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Coefficient inequalities for a subclass of Bazilevič functions

Fitri Sa’adatul, Marjono, Thomas Derek K., Wibowo R. B. E.

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

27--37

EN

Let f be analytic in D={z:|z| < 1} with f(z)=z+∑∞n=2anzn, and for α ≥ 0 and 0 < λ ≤ 1, let B1(α,λ) denote the subclass of Bazilevič functions satisfying (…) <λ for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f ∈ B1(α,λ), thus extending recent work in the case λ = 1.

2

A numerical algorithm for computing the inverse of a Toeplitz pentadiagonal matrix

Talibi B., Hadj D. A., Sarsri D.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 3

83--95

EN

In the current paper, we present a computationally efficient algorithm for obtaining the inverse of a pentadiogonal toeplitz matrix. Few conditions are required, and the algorithm is suited for implementation using computer algebra systems.

3

Trefftz function for solving a quasi-static inverse problem of thermal stresses

Grysa K., Maciąg A., Maciejewska B.

Computer Assisted Mechanics and Engineering Sciences

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2009

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Vol. 16, No. 3/4

251-266

EN

The problem of thermal stresses in a hollow cylinder is considered. The problem is two-dimensional and the cross-section of the hollow cylinder is approximated as a long and thin rectangle as the ratio of the inner and outer radiuses is close to one. On the outer boundary of the hollow cylinder the heat source moves with a constant velocity. In the case of the rectangle the heat source moves on the upper side and the conditions of eąuality of temperatures and heat fluxes are assumed on the left and right boundaries. The stresses are to be found basing on the temperature measured inside the considered region, which means that an inverse problem is considered. Both for the temperature field and the displacements and stresses the finite element method is used. Thermal displacement potentials are introduced to find displacements and stresses. In order to construct the base functions in each element the Trefftz functions are used. For the temperature field the time-space finite elements are used and for the thermal displacement potentials the spatial elements are applied. Thanks to the use of the Trefftz functions a low-order approximation has given a solution very close to the exact one.

4

Recent developments in numerical homogenization

Boso D. P., Lefik M., Schrefler B. A.

Computer Assisted Mechanics and Engineering Sciences

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2009

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Vol. 16, No. 3/4

161-183

EN

This paper deals with homogenization of non linear fibre-reinforced composites in the coupled thermo-mechanical field. For this kind of structures, i.e. inclusions randomly dispersed in a matrix, the self consistent methods are particularly suitable to describe the problem. Usually, in the framework of the self consistent scheme the homogenized material behaviour is obtained with a symbolic approach. For the non linear case, that method may become tedious. This paper presents a different, fully numerical procedure. The effective properties are determined by minimizing a functional expressing the difference (in some chosen norm) between the solution of the heterogeneous problem and the equivalent homogenous one. The heterogeneous problem is solved with the Finite Element method, while the second one has its analytical solution. The two solutions are written as a function of the (unknown) effective parameters, so that the final global solution is found by iterating between the two single solutions. Further, it is shown that the considered homogenization scheme can be seen as an inverse problem and Artificial Neural Networks are used to solve it.