On a new class of dynamic Hardy-type inequalities and some related generalizations

Aequationes mathematicae - In this paper, we establish a new class of dynamic inequalities of Hardy’s type which generalize and improve some recent results given in the literature. More...     

On some generalizations of denting points

In this paper a local version is given of a well-known theorem for uniform rotund renorming of superreflexive Banach spaces.     

On Jonsson stability and some of its generalizations

We consider Jonsson analogues of the concepts of stability and P-stability. We also consider properties and connections of a Jonsson theory and its center that concern these concepts.     

On three Krein extension problems and some generalizations

Three basic extension problems which were initiated by M. G. Krein are discussed and further developed. Connections with interpolation problems in the Carathéodory class are explained. Some tangential and bitangential versions are considered. Full characterizations of the classes of resolvent matrices for these problems are given and formulas for the resolvent matrices of left tangential problems are obtained using reproducing kernel Hilbert space methods.Dedicated to the memory of M. G. Krein, a beacon for us both.The authors wish to acknowledge the partial support of the Israel-Ukraine Exchange Program. D. Z. Arov also wishes to thank the Weizmann Institute of Science for partial support and hospitality; H. Dym wishes to thank Renee and Jay Weiss for endowing the chair which supports his research.     

On some generalizations of the factorization method

The classical factorization method reduces the study of a system of ordinary differential equations U_t=[U₊, U] to solving algebraic equations. Here U(t) belongs to a Lie algebra which is the direct sum of its subalgebras and , where “+” signifies the projection on . We generalize this method to the case . The corresponding quadratic systems are reducible to a linear system with variable coefficients. It is shown that the generalized version of the factorization method can also be applied to Liouville equation-type systems of partial differential equations. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 3, pp. 339–350, March, 1997.     

Groupwise density and related cardinals

We prove several theorems about the cardinal associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps from to, all families of size are below all unbounded families. With respect to a natural ordering of filters on, all filters generated by sets are below all non-feeble filters. If then and . (The definitions of these cardinals are recalled in the introduction.) Finally, some consequences deduced from by Laflamme are shown to be equivalent to .     

On some generalizations of Lorentz's almost convergence

We investigate an extension of the almost convergence of G.G. Lorentz, further weakening the notion of M-almost convergence we defined in [S. Mercourakis, G. Vassiliadis, An extension of Lorentz's almost convergence and applications in Banach spaces, Serdica Math. J. 32 (2006) 71–98] and requiring that the means of a bounded sequence restricted on a subset M of converge weakly in ℓ^∞(M). The case when M has density 1 is of special interest and in this case we derive a result in the direction of the Mean Ergodic Theorem (see Theorem 2).     

A note on tall cardinals and level by level equivalence

Starting from a model “κ is supercompact” + “No cardinal is supercompact up to a measurable cardinal”, we force and construct a model such that “κ is supercompact” + “No cardinal is supercompact up to a measurable cardinal” + “δ is measurable iff δ is tall” in which level by level equivalence between strong compactness and supercompactness holds. This extends and generalizes both [ 4 , Theorem 1] and the results of 5 .     

On some generalizations of Hopfian and co-Hopfian Abelian groups

The notions of Hopfian and co-Hopfian groups have been of interest for some time. In this present work we consider generalizations of the classes of hereditarily Hopfian (co-Hopfian) and super Hopfian (co-Hopfian) Abelian groups by requiring only that countable subgroups or images inherit the Hopfian (co-Hopfian) property.     

On some generalizations of the classical Riemann problem

The special class of the homogeneous vector boundary Riemann problems on the finite sequence of algebraic surfaces is investigated completely. Its coefficients are the noncommutative permutative matrices of the arbitrary but not prime order, and boundary conditions are given on the system of open contours. The constructive solution procedure and definite structure of the canonical solution matrix are obtained and present some generalizations of the classical Riemann problem. Simultaneously the corresponding class of algebraic equations for the appropriate covering surfaces is formed explicitly too. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On some nonlinear generalizations of Gronwall’s inequality

Some useful nonlinear generalizations of the Gronwall’s inequality which contain, as special cases, the recent generalizations of this inequality given by I. Bihari, D. Willett and J. S. W. Wong and several recent works are presented.     

On some generalizations of the second grade fluid model

In this article, we provide a brief review of some generalizations of the second grade fluid model. We discuss certain similarities between these fluids and fluids of higher grades, while also describing certain limitations of these models. The new models that we put forth are based upon some interesting experimental results which suggest that not only can normal stress coefficients depend upon the shear rate, but that this dependency is in fact not the same rate as that of shear viscosity variation with shear rate. We then discuss some steady flows of these generalized second grade fluid models.     

On some integrable generalizations of the continuous Toda system

In the present paper, we obtain some integrable generalizations of the continuous Toda system generated by a flat connection form taking values in higher grading subspaces of the algebra of the area-preserving diffeomorphism of the torus T² and construct their general solutions. The grading condition we use here, imposed on the connection, can be realized in terms of holomorphic distributions on the corresponding homogeneous spaces.On leave of absence from the Institute for High Energy Physics, 142284, Protvino, Moscow region, Russia; saveliev@mx.ihep.su.Republished from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 2, pp. 193–204, August, 1996.     

On some generalizations of theorems by Landau and Pólya

If F(s), the Mellin transform ?(x) (real valued), satisfies certain regularity conditions and if its behaviour on the abscissa of convergence is known, then theorems of Landau and Pólya give information concerning sign changes of ?(x). In the present paper, corresponding conclusions are obtained when F(s) does not satisfy the regularity conditions of the theorems of Landau Pólya.