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1
Content available UV-Induced Anisotropy in CdBr2-CdBr2: Cu Nanostructures
El-Naggar A. M., Albassam A. A., Oźga K., Szota M., Kityk I. V.
Archives of Metallurgy and Materials
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2015
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Vol. 60, iss. 3A
2029--2032
EN
We have found an occurrence of anisotropy in the nanostructure CdBr2-CdBr2: Cu nanocrystalline films. The film thickness was varied from 4 nm up to 80 nm. The films were prepared by successive deposition of the novel layers onto the basic nanocrystals. The detection of anisotropy was performed by occurrence of anisotropy in the polarized light at 633 nm He-Ne laser wavelength. The occurrence of anisotropy was substantially dependent on the film thickness and the photoinduced power density. Possible mechanisms of the observed phenomena are discussed.
PL
Wykryto pojawienie się anizotropii w nanostrukturalnych warstwach nanokrystalicznych CdBr2-CdBr2: Cu. Grubość warstwy zmieniano w zakresie od 4 nm do 80 nm. Nanostrukturalne warstwy otrzymano poprzez kolejne osadzanie na nowych warstwach na podstawie nanokrystalitów. Detekcję anizotropii wykonano w spolaryzowanym świetle lasera gazowego He-Ne o długości fali 633 nm. Anizotropia optyczna występująca w warstwach w znacznym stopniu zależy od grubości warstwy i gęstości mocy indukowanej światłem. Omówiono możliwe mechanizmy obserwowanego zjawiska.
2
Nondifferentiable (Phi,rho)-type I and generalized (Phi,rho)-type I functions in nonsmooth vector optimization
Antczak T.
Journal of Applied Analysis
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2013
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Vol. 19, nr 2
247--270
EN
In this paper, new classes of nondifferentiable generalized invex functions are introduced. Further, nonsmooth vector optimization problems with functions belonging to the introduced classes of (generalized) (Phi,rho)-type I functions are considered. Sufficient optimality conditions and duality results for such classes of nonsmooth vector optimization problems are established. It turns out that the presented results are proved also for such nonconvex vector optimization problems in which not all functions constituting them possess the fundamental property of invexity.
3
Semiinfinite multiobjective fractional programming. P. II. Duality models
Zalmai G. J., Zhang Q.
Journal of Applied Analysis
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2011
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Vol. 17, nr 1
1-35
EN
In this paper, we discuss a fairly large number of parametric and semiparametric duality results under various generalized (η, ρ)-invexity assumptions for a semiinfinite multiobjective fractional programming problem.
4
Optimality and duality for nonsmooth multiobjective optimization problems with generalized V-r-invexity
Mishra S. K., Singh V., Wang S. Y., Lai K. K.
Journal of Applied Analysis
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2010
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Vol. 16, nr 1
49-58
EN
In this paper, a new concept of invexity for locally Lipschitz vector-valued functions is introduced, called V-r-type I functions. The generalized Karush-Kuhn-Tucker sufficient optimality conditions are proved and duality theorems are established for a non-smooth multiobjective optimization problems involving K-r-type I functions with respect to the same function η.
5
Content available remote On a non-local parabolic problem
Akila Y.
Demonstratio Mathematica
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2009
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Vol. 42, nr 4
745-755
EN
The aim of this paper is to investigate the existence of solutions of a nonlocal parabolic problem. The method of upper and lower solutions and the classical maximum principle are used to obtain our results.
6
Content available remote Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids
Bresch D., Koko J.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no 4
419-429
EN
We present a numerical simulation of two coupled Navier-Stokes flows, using operator-splitting and optimization-based nonoverlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid in rest.
7
Content available remote Analysis of some dual properties in discrete dynamic systems
Zhirabok A.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no 3
297-308
EN
The problem of duality in nonlinear and linear systems is considered. In addition to the known duality between controllability and observability, new dual notions and their properties are investigated. A way to refine these properties through an isomorphic transformation of the original systems is suggested.
8
Content available remote Rotundity, smoothness and duality
Penot J.-P.
Control and Cybernetics
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2003
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Vol. 32, no 4
711-733
EN
The duality between smoothness and rotundity of functions is studied in a nonlinear abstract framework. Here smoothness is enlarged to subdifferentiability properties and rotundity is formulated by means of approximation properties.
9
Content available Weak sharp minima revisited Part I : basic theory
Burke J., Deng S.
Control and Cybernetics
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2002
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Vol. 31, no 3
439-469
EN
The notion of sharp minima, or strongly unique local minima, emerged in the late 1970's as an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. The work of Cromme and Polyak is of particular importance in this development. In the late 1980's Ferris coined the term weak sharp minima to describe the extension of the notion of sharp minima to include the possibility of a non-unique solution set. This notion was later extensively studied by many authors. Of particular note in this regard is the paper by Burke and Ferrris which gives an extensive exposition of the notion and its impact on convex programming and convergence analysis in finite dimensions. In this paper we build on the work of Burke and Ferris. Specifically, we generalize their work to the normed linear space setting, further dissect the normal cone inclusion characterization for weak sharp minima, study the asymptotic properties of weak sharp minima in terms of associated recession functions, and give new characterizations for local weak sharp minima and boundely weak sharp minima. This paper is the first of a two part work on this subject. In Part II, we study the links between the notions of weak sharp minima, bounded linear regularity, linear regularity, metric regularity, and error bounds in convex programming. Along the way, we obtain both new results and reproduce many existing results from a fresh perspective.
10
Content available On some optimization problem related to economic equilibrium
Naniewicz Z.
Control and Cybernetics
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2002
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Vol. 31, no 1
141-165
EN
The paper considers an optimization problem in which the minima of a finite collection of objective functions satisfy some unilateral constraints and are linked together by a certain subdifferential relationship. The governing relations are stated as a variational inequality defined on a nonconvex feasible set. By the reduction to the variational inequality involving nonmonotone multivalued mapping, defined over nonnegative orthant, the existence of solutions is examined. The prototype is the general economic equilibrium problem. The exemplification of the theory for the quadratic multi-objective function is provided.
11
Content available Convergence and extensions of variational problems with non-coercive functionals
Ioffe A.
Control and Cybernetics
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2002
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Vol. 31, no 3
507-519
EN
The paper is a transcript of the lecture given at the European Symposium on Well-Posedness in Optimization in Warsaw. It contains a complete theory of variational problems with integrands not depending on x, including existence and relaxation theorems, a complete description of solutions and the connection between variational convergences of functionals and convergence of value functions and solutions of associated variational problems with the main emphasis on functionals that lack coercivity.
12
Content available remote A duality for starshaped functions
Penot J.-P.
Bulletin of the Polish Academy of Sciences. Mathematics
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2002
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Vol. 50, no 2
127-139
EN
A conjugacy is introduced for the class of starshaped functions from [0, infinity] into [0, infinity], i.e. the class of functions f such that their slope s : t --> f (t)/t is nondecreasing. This class is stable by several operations and plays a key role in the study of uniformly convex and uniformly smooth convex functions and in the geometry of Banach spaces. Here the inversion of the subdifferential as in the Legendre-Fenchel transform is replaced by an inversion device of the slope s which uses the ordering of R.
13
Content available Optimality conditions and a classification of duality schemes in vector optimization
El Ghali B.
Control and Cybernetics
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2000
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Vol. 29, no 4
839-860
EN
Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x[0] belongs to A, w[0] belongs to Fx[0] such that w[0] is minimal in FA. To a family of vector minimization problems minimize[x belongs to X] F(x, y), y [belongs to] Y, one associates a Lagrange relation [L(x, [xi], y[0]) = union of sets y belongs to Y(F(x, y)-xi(y)+(y[0]))] where [xi] belongs to an arbitrary class [Xi] of mappings. For this type of problem, there exist several notions of solutions. Some useful characterizations of existential solutions are established and, consequently, some necessary conditions of optimality are derived. One result of intermediate duality is proved with the aid of the scalarization theory. Existence theorems for existential solutions are given and a comparison of several exact duality schemes is established, more precisely in the convex case it is shown that the majority of exact duality schemes can be obtained from one result of S. Dolecki and C. Malivert.
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