Groups satisfying the minimality condition for non-almost-layer-finite subgroups

The following theorem characterizing the class of almost layer-finite groups in the class of periodic groups without involutions is proved: Each conjugate-biprimitively finite group without involutions that satisfies the minimality condition for non-almost-layer-finite subgroups is almost layerfinite.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1002–1008, July–August, 1991.     

Exponential stability of hybrid stochastic recurrent neural networks with time-varying delays

In this paper, we consider a class of hybrid Stochastic recurrent neural networks with time-varying delays. By using Razumikhin-type theorem, we not only obtain–almost surely–the exponential stability but also estimate the exponentially convergent rate.     

A Generalization of Herrlich's Question on Almost Reflective and Coreflective Subclasses of Top and Unif

H. Herrlich asked in Topology Appl. 49 (1993), 251–264, whether there are nontrivial classes of topological spaces that are almost reflective and almost coreflective at the same time. This question was dealt with (in Huek and Tozzi, Appl. Categ. Structures 4 (1996), 57–68) in a more general setting than almost reflective and almost coreflective classes. The present paper investigates a modified question: when a nontrivial generalized reflective class of topological or uniform spaces is equivalent to a generalized coreflective class of spaces.     

Equilibria of noncompact abstract economies in general almost convex strategy spaces

We first extend the concept of almost convex condition and establish a fixed point theorem for correspondences with convex values only on an almost convex subset for their ranges. This generalizes both results of Himmelberg [C.J. Himmelberg, Fixed points of compact multifunctions, J. Math. Anal. Appl. 38 (1972) 205–207] and the result of Jafari and Sehgal [F. Jafari, V.M. Sehgal, An extension to a theorem of Himmelberg, J. Math. Anal. Appl. 327 (2007) 298–301]. Furthermore, applying it, we have existence theorems for equilibria of noncompact abstract economies in general almost convex strategy spaces. Our theorems generalize the corresponding results of Zhou [Jianxin Zhou, On the existence of equilibrium for abstract economies, J. Math. Anal. Appl. 193 (1995) 839–858], Tan and Wu [K.-K. Tan, Z. Wu, A note on abstract economies with upper semicontinuous correspondence, Appl. Math. Lett. 11 (5) (1998) 21–22] in several ways. In particular, we answer the question raised by Zhou in the reference cited above in the affirmative with weaker hypotheses.     

Almost Sure Convergence of the Numerical Discretization of Stochastic Jump Diffusions

Based on the shuffle product expansion of exponential Lie series in terms of a Philip Hall basis for the stochastic differential equations of jump-diffusion type, we can establish Stratonovich–Taylor–Hall (STH) schemes. However, the STHr scheme converges only at order r in the mean-square sense. In order to have the almost sure Stratonovich–Taylor–Hall (ASTH) schemes, we have to include all the terms related to multiple Poissonian integrals as the moments of multiple Poissonian integrals always have lower orders of magnitudes as compared with those of multiple Brownian integrals.     

On deformation of associative algebras and graph homology

Deformation theory of associative algebras and in particular of Poisson algebras is reviewed. The role of an “almost contraction” leading to a canonical solution of the corresponding Maurer–Cartan equation is noted. This role is reminiscent of the Homotopical Perturbation Lemma, with the infinitesimal deformation cocycle as “initiator.”Applied to star-products, we show how Moyal's formula can be obtained using such an almost contraction and conjecture that the “merger operation” provides a canonical solution at least in the case of linear Poisson structures.     

The admissibility of the empirical mean location for the matrix von Mises–Fisher family

In this note we consider von Mises–Fisher families of probability densities on spheres and more generally on Stiefel manifolds, which include the orthogonal groups. It addresses the estimation of the mean direction or the mean location by empirical mean location, which for the von Mises–Fisher family coincides with the maximum likelihood estimator. It is shown that (with a few exceptions) the empirical mean location of a sample is almost surely uniquely defined and that it is unbiased in the sense that its mean location coincides with the mean location of the von Mises–Fisher distribution. The main goal, however, is to show that empirical mean location is an admissible estimator for the mean location of the von Mises–Fisher distribution.     

Cold flow and melting of plastics under severe friction conditions

Dry friction of a series of crystalline polymers (polypropylene, nylon, PTFE) against steel over a wide range of sliding velocities (4.4–4.4×10^–4 cm/sec) and loads (P=7.5–360 kg) with almost complete mutual overlap of the friction surfaces is studied. It is shown that friction of polymer materials against steel may be accompanied by melting of the crystalline polymer (at high velocities) or cold flow (at low velocities) in the surface layers associated with an orientation effect and the appearance of anisotropy.Mekhanika Polimerov, Vol. 1, No. 5, pp. 95–100, 1965     

Strain distribution in composites

The strains in specimens of epoxy-furan resin and rubber simulating the structure of a composite material have been experimentally investigated by the network method. The strains in the components are distributed in accordance with an almost normal Iaw.Gomel's State University. Translated from Mekhanika Polimerov, No. 4, pp. 731–734, July–August, 1974.     

Validation of a Structural Optimization Algorithm Transforming Dynamic Loads into Equivalent Static Loads

Generally, structural optimization is carried out based on external static loads. However, all forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is almost impossible in a large-scale problem. Therefore, in engineering practice, dynamic loads are often transformed into static loads via dynamic factors, design codes, and so on. Recently, a systematic transformation of dynamic loads into equivalent static loads has been proposed in Refs. 1–3. Equivalent static loads are made to generate at each time step the same displacement field as the one generated by the dynamic loads. In this research, it is verified that the solution obtained via the algorithm of Refs. 1–3 satisfies the Karush–Kuhn–Tucker necessary conditions. Application of the algorithm is discussed.     

On the Kenmotsu Hypersurfaces of Special Hermitian Manifolds

We consider almost contact metric hypersurfaces of almost Hermitian manifolds of class W₃ (in the Gray–Hervella terminology). We establish a criterion for minimality of such hypersurfaces in the case when the contact metric structure is cosymplectic.     

Cobordism of hyperframed manifolds and the stable J-homomorphism

This paper considers the cobordism groups of hyperframed manifolds; that is, manifolds which are framed off a codimension one submanifold. These groups are related to thestable J-homomorphism in the same way that the cobordism groups of almost parallelizable manifolds are related to the J-homomorphism. We compute characteristic numbers and present some low dimensional examples.Research partially supported by NSF Grant MCS76–06973Research partially supported by NSF Grant MPS74–22738     

Unbounded functions with almost periodic differences

The structure of continuous real-valued functions F(t) on the real line, such that for any fixed y the difference F(t+y)–F(t) is an almost periodic Bohr function, is investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1409–1413, October, 1991.     

On the ranks of bent functions

The rank of a bent function is the 2-rank of the associated symmetric 2-design. In this paper, it is shown that it is an invariant under the equivalence relation among bent functions. Some upper and lower bounds of ranks of general bent functions, Maiorana–McFarland bent functions and Desarguesian partial spread bent functions are given. As a consequence, it is proved that almost every Desarguesian partial spread bent function is not equivalent to any Maiorana–McFarland bent function.     

On linear almost periodic pulse systems

For a linear almost periodic system under pulse influence, the conditions are established under which this system is reducible (by a linear change of variables with a discontinuous almost periodic matrix) to a system without pulses but with a Bohr almost periodic right-hand side. The set of linear almost periodic pulse systems possessing only bounded solutions is studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 105–113, January, 1993.     

Jessen's theorem for holomorphic almost periodic maps

An analog of Jessen's theorem on the existence of a Jessen function and its relation to the distribution of roots of a holomorphic almost periodic function in a strip is obtained for almost periodic maps.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1094–1107, August, 1990.     

Theory of characteristic Lyapunov indices

It is proved that for almost every linear system of differential equations, almost all systems close to it have indices close to its indices.Translated from Matematicheskie Zametki, Vol. 7, No. 4, pp. 503–513, April, 1970.     

Convergence rate of Fourier–Laplace series of L-functions

The almost everywhere convergence rates of Fourier–Laplace series are given for functions in certain subclasses of L²(Σ_n−1) defined in terms of moduli of continuity.     

A new class of Ornstein transformations with singular spectrum

It is shown that for any family of probability measures in Ornstein type constructions, the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem [J. Bourgain, On the spectral type of Ornstein class one transformations, Israel J. Math. 84 (1993) 53–63], same result is proved for Rudolph's construction [D. Rudolph, An example of a measure-preserving map with minimal self-joining and applications, J. Anal. Math. 35 (1979) 97–122].     

Correlation analysis and strength of glass-reinforced plastic pipe

The correlation between certain input characteristics of glass cloth reinforced plastic pipe and product quality is evaluated. The almost total lack of both interfactor and multiple correlation is noted. The parameters that should be controlled in manufacturing pipe for purposes of obtaining the necessary correlation are listed.Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1014–1019, November–December 1968.