomials of degree K are used then finite element type error bounds are obtained for the approximate solution in two dimensions.We also consider the numerical implementation of the method through the factorization method and efficient initial value methods. Several numerical examples showing the efficiency of the method are presented.
    Additional Material: 5 Tab.
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  • 107
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 415-432 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Details are given of a finite element scheme for the determination of the elastic buckling loads of thin flat plates of arbitrary shape under general kinematic and traction boundary conditions. The buckling loads are calculated using a triangular finite element with corner connections which is based on a previously derived variational principle combining both stresses and displacements. Numerical solutions are presented to a number of example problems, including plates with reinforcing members, and comparisons are made, where possible, with results from the finite element analyses of other authors and with exact or classical Rayleigh-Ritz solutions.
    Additional Material: 5 Ill.
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  • 108
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 477-483 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper considers the question of reduction of loads on a pipe network, which may be necessary as a result of failure in supply or interruption of a pipe. The non-linear relationship between pressure loss and flow along a pipe makes the problem of minimizing the reduction of loads also non-linear. An iterative linear approximation technique is therefore adopted. When the question is formulated as a problem in linear programming, the constraints include nodal pressures as well as loads. It is shown how the number of these constraints may be reduced.
    Additional Material: 1 Ill.
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  • 109
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
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  • 110
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 111
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 551-561 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method is developed by which it is possible to obtain the general solution of an ordinary differential equation directly. The procedure consists of approximating the differential equation with a rectangular matrix equation and of solving the latter equation by using generalized matrix inversion. It is shown in the paper that the homogeneous and inhomogeneous solutions of the two systems correspond and that the approximate solutions produced form the complete general solution of the original differential equation.
    Additional Material: 2 Ill.
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  • 112
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 601-615 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Alternate hybrid stress finite element models in which the internal equilibrium equations are satisfied on the average only, while the equilibrium equations along the interelement boundaries and the static boundary conditions are adhered to exactly a priori, are developed. The variational principle and the corresponding finite element formulation, which allows the standard direct stiffness method of structural analysis to be used, are discussed. Triangular elements for a moderately thick plate and a doubly-curved shallow thin shell are developed. Kinematic displacement modes, convergence criteria and bounds for the direct flexibility-influence coefficient are examined.
    Additional Material: 8 Ill.
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  • 113
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 679-689 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the phenomenon of ‘noise’ which is common in most time-dependent problems. The emphasis is on the achievable accuracy that is obtained with various time-stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level. A series of experiments are made where the space domain is discretized using the finite element method and the variation with time is approximated by several finite difference methods. The conclusion is reached that the Crank-Nicolson scheme with a simple averaging process is superior to the other methods investigated.
    Additional Material: 7 Ill.
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  • 114
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 732-732 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 115
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 734-735 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 116
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 775-831 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Solutions of elliptic boundary value problems are obtained with variational formulations by minimization of functionals.Conventional tools of the finite element strategy are emphasized; linear or quadratic approximations on triangular elements, curved iso-parametric elements, Ni shape funtions, Li homogeneous co-ordinates. High speed of computation of the final assembled matrices require the use of the Formal-FORMAC calculus. Illusrations of the finite element method are chosen in the class of the 2d-3d compressible subsonic irrotational flows in a nozzle and around one or several lifting bodies of arbitary shape.
    Additional Material: 40 Ill.
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  • 117
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 903-911 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element methods are used to solve hydrodynamic lubrication problems involving compressible lubricants and porous bearing solids. The particular calculation scheme permits solution at high compressibility numbers (Λ 〉 100) to be obtained without any numerical difficulty. Finite element and finite difference results for the porous, gas lubricated journal bearing are presented and compared.
    Additional Material: 5 Ill.
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  • 118
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 492-492 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 119
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 509-533 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the computational aspects of an earlier analytical study1,2 of the problem of maximizing a linear combination of the natural frequencies of vibration of a turbine disc idealization subject to weight and fabrication constraints. The problem was formulated as an optimal control problem and solutions to the adjoint equations of the Pontryagin formalism obtained using perturbation techniques. These techniques transformed the problem to a non-linear program. This paper gives detailed computational solutions to the non-linear program which is characterized by pockets of relative optima. In addition, the dual problem of minimizing the weight subject to a frequency constraint is considered within the optimal control framework. The duality results are confirmed computationally for the two non-linear programs.A description of some practical procedures for improving the convergence characteristics of these highly non-linear programs is included.
    Additional Material: 11 Ill.
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  • 120
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 617-629 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The number of equations which relate the mesh parameters (number of nodes, number of elements etc.) to each other is smaller than the number of unknowns contained therein. These rules are only applicable when several parameters of a defined mesh are known, but are unsuitable for use in the particularly interesting field of mesh projection unless additional inter-relationships can be found. Such relationships are given for uniform meshes in which besides the characteristics of the element type the ‘solidity value’ of the structure plays an important role.The equations are derived for two-dimensional triangular and quadrilateral elements and also for three-dimensional tetrahedral and hexahedral elements. The fact that these relationships are also suitable for estimating the parameters of any non-uniform mesh, discloses a wide field of application in the management of storage and in the control of programs for automatic mesh generation.
    Additional Material: 3 Ill.
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  • 121
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is described whereby the formulation for non-conforming bending elements includes the work dissipated across the inter-element boundaries. For the examples considered, this correction is shown to lead to a significant improvement in accuracy at little extra cost. Since the solution procedure is based on an iterative technique, the method would be particularly suitable if applied to non-linear problems.
    Additional Material: 2 Ill.
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  • 122
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 727-731 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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  • 123
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 733-733 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 124
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 125
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 765-773 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper examines two triangular finite elements used in plate bending analyses for which Lagrange multiplier techniques have been used to set up the necessary equations for the solution. These equations involve either equilibrium of the system or the inter-element compatibility. Starting from only the notions of equilibrium and continuity as used in the analyses of redundant structures, the paper proceeds to solutions of the same problems. It is found that end results are the same when the equations obtained from the minimization techniques are reduced by Gauss-elimination in partitioned from.
    Additional Material: 4 Ill.
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  • 126
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 869-902 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present study is intended as a guide for those who wish to undertake spectral analyses using Discrete Fast Fourier Transforms. Points of particular difficulty in using Fourier Transforms are derived in some detail. Experimental results are offered to illustrate the mathematical derivations. Finally the case of a signal with discontinuities along the time-axis is discussed.
    Additional Material: 21 Ill.
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  • 127
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 933-938 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 128
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 1-15 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple mixed finite element method is developed. The finite element is a rectangular triangle and rectangle. In the element the deflections are assumed to be simple four-element polynomials, bending moments, Mx and My with a partially linear distribution, and a constant, Mxy, expressed in terms of the node deflections. The element matrix is of the order of 8 × 8. It is derived in a common engineering way. The unknowns are the deflections at the nodes and mid-diagonal, the two moments at the end of the diagonal and the two moments on the cathetus. The results obtained by this method show good convergence and an improvement in the accuracy of the moments as well as in the deflections, compared with results obtained by similar methods, such as those of Herrmann.
    Additional Material: 6 Ill.
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  • 129
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 73-84 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present work the authors have developed a finite difference method of analysis for any circular plate with any kind of loading on semi-infinite elastic foundations. No assumption regarding the contact pressure distribution has been made. The equations have been developed in non-dimensional form and also the results have been obtained in non-dimensional form. These results have been compared with the available experimental results and the agreement between them is found to be much better than that of the previous works. The same method with slight modification can be applied for Winkler type foundations and problems of circular plates with varying thickness.
    Additional Material: 6 Ill.
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  • 130
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 109-127 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical stability of simple marching schemes used in elasto/visco-plasticity is investigated. An assumption of convexity renders possible the derivation of a theoretical stability criterion based on the identification of the numerical process with the integration of a non-linear, first order, system of ordinary differential equations. Explicit stability criteria are obtained for commonly used visco-plastic laws. Selected examples illustrate the necessity and effectiveness of the proposed stability criteria in actual computations.
    Additional Material: 6 Ill.
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  • 131
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 187-207 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The measurement of energy release rates using virtual crack extensions has been made using finite element techniques. An economic and accurate technique for calculating energy changes due to any number of virtual tip changes is presented. Mixed-mode situations can be dealt with by observing the direction of maximum energy release rate. Examples are given including various cracks in a plate in tension, a curving crack in a general two-dimensional shape, and a three-dimensional crack in a plate.
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  • 132
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 239-245 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 133
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 253-256 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 134
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 271-296 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A gradient projection optimal control algorithm incorporating conjugate gradient directions of search is described and applied to several minimum weight panel design problems subject to a flutter speed constraint. New numerical solutions are obtained for both simply-supported and clamped homogeneous panels of infinite span for various levels of inplane loading and minimum thickness. The minimum thickness inequality constraint is enforced by a simple transformation of variables.
    Additional Material: 8 Ill.
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  • 135
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 353-386 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Starting from continuum mechanics principles, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived. The aim in this paper is a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure. The general formulations include large displacements, large strains and material non-linearities. For specific static and dynamic analyses in this paper, elastic, hyperelastic (rubber-like) and hypoelastic elastic-plastic materials are considered. The numerical solution of the continuum mechanics equations is achieved using isoparametric finite element discretization. The specific matrices which need be calculated in the formulations are presented and discussed. To demonstrate the applicability and the important differences in the formulations, the solution of static and dynamic problems involving large displacements and large strains are presented.
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  • 136
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 433-448 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is outlined for determining the movement of a gas-liquid interface in a porous medium following the withdrawal of gas from an underground reservoir. The governing equations for the flow of both gas and the underlying liquid are formulated in terms of the finite element process using the Galerkin approach. The method consists of an iterative technique in which solution of the basic equations is dependent on the location of the interface. Cubic isoparametric elements are employed to allow accurate modelling of the curved boundary and to provide a relatively large number of interface points for a small number of elements. Extensions of the method are indicated in the text.
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  • 137
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 483-487 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
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  • 138
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  • 139
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 535-550 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Incremental equations of motion are derived from a Lagrangian variational formulation for the large displacement elastic-plastic and elastic-viscoplastic dynamic analysis of deformable bodies. The material constitutive behaviour is described in terms of the symmetric Piola-Kirchhoff stress and Lagrangian strain tensors. Degenerate isoparametric elements, permitting relaxation of the Kirchhoff-Love hypothesis, are used in a finite element formulation specialized for the analysis of shells of revolution subjected to axisymmetric loading. The linearized incremental equations of motion are solved using direct integration procedures, with added accuracy obtained from application of equilibrium correction at each step. The effectiveness of the numerical techniques is illustrated by the dynamic response analyses carried out on a shallow spherical cap subjected to uniform external step pressure loadings.
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  • 140
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 581-599 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A discretization process is described by which it is possible to generate finite difference formulas for arbitrary linear two-dimensional partial differential equations. The process is based on a novel approach to finite difference analysis in which differential operators are approximated by rectangular matrices. In this approach, the discrete form of a complicated operator is obtained by performing simple numerical operations on elementary matrix factors. The analysis is augmented by a listing of a computer program based on the method for the automatic generation of finite difference formulas.
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  • 141
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 631-639 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Preliminary studies of computation with velocity potential are made with a view to the analysis of complex three-dimensional flows. The methods used are applicable more generally to quasilinear elliptic problems with derivative boundary conditions on irregular domains. Second order finite difference approximations are constructed in simple form for plane ducts of general shape by using an irregular net. Derivative boundary conditions are handled quite easily. An iterative method is described which corresponds to freezing the coefficients in the quasilinear differential equation for velocity potential. The discretization is such that this is a ‘generalized Newton’ method for the non-linear algebraic equations. Good convergence has been found in practice even when there are small supersonic zones. The discretization accuracy is tested by comparisons with the exact solution for incompressible flow between confocal hyperbolas.
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  • 142
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 669-678 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fully implicit numerical method for linear parabolic free boundary problems with coupled and integral boundary conditions is described. The partial differential equation and the boundary conditions are time discretized with the method of lines. An auxiliary function is introduced to remove the coupled and integral boundary conditions from the resulting free boundary problem for ordinary differential equations. Once separated boundary conditions are obtained, invariant imbedding is used to solve the free boundary problem numerically. The method is illustrated by solving the heat transfer equations for the fluidized-bed coating of a thin-walled cylinder.
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  • 143
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 649-667 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for solving structural design problems that allows a continuous distribution of material along structural elements is presented. The method is an extension of the generalized steepest descent method presented in Reference 1. Inequality constraints on design variables, displacement, natural frequency, and buckling are explicitly treated and a minimum weight cost function is employed. A steepest descent method for boundary-value state equations is developed and a computational algorithm is given. Several example problems in minimum weight structural design are solved and compared with results obtained by discretization techniques.
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  • 144
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 701-709 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A symmetric central finite difference operator is derived for the small deflection analysis of transversely loaded, ‘thin’, elastic plates, whose stiffnesses vary as functions of the in-plane co-ordinates. The operator is written here in Cartesian co-ordinates for a square mesh, but the same technique can also be used to construct an operator for a rectangular mesh.
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  • 145
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 721-726 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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  • 146
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 733-733 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 147
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 739-763 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 148
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 855-868 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness matrix and consistent nodal load vector for a general quadrilateral plate element are developed for both in-plane and bending analysis. The basis chosen for the development is the hybrid stress method because iit has been shown to produce results of relatively high accuracy.iiit employs only primary nodes andiiiall integration required in the derivations can be achieved in closed form.Various numerical examples, relating to both plane stress and bending conditions, are considered in order to establish the validity and generality of the derivations.
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  • 149
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 847-853 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper an economical method for calculating the stress and displacement fields in an elastic body for a range of Poission's ratios is given. The solution is expanded as a power series in Poission's ratio, the coefficients of the series being determined successively. The range of convergence of the solution is examined, and it is shown that the power series converges for values of Poission's ratio in the range zero to a half, provided a suitable point of expansion is chosen. Particular features of the method are firstly that only one effective inversion of the stiffness matrix, for Poission's ratio zero, is required to obtain the solution for all Poission's ratio and secondly that no special formulation for an incompressible material is required.
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  • 150
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 925-932 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The constraint of incompressibility is incorporated into the finite element method for plane strain through the use of a Lagrange multiplier. Depending on the approximating function chosen for this multiplier, the constraint condition can be satisfied everywhere within the element or only in an average sense for the entire element. A study of these two approaches from the point of view of rate of convergence and computer time is presented.
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  • 151
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    International Journal for Numerical Methods in Engineering 9 (1975) 
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    Keywords: Engineering ; Engineering General
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  • 152
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 51-62 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Accounting for shear deformations and rotary inertia effects, necessary condition for optimum fundamental frequency of a vibrating beam of constant volume and with a given distribution of non-structural mass, is obtained through the calculus of variations. Minimum cross-section of the beam is controlled by the introduction of an inequality constraint. A finite element displacement formulation is then used in an iterativve manner to arrive at the optimum fundamental frequency and the corresponding material distribution for the discretized beam models with various boundary conditions. A comparison is then made with the corresponding results of an Euler beam.
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  • 153
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 129-147 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The formulation of finite element models on the basis of different variational principles is reviewed. The degrees-of-freedom of the elements are defined in an abstract way without the help of nodal points. In this manner it is possible to describe elements of arbitrary shape and accuracy. The formulation is confined to linear elasto-statics. For two-dimensional structures two hybrid element models are developed using Legendre polynomials on the element boundaries. Examples of plane stress problems are used to test the generation of convergence by increasing the accuracy of the elements vs. by increasing the number of elements.
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  • 154
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    Notes: It is shown that a singularity occurs in isoparametric finite elements if the mid-side nodes are moved sufficiently from their normal position. By choosing the mid-side node positions on standard isoparametric elements so that the singularity occurs exactly at the corner of an element it is possible to obtain quite accurate solutions to the problem of determining the stress intensity at the tip of a crack. The solutions compare favourably with those obtained using some types of special crack tip elements, but are not as accurate as those given by a crack tip element based on the hybrid principle. However, the hybrid elements are more difficult to use.
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  • 155
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 563-580 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The typical numerical problem associated with finite element approximations is a quadratic programming problem with linear equality constraints. When nodal variables are employed, the coefficient matrix of the constraint equations, [A], acquires a block-diagonal structure. The transformation from polynomial coefficients to nodal variables involves finding a basis for [A] and computing its inverse.Simultaneous satisfaction of completeness and C1 (or higher) continuity requirements establishes linear relationships among the nodal variables and precludes inversion of the basis by exclusively element-level operations.Linear dependencies among the constraint equations and among the nodal variables can be evaluated by the simplex method. The computational procedure is outlined.
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 731-732 
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    Keywords: Engineering ; Engineering General
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  • 157
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 732-732 
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    Keywords: Engineering ; Engineering General
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  • 158
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 938-943 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A comparison is made of the Crandall and Crank-Nicolson methods applied to a transient heat conduction problem with a convective boundary layer on its surface for a range of values of Nusselt modulus and Fourier modulus. A new equation is derived to handle the convective boundary condition. For reasonable accuracy requirements the Crank-Nicolson method gives superior performance with respect to accuracy.
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  • 159
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    International Journal for Numerical Methods in Engineering 9 (1975), S. 913-924 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple procedure of obtaining flexibility matrices in terms of contact pressures at possible contact points of two bodies allows the frictionless contact pressures to be solved as a quasi-linear problem. Iteration is limited in general to very few cycles and, as small matrices are handled, can be very economical.Excellent accuracy of this procedure is demonstrated.
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  • 160
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 73-80 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Es wurde die Kinetik der Hydrolyse von substituierten Thiokohlensäure-O-arylester-chloriden in wäßrigen Acetonlösungen untersucht. Mit Hilfe der Korrelation der Geschwindigkeitskonstanten mit den Lösungsmittelparametern ET, der Aktivierungsenthalpie und -entropie und des kinetischen Deuterium-Isotopeneffektes konnte der Reaktionsmechanismus geklärt werden. Es ist in allen Fällen ein Additions-Eliminierungsmechanismus mit dem nucleophilen Angriff als langsamer Stufe. Die HAMMETT-Korrelation der Geschwindigkeitskonstanten mit den σ°-Werten zeigt, daß keine direkte Konjugation zwischen dem Arylsystem und dem Reaktionszentrum der Thiokohlensäure-O-arylester-chloride vorliegt.
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  • 161
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Darstellung der isomeren Ring D-anellierten Steroidlactone 6 und 12 aus den 16-Acetoxy-17-ketosteroiden 1 bzw. 9 wird beschrieben. Der Verlauf der Äthinylierung zur Einführung der 17-ständigen α,β-ungesättigten Estergruppierung wird durch die Konfiguration an C-16 bestimmt:Die Umsetzung der 16β-Acetoxy-Verbindung führt zu dem erwarteten Äthoxyäthinylcarbinol 2b, das nach Desacetylierung in den α,β-ungesättigten 3β,14,16β-Trihydroxy-5β,14β-pregn-17(20)-en-21-säureäthylester 4 umgelagert wird. 4 wird in siedendem Eisessig direkt zum 3β-Acetoxy-14-hydroxy-5β,14β-pregn-17(20)-en-21,16β-lacton 6 cyclisiert.Aus der 16α-Acetoxy-Verbindung dagegen entsteht unmittelbar das 3β-Acetoxy-14,17-dihydroxy-5β,14β,17α-pregnan-21,16α-lacton 11, dessen 17β-OH-Gruppe unter Bildung des instabilen 3β-Acetoxy-14-hydroxy-5β,14β-pregn-17(20)-en-21,16α-lactons 12 eliminiert werden kann. 12 stabilisiert sich durch Verlagerung der Doppelbindung zum 3β-Acetoxy-14-hydroxy-5β,14β-pregn-16-en-21,16-lacton 13. Die anellierten Steroidlactone 6 und 13 erweisen sich bei der molekularbiologischen Wertbestimmung (ATPase-Test) als unwirksam.
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  • 162
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 143-152 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Tetrabenzyltitanium and its o-halogenbenzyl derivates have only a small activity for polymerizing butadien. Aluminium trialkyls accelerate the catalytic activity. A very suitable system for preparing 1,4-cis or 1,4-trans polybutadien under normal pressure is formed by tetrabenzyl titanium and aluminium chloride as a co-catalyst.
    Notes: Titantetrabenzyl sowie die erstmals näher beschriebenen Titantetra-o-halogenbenzyle weisen eine geringe Aktivität zur Polymerisation von Butadien auf. Aluminiumtriäthyl erhöht die Aktivität. Günstiger wirkt Aluminiumchlorid als Cokatalysator, wobei unter Normaldruck stereoreguläres Polybutadien mit vorwiegend 1,4-trans- bzw. 1,4-cis-Anteilen erhalten werden konnte.
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 169-171 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 164
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 185-198 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Verbindung kristallisiert in der Raumgruppe P1 mit den Gitterkonstanten a = 7,812 Å, b = 8,959 Å, c = 5,293 Å, α = 93,41°, β = 106,04°, γ = 66,90°. Das Strukturprinzip ergab sich durch Anwendung der Methode der thermischen Untergrundstreuung und der Faltmolekül-methode. Die Struktur wurde räumlich und anisotrop bis zu einem Diskrepanzfaktor von R = 0,096 verfeinert. Die durch relativ lockere Packung der Bausteine begünstigte thermische Schwingung der Atome und Bausteine erschwerte die Verfeinerung. Der Kristall wird aus Farbstoff-Kationen, Chlor-Anionen und Wassermolekülen aufgebaut. Die Kationen zeigen den für offenkettige Polymethine charakteristischen Bindungslängenausgleich zwischen den C—C-Bindungslängen (1,37 Å im Mittel) und im Vergleich zu N—C-Einfachbindungen verkürzte N—C-Abstände (1,34 Å im Mittel). Die Bindungswinkel innerhalb der Pentamethinkette zeigen eine auch an anderen Strukturen beobachtete alternierende Abweichung von 120°. Die Kationen sind mit ihren Ebenen parallel zueinander als polymere Aggregate assoziiert, die sich in eindimensionalen Stapeln (Fäden) durch den Kristall ziehen. Der senkrechte Ebenenabstand beträgt 3,55 Å. Der Winkel zwischen Fadenachse und Kationlängsachse beträgt 42°. Die Anordnung der Chlorionen und Wassermoleküle läßt auf Wasserstoffbrückenbindungen Cl- … H—O schließen, die den Kristall kettenförmig durchziehen und parallel zu den Achsen der eindimensionalen Kationstapel liegen.
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 293-297 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Imino-bis-carbimidsäuremethylester 1 reagiert mit Diarylcarbodiimiden unter Cyclisierung zu Gemischen aus 5-Aryl-4-arylimino-6-imino-2-methoxy-1, 4, 5, 6-tetrahydro-1, 3, 5-triazinen 4 und 4-Arylamino-2, 6-dimethoxy-1, 3, 5-triazinen 6.
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 335-336 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 167
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    Keywords: Chemistry ; Organic Chemistry
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  • 168
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 298-306 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Es wird die Synthese von 5α, 10α-Epoxy-östran-Derivaten 7 beschrieben. Ausgehend vom 1, 4-Dihydro-östradiol-3-methyläther erhält man durch Enolätherspaltung und nachfolgende Addition von unterbromiger Säure an die Δ5(10)-Doppelbindung 10β-Brom-5α,17β-dihydroxy-östran-3-on 4a. Nach Maskierung der Ketogruppe durch Reduktion, Ketalisierung oder Oximbildung führt die anschließende Alkalibehandlung zu den entsprechenden 5α,10α-Epoxy-östran-Derivaten. In analoger Reaktionsfolge werden 17α-Methyl- und 17α-Äthinyl-Epoxyverbindungen erhalten.
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  • 169
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 329-334 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: α-Arylhydrazono-thioamide 1  -  erhältlich aus Arylhydrazono-cyanessigsäurederivaten und Schwefelwasserstoff  -  werden mit Brom zu 5-Amino-2-aryl-1,2,3-thiadiazoliumsalzen 2 oxydiert. Die Verbindungen sind acylierbar und reagieren mit Acetessigester sowie methylenaktiven Nitrilen unter Spaltung der N-S-Bindung und erneuter Cyclisierung zu substituierten 4-Aminothiazolen 4,5. Dagegen führt die Behandlung mit anderen Basen zur Entschwefelung und Rückbildung des α-Arylhydrazono-nitrils.
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 352-352 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 172
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 387-393 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Michael condensation of benzal-α-acetothienone 1 with ethyl cyanoacetate, cyanoacetamide and acetoacetamide led to the 2(1H)-pyridone derivatives 2 and 3. Compound 2 was condensed with aldehydes, and compound 3 with ethyl acetate, to yield the chalcone analogues 4 and the diketone 7, respectively. By action of phenylhydrazine and hydroxylamine on 4 and 7, the corresponding pyrazole and isoxazole derivatives 5, 6 and 9 were obtained. Reaction of urea and thiourea with 1 gave the dihydropyrimidine derivatives 10 and 11, respectively.
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  • 173
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 369-378 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Das Isomerengemisch von 1-und 2-Phenyläthyl-aluminiumdichlorid (PADC) überträgt Phenyläthylreste auf Carbonsäurechloride und -anhydride. Dabei reagieren langkettige Carbonsäurechloride zu 1-Phenylalkanonen-(3) und 2-(4-Acylphenyl)-alkanonen-(3). Dagegen bilden Acetyl- und Benzoylchlorid kompliziert zusammengesetzte Gemische an Endprodukten. PADC und Dicarbonsäuredichloride ergeben abweichend vom bekannten Verhalten anderer Alkylaluminiumdichloride keine phenyläthylsubstituierten Oxoalkansäuren, sondern Äthylaroylcarbonsäuren. Analog setzen sich die entsprechenden Dicarbonsäureanhydride um.
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  • 174
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 394-408 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Thermolyse von Diarylphosphinsäureaziden 1a-k im Temperaturbereich zwischen 220 und 245°C führt unter geschwindigkeitsbestimmender Stickstoff-Abspaltung zu Diarylphosphinyl-nitrenen 3 im Singulett-Zustand, die unterschiedliche Stabilisierungsreaktionen zeigen. Unter P—N-Arylwanderung entstehen Produkte mit Arylphosphonsäurearylimid-Struktur 4. Desaktivierung von 3 gibt das Triplett-Nitren 7, das unter Wasserstoffabstraktion in das Diarylphosphinsäureamid 8 übergeht. Diphenylphosphinylnitren im Triplett-Zustand initiiert die radikalische Polymerisation von Acrylnitril. Die Geschwindigkeitskonstanten der Zersetzung von 1a-k liegen in der Größenordnung von 10-3 bis 10-4 s-1 und unterliegen nur einem geringen Substituenteneffekt. Die relativen Geschwindigkeitskonstanten zeigen Werte zwischen 0,81 und 1,17 (bei 230°C). Für die relativen Arylwanderungstendenzen in der Thermolyse der Aryl-phenyl-phosphin-säureazide 1 f-k wurde folgende Abstufung gefunden:p-ClC6H4 〉 p-CH3C6H4 〉 o-CH3C6H4 〉 m-ClC6H4 〉 C6H5 〉 m-CH3C6H4.In Übereinstimmung mit einem Nitrenmechanismus der Thermolyse von Diarylphosphinsäureaziden zeigt die o-Tolylgruppe keine sterische Beeinflussung der Umlagerung, sondern ihre Wanderungstendenz ist mit der des elektronisch etwa gleichwertigen p-Tolylrestes vergleichbar. Der Substituenteneinfluß auf die relative Wanderungstendenz läßt sich dadurch deuten, daß die Wanderung des Arylrestes eine aromatische Substitution durch den elektrophilen Nitren-Stick-stoff einschließt. Die Korrelation der relativen Arylwanderungstendenzen mit Substituentenkonstanten zeigt, daß dabei mesomere Einflüsse der Substituenten überwiegen. Bei der Umlagerung entstehen Gemische isomerer Arylphosphonsäurearylimide 4.
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  • 175
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 527-528 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 176
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 533-539 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The present paper deals with the separation and distribution of n-paraffins in Marine Belayim wax distillate fractions (300-500°C) using molecular sieves adsorption and gas chromatography.The method used consists in dewaxing the wax distillate fractions and selectively adsorbing the n-paraffins present in the waxes by refluxing their benzene solutions with Type 5 A pelleted molecular sieves. The sieve crystal structure is then destroyed with HF and the liberated n-paraffins are quantitatively determined.
    Additional Material: 2 Ill.
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  • 177
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 812-816 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Gleichgewichtskonstanten der Eigenassoziation von Acrylsäure-(ASE), Methacrylsäure-(MASE) und Crotonsäureäthylester (CSE) werden bestimmt. Aus der Konzentrationsabhängigkeit der 1H-NMR-chemischen Verschiebungen ergeben sich Dimerisierungskonstanten zwischen K2 = 0,137 [Molenbruch-1] für ASE in C6H12 und K2 = 5,219 [Molenbruch-1] für CSE in C6D12. Die experimentellen Ergebnisse lassen sich am besten durch eine Kopf-Kopf-Dimerisierung über die Carbonylgruppe interpretieren.
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  • 178
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 840-852 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Bei der Umsetzung trivalenter P-Ester mit Chlormethan-phosphon-säurediäthylester laufen ARBUZOV-Reaktion und Alkylierung des P-Esters etwa in gleichem Maße ab. Die Ausbeute an ARBUZOV-Produkt 3 ist mäßig, seine Reingewinnung schwierig. Bei der analogen Umsetzung mit Chlormethan-phosphonsäure-diphenylester ist die ARBUZOV-Reaktion eindeutig die Hauptreaktion, die in guten Ausbeuten Methylen-bis-P(O)-Verbindungen 3 mit ungleich substituierten P-Atomen ergibt. Die Einführung eines Phenylrestes in die Chlormethyl-Gruppe begünstigt stark die Halogenübertragung auf das trivalente P-Atom als Konkurrenzreaktion zur ARBUZOV-bzw. besonders zur MICHAELIS-BECKER-Reaktion.Ein weiterer Syntheseweg für Methylen-bis-P(O)-Verbindungen besteht in der „Acylierung“ methylenaktiver P(O)-Verbindungen durch trivalente P-Chloride mit nachfolgender Oxydation. In speziellen Fällen kann dieser Weg der ARBUZOV-Reaktion ausbeutemäßig überlegen sein.
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  • 179
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 877-880 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 180
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    Keywords: Chemistry ; Organic Chemistry
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    Topics: Chemistry and Pharmacology
    Notes: 17β- und 17α-Cardenolide erfahren bei der Oxydation mit Selendioxid in Dioxan primär eine Hydroxylierung zu 17α- und/oder 17β-Hydroxy-cardenoliden. Neben der Konfiguration an C-17 übt auch die Stellung einer 16-Acetoxygruppe einen, wenn auch geringeren Einfluß auf den sterischen Verlauf der Hydroxylierung aus und beeinflußt die Stabilität der Hydroxylierungsprodukte. Bei Einwirkung von Selendioxid auf 17-Hydroxy-cardenolide wird eine zweite Hydroxygruppe in die C-21-Position eingeführt, die im Falle der 17β-Cardenolide intramolekular mit der 14β-OH-Gruppe unter Bildung der 14,21-Epoxy-17α-hydroxy-cardenolide 3a oder 3b reagiert.
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  • 181
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 38-52 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Titelverbindung kristallisiert in der Raumgruppe Pbca. Die Abmessungen der Elementarzelle sind a = 14,458 Å; b = 15,940 Å; c = 12,162 Å. Die Struktur wurde mit Fourier- und least-squares-Methoden bis auf einen Diskrepanzfaktor von R = 0,10 räumlich verfeinert. Das Kation zeigt den für Polymethinstrukturen typischen Bindungslängenausgleich zwischen den Methin-Kohlenstoffatomen (1,37 Å) sowie den für partielle Doppelbindungen zwischen Stickstoff- und Kohlenstoffatomen in derartigen Verbindungen charakteristisch kurzen Abstand von 1.32 Å. Das Polymethingerüst ist im wesentlichen eben. Eine durch sterische Hinderung bedingte geringe Durchbiegung dieser Ebene konnte signifikant nachgewiesen werden. Die Winkel N—C—C und C—C—C der Trimethinkette weichen signifikant von dem für den sp2-Hybridzustand der C-Atome postulierten Wert von 120° ab. In Korrelation zur Gesamtladung der Scheitelatome C5, C6 und C7 alternieren diese Winkel mit Werten ≶ 120°. Die ClO4-Tetraeder zeigen eine fehlordnungsähnliche Lageverteilung im Kristallverband, die in ungewöhnlich großen Schwingungsamplituden der O-Atome zum Ausdruck kommt. Benachbarte Trimethin-Kationen ordnen sich mit ihren mittleren Ebenen gewinkelt zueinander an. Es gibt keine aggregationsähnliche Packung der Kationen im Kristallverband.
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  • 182
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    Keywords: Chemistry ; Organic Chemistry
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    Topics: Chemistry and Pharmacology
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  • 183
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 123-136 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Synthese von substituierten 1,3-Dithiol-thionen-(2) 6 a - s aus Enaminen bzw. Ketiminen, Tetramethylthiuramdisulfid und Schwefelwasserstoff sowie aus N-Dimethyldithiocarbamidsäure-(2-oxo-alkyl)-estern 4 und der Abbau der 6 durch primäre aliphatische Amine wird beschrieben.
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  • 184
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 161-165 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 185
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 172-175 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Ill.
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  • 186
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    Keywords: Chemistry ; Organic Chemistry
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    Topics: Chemistry and Pharmacology
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  • 187
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 199-213 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Verbindung kristallisiert in der Raumgruppe Cc2 mit den Gitterkonstanten a = 18,70 Å; b = 21,06 Å; c = 15,69 Å; β = 119,8°.Das Strukturprinzip ergab sich aus der Anwendung statistischer Methoden zur Phasenbestimmung. Die Struktur wurde mit FOURIER- und LS-Methoden räumlich und anisotrop bis zu einem Diskrepanzfaktor von R = 0,13 für alle Reflexe verfeinert. Das Farbstoffkation enthält als wesentliches Bauelement eine Pentamethinkette mit Stickstoffatomen als Kettenendatomen. Die C—C-Bindungen in der Pentamethinkette zeigen den für offenkettige Polymethine typischen Bindungslängenausgleich sowie eine Alternierung der Valenzwinkel an den C-Atomen der Kette. Die C—N-Bindungen der Kette zeigen merkliche Verkürzung in Richtung partieller Doppelbindungen. Tendenziell ähnliche Verkürzungen zeigen die C—N-Bindungen zum Benzolring hin. Die Ringsysteme des Kations sind um 12,3° gegeneinander verdreht. Diese Verdrillung wird im Unterschied zu anderen Autoren als intramolekularer und nicht als Kristall-Packungseffekt interpretiert. Die Kationen sind in nichtäquivalenten Dimerenpaaren AA und AB polymer als eindimensionale Stapel gepackt, wobei jedes Kation sowohl einem Dimer AA als auch einem Dimer AB angehört. Diese Aggregate liegen im Kristallparallel zueinander. Die Struktur des Anions wird diskutiert. Es werden schwache Wasserstoffbrückenbindungen zwischen den Kristallwassermolekülen und den Anionen angenommen. Der Zusammenhang der Bauteile im Kristallverband wird durch Anion-Kation-Wechselwirkung, durch die Packungskräfte (Dispersionskräfte) zwischen den polymer gepackten Kationen sowie schwache Wasserstoffbrückenbindungen bewirkt.
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  • 188
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 379-386 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 3-Hydroxymethyl-benzoxazolon 2 und 3-Mercaptomethyl-benzoxazolon 10 werden mit Carbonsäurechloriden und Chlorkohlensäureestern zu den Carbonsäureestern 4 und den Kohlensäureestern 1 bzw. zu den Thiocarbonsäureestern 12 und den Thiokohlensäureestern 9 acyliert. Die Carbonsäureester 4 lassen sich auch gut aus den Trimethylammoniumsalzen von Carbonsäuren durch Amidomethylieren mit 3-Chlormethyl-benzoxazolon 6 darstellen. Die Amidomethylierung von Kaliumxanthogenaten mit 6 führt zu den Dithiocarbonaten 7. Isocyanate und Isothiocyanate addieren 3-Hydroxymethyl-oder 3-Mercaptomethyl-benzoxazolon unter Bildung der Carbamate 3 und des Thiocarbamats 5 bzw. der Thiocarbamate 11 und der Dithiocarbamate 13. Das N,N-Dimethyl-thiocarbamat 14 und das N,N-Dimethyl-dithiocarbamat 15 sind durch Acylieren von 3-Mercaptomethyl-benzoxazolon mit N,N-Dimethyl-carbamoyl- bzw. mit N,N-Dimethyl-thiocarbamoylchlorid gut zugänglich.
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  • 189
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 425-430 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Es wurde versucht, durch UV-, IR-, hochauflösende 1H- und 31P-NMR-Messungen für eine Reihe neu synthetisierter (1-Phenyl-2-aryl-vinyl)-diphenylphosphinoxide 1-5 eine Zuordnung zur cis- bzw. trans-Konfiguration durchzuführen. Wie sich heraustellte, ist dies mit allen diesen Meßmethoden in der konventionellen Aufnahmetechnik nicht möglich, Erst auf Grund der durch Eu(fod)3-Zusätze induzierten paramagnetischen Verschiebung der 1H-NMR-Signale, die eine Bestimmung der vicinalen Kopplungskonstante JP-H zuläßt, können cis- und trans-Vinylphosphinoxide unterschieden werden. Die JP-Hcis betragen im Mittel 22 Hz, die JP-Htrans 37 Hz.
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  • 190
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 455-462 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die katalytische Umsetzung von Arylaziden mit Kohlenmonoxid in Gegenwart von planaren d8-Komplexen des Rhodiums verläuft selektiv zu Arylisocyanaten. Das Geschwindigkeitsgesetz ist von erster Ordnung bezüglich Azid. Der Partialdruck des Kohlenmonoxids hat, vorausgesetzt, das Gas wird im Überschuß angeboten, zwischen 0,33 und 2,00 atm keinen Einfluß auf die Reaktionsgeschwindigkeit. Dies sowie die Lösungsmittelabhängigkeit der Reaktionsgeschwindigkeit, der Einfluß der Liganden im Edelmetallkomplex und der Einfluß der Substituenten in der Nitroverbindung auf die Reaktionsgeschwindigkeit weisen darauf hin, daß die oxydative Addition des Azids der geschwindigkeitsbestimmende Schritt der Reaktion ist.
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  • 191
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 503-509 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Oligomerisierung von Butadien-(1,3) in Gegenwart von π-Methylheptadienyl-π-butadien-(1,3)-kobalt(I) 1, π-Cyclooctenyl-π-cyclooctadien-(1,5)-kobalt(I) 2, π-Crotyl-π-butadien-(1,3)-tricyclohexylphosphin-kobalt(I) 3, π-Crotyl-π-butadien-(1,3)-tri-n-butylphosphinkobalt(I) 4 und π-Crotyl-π-butadien-(1,3)-triphenylphosphin-kobalt(I) 5 wird beschrieben. Für alle diese π-Komplexe gilt, daß die Bildung offenkettiger Oligomere gegenüber der Cyclooligomerisierung stark begünstigt ist. Koordinierte Phosphine beeinflussen den selektiven Ablauf der acyclischen Butadienoligomerisierung nicht.Die katalytische Wirksamkeit der Phosphinkomplexe wird durch die Substituenten am Phosphor beeinflußt. Die große Zahl an gebildeten Oligomeren läßt sich auf wenige Reaktionsschritte zurückführen.
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  • 192
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 525-526 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Ill.
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  • 193
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    Keywords: Chemistry ; Organic Chemistry
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    Topics: Chemistry and Pharmacology
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  • 194
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 540-544 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Reactions of molybdenum oxy tetrachloride with mono-, di-, and trihydroxy phenols have been carried out and molybdenum oxy phenoxides isolated. Alternative method for the preparation of these oxy phenoxides by the interaction between molybdenum oxy tetraethoxide and corresponding phenols has been reported. I. R. spectra of the oxy phenoxides have been discussed.
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  • 195
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    Topics: Chemistry and Pharmacology
    Notes: 6-Nitrobenzalphthalides reacted with amines to give 6-nitrobenzalphthalimidines. Reduction (H2S/NH3) of the 6-nitrobenzalphthalides gave open chain desoxybenzoin derivatives. 6-Aminophthalide condensed with aldehydes to give the corresponding arylidene aminophthalides only.
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  • 196
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 610-616 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Am Ring A substituierte erythro-Chalkondihalogenide zeigen einen anderen Trend bei den ϱ-Werten der Korrelationen zwischen Dipolmomenten und Substituentenkonstanten als die am Ring B substituierten Verbindungen. Die Differenzen zwischen den ϱ-Werten jeder Serie und die unterschiedlichen Trends werden diskutiert und können auf Unterschiede in der Gesamtpolarisierbarkeit der jeweiligen Halogenkombination X und Y in der aliphatischen Kette Z sowie auf unterschiedlich geartete Einflußnahme von Z auf die Wirkung von A- bzw. B-Substituenten zurückgeführt werden.
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  • 197
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 648-652 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 2,4-Bis-(alkoxycarbonyl-cyan-methylen)-1,3-dithietane 1 reagieren mit o-Aminophenolen zu den Dihydro-benz[b][1,4]oxazepinen 3, deren Struktur spektroskopisch und durch chemische Reaktionen bewiesen wird.
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  • 198
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    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 675-681 
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    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Durch Chlormethylierung von schwach vernetztem Polystyrol gelingt die Ankettung von Hydrazid- und Verdazylgruppierungen. Die Polymeren werden dadurch koordinationsaktiv gegenüber Cu2+-Ionen. Eine Fixierung der Cu(II)-Verbindungen an den Polymeren wird ESR-spektroskopisch bewiesen.Polymere Verdazyle aus 1,3,5-Triphenylformazan und chlormethyliertem Polystyrol können Cu(II)-Salze reduzieren. Ihre Reaktivität wird vom Lösungsmittel (Äthanol 〉 Acetonitril 〉 Dimethylformamid 〉 Dimethylsulfoxid) und vom Anion (Cl- 〉 SO42-, NO3-) beeinflußt.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 199
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 694-704 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Die Wirksamkeit von Zeolithen des Typs Y für die Alkylierung von niederen Paraffinen mit Olefinen wurde untersucht. Die Aktivität der Katalysatoren war, unabhängig von der Art der ausgetauschten Kationen und den Prozeßparametern, in flüssiger Phase sehr hoch. Die Isooctanausbeuten als Maß der Selektivität sind mit kommerziellen Alkylierungskatalysatoren vergleichbar. Durch Verwendung spezieller Einsatzprodukte unterschiedlicher C-Zahlen konnten mechanistische Vorstellungen über den Ablauf der Alkylierungsreaktion bestätigt werden.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 200
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 317 (1975), S. 752-756 
    ISSN: 0021-8383
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Durch Reaktion von Tetra-O-acetyl-L-arabinose bzw. 1, 2, 3, 4-Tetra-O-acetyl-β-D-xylose sowie Octa-O-acetyl-β-cellobiose mit 4-[N, N-Bis-(2-chloräthyl)-amino]-phenol · HCl entsprechend dem HELFERICH-Verfahren und anschließende ZEMPLÉN-Entacetylierung werden die Glykoside 1f, 2b und 3 b erhalten, in denen die alkylierende Aktivität der N-Lost-Gruppierung herabgesetzt ist. Über die pH-abhängige Spaltung dieser Glykoside und ein daraus resultierendes Therapie-Konzept wird kurz berichtet.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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