On Γ-convergence of integral functionals defined on various weighted Sobolev spaces

We consider weighted Sobolev spaces correlated with a sequence of n-dimensional domains. We prove a theorem on the choice of a subsequence Γ-convergent to an integral functional defined on a “limit” weighted Sobolev space from a sequence of integral functionals defined on the spaces indicated. Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 99–115, January, 2009.     

Some properties of Γ-limits of integral functionals

Summary We prove some integral representation theorems for the Γ limit in L¹ of sequences of the form dx in coercivity and bounded growth hypothesis which are optimal as it is checked with examples. These results are utilized to describe the L¹ lower semicontinuous envelope of a given functional. We consider also the stability of Γ limits with respect to obstacle type perturbations and prove the homogenization formulas in conditions more generals of those already considered by several authors. Entrata in Redazione il 10 gennaio 1978.     

On differential Sandwich theorems of analytic functions defined by generalized Sălăgean integral operator

In this paper we obtain some applications of first order differential subordination and superordination results involving generalized S?l?gean integral operator for certain normalized analytic functions. Some of our results generalize previously known results.     

The Reissner-Mindlin plate is the Γ-limit of Cosserat elasticity

The linear Reissner-Mindlin membrane-bending plate model is the rigorous Γ-limit for zero thickness of a linear isotropic Cosserat bulk model with symmetric curvature. For this result we use the natural nonlinear scaling for the displacements u and the linear scaling for the infinitesimal microrotations Ā ∈ so(3) affecting the in-plane drill rotations. No boundary conditions on the microrotations are prescribed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Ω-limit Sets of Discrete-time Dynamical Systems

The paper investigates z -limit sets for discrete-time dynamical systems of the form x n +1 = f n +1 ( x n ), n S 0, with each f n mapping an interval I of R into itself. For autonomous systems, i.e. f n = f for all n , and f continuous on I =[ a , b ], the case that all z -limit sets consist of one point only is characterized by several equivalent conditions, one being that f has no 2-periodic points. The non-autonomous case assumes that the functions f n converge uniformly to a continuous function f X that has no 2-periodic points. It is shown that the z -limit sets are closed intervals consisting of fixed points of f X only. Under certain conditions these closed intervals contain exactly one point each. This allows a treatment of certain discrete-time dynamical systems in R n .     

Some subordination results for classes of analytic functions defined by the Al-Oboudi–Al-Amoudi operator

In this paper, we investigate several interesting subordination results of some classes of analytic functions defined by means of the Al-Oboudi–Al-Amoudi operator. Received: 15 August 2008, Revised: 19 November 2008     

On the ω-limit Set Dichotomy of Cooperating Kolmogorov Systems

The authors study the -limit set dichotomy of the Kolmogorov systems _i=x_i f _i(x)x _i0, 1in with the cooperative and irreducible hypotheses and obtain the quasiconvergence almost everywhere when n=3, which gives an affirmative answer to the open problem by Smith [9, p.72] in the case of n=3.     

On the Operator Semirings of a Γ-Semiring

In this paper we introduce the notion of operator semirings of a -semiring to study -semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a -semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various -semirings.AMS Subject Classification (2000): 16Y60, 16Y99     

Plasticity as the Γ-limit of a Nonlinear Dislocation Energy with Mixed Growth

We consider a model for straight parallel edge dislocations with a nonlinear elastic energy with mixed growth. By means of Γ-convergence we show that the suitably rescaled energy converges to a strain-gradient plasticity model. As a tool we proof a generalized rigidity estimate which bounds the distance of a field with non-vanishing curl to a specific rotation by the distance to all rotations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the ε-entropy of classes of holomorphic functions

Suppose thatB _R ^d is a ball of radiusR in ℂ ^d and σ is the standard measure on the unit sphere in ℂ ^d . ForR>1, 1≤p≤∞, and for the natural numbersl, d, byH _R ⁰ (l, p, d) we denote the class of functionsf holomorphic inB _R ^d and such that in the homogeneous polynomial expansion of the firstl summands the zero and radial derivatives of orderl belong to the closed unit ball of the Hardy spaceH ^p (B _R ^d ). In this paper an asymptotic formula for the ε-entropy of the classH _R ⁰ (l, p, d) in the spacesL ^p (σ), 1≤p<∞, and is obtained. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 286–293, August, 2000.     

On Γ−-convergence of functionals with analytic integrand

Sunto Si dimostra, sotto opportune ipotesi l'analiticità dell'integrando del ^–-limite di una successione di funzionali semplici del C.d.V. ad integrando analitico.

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This work has been performed as a part of a National Research Project supported by M.P.I. (40% 1987).     

On the approximation of conjugate functions from Holder classes by Fejér means

Получены асимптотич еские равенства для в еличин гдеr≧0 — целое, ω(t) — выпу клый модуль непрерыв ности и $$\bar \sigma _n (f;x) = - \frac{1}{\pi } \mathop \smallint \limits_{ - \pi }^\pi f(x + t)\left( {\frac{1}{2}ctg\frac{t}{2} - \frac{1}{{4(n + 1)}}\frac{{\sin (n + 1)t}}{{\sin ^2 \tfrac{1}{2}t}}} \right)dt$$ сумма Фейера функцииf(х), сопряженной сf(x).     

On ω-limit Sets of Triangular Maps on the Unit Cube

We consider Sturm–Liouville eigenvalue problems of second order with arbitary seperated boundary conditions and perform a suitabl discretization of them. The obtained discrete Sturm–Liouville eigenvalue problems are examined and the asymptotic behavior of their eigenvalue as the norm of the partition tends to zero is investigated.     

On infinite-rank singular perturbations of the Schrödinger operator

Schrödinger operators with infinite-rank singular potentials V=Σ _i,j=1 ^∞ b _ij〈φ_j,·〉φ_i are studied under the condition that the singular elements ψ _j are ξ _j(t)-invariant with respect to scaling transformationsin ?³.