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  • 1
    Electronic Resource
    Electronic Resource
    Modelling of small-angle X-ray scattering data using Hermite polynomials (2001)
    Copenhagen : International Union of Crystallography (IUCr)
    Applied crystallography online 34 (2001), S. 510-518 
    Details
    ISSN: 1600-5767
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Geosciences , Physics
    Notes: A new algorithm, called the term-selection algorithm (TSA), is derived to treat small-angle X-ray scattering (SAXS) data by fitting models to the scattering intensity using weighted Hermite polynomials. This algorithm exploits the orthogonal property of the Hermite polynomials and introduces an error-reduction ratio test to select the correct model terms or to determine which polynomials are to be included in the model and to estimate the associated unknown coefficients. With no a priori information about particle sizes, it is possible to evaluate the real-space distribution function as well as three- and one-dimensional correlation functions directly from the models fitted to raw experimental data. The success of this algorithm depends on the choice of a scale factor and the accuracy of orthogonality of the Hermite polynomials over a finite range of SAXS data. An algorithm to select a weighted orthogonal term is therefore derived to overcome the disadvantages of the TSA. This algorithm combines the properties and advantages of both weighted and orthogonal least-squares algorithms and is numerically more robust for the estimation of the parameters of the Hermite polynomial models. The weighting feature of the algorithm provides an additional degree of freedom to control the effects of noise and the orthogonal feature enables the reorthogonalization of the Hermite polynomials with respect to the weighting matrix. This considerably reduces the error in orthogonality of the Hermite polynomials. The performance of the algorithm has been demonstrated considering both simulated data and experimental data from SAXS measurements of dewaxed cotton fibre at different temperatures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0021889801006951
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  • 2
    Electronic Resource
    Electronic Resource
    Duality and existence theory for nondifferentiable programming (1986)
    Springer
    Journal of optimization theory and applications 48 (1986), S. 451-458 
    Details
    ISSN: 1573-2878
    Keywords: Optimality conditions ; directional derivatives ; subdifferentials ; constraint qualifications ; stationary point problems ; duality theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Necessary and sufficient conditions of optimality are given for a nonlinear nondifferentiable program, where the constraints are defined via closed convex cones and their polars. These results are then used to obtain an existence theorem for the corresponding stationary point problem, under some convexity and regularity conditions on the functions involved, which also guarantee an optimal solution to the programming problem. Furthermore, a dual problem is defined, and a strong duality theorem is obtained under the assumption that the constraint sets of the primal and dual problems are nonempty.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940571
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A class of nonlinear complementarity problems for multifunctions (1987)
    Springer
    Journal of optimization theory and applications 53 (1987), S. 105-113 
    Details
    ISSN: 1573-2878
    Keywords: Complementarity problems ; subdifferentials ; multifunctions ; existence theorems ; regular functions ; monotone functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a continuous mapF:R n →R n and a lower semicontinuous positively homogeneous convex functionh:R n →R, the nonlinear complementarity problem considered here is to findxεR + n andy∈∂h(x), the subdifferential ofh atx, such thatF(x)+y≥0 andx T (F(x)+y)=0. Some existence theorems for the above problem are given under certain conditions on the mapF. An application to quasidifferentiable convex programming is also shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938819
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  • 4
    Electronic Resource
    Electronic Resource
    Thermal stresses in a thin circular disc of orthotropic material due to an instantaneous point heat source (1972)
    Springer
    Acta mechanica 13 (1972), S. 205-214 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wurde das instationäre ebene Wärmespannungsproblem einer Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle untersucht. Die Veränderung von σθθ über die Zeit für verschiedene Radien ist graphisch dargestellt und wird mit dem isotropen Fall verglichen.
    Notes: Summary In this paper, we have analysed the transient plane thermal stress problem of a circular disc of orthotropic material with instantaneous point heat source. The variation of σθθ with time along different radius vectors is exhibited graphically and compared with that of the isotropic case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586793
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    Paper (German National Licenses)
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