Varieties Defined by Permutations

We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form . A criterion is given determining whether a cyclic variety is interpretable in . For a permutation without fixed elements, it is stated that a set of primes for which is interpretable in in the lattice is finite. It is also proved that for distinct primes , the Helly number of a type in coincides with dimension of the dual type and equals .     

On intervals and isometries of MV-algebras

Let Int be the lattice of all intervals of an MV-algebra . In the present paper we investigate the relations between direct product decompositions of and (i) the lattice Int , or (ii) 2-periodic isometries on , respectively.     

Boundedness of Riesz Potential Generated by Generalized Shift Operator on B<Emphasis Type="Italic">a</Emphasis> Spaces

In this paper, the boundedness of the Riesz potential generated by generalized shift operator from the spaces to the spaces is examined.     

Determinants of Matrices Associated with Incidence Functions on Posets

Let S = x ₁,...,x _n} be a finite subset of a partially ordered set P. Let f be an incidence function of P. Let denote the n × n matrix having f evaluated at the meet of x _i and x _j as its i, j-entry and denote the n × n matrix having f evaluated at the join of x _i and x _j as its i, j-entry. The set S is said to be meet-closed if for all 1 i, j n. In this paper we get explicit combinatorial formulas for the determinants of matrices and on any meet-closed set S. We also obtain necessary and sufficient conditions for the matrices and on any meet-closed set S to be nonsingular. Finally, we give some number-theoretic applications.     

Asymptotic behavior of solutions of A 2nth order nonlinear differential equation

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for

A Comparison on the Commutative Neutrix Convolution of Distributions and the Exchange Formula

Let , be ultradistributions in and let and where is a sequence in which converges to the Dirac-delta function . Then the neutrix product is defined on the space of ultradistributions as the neutrix limit of the sequence provided the limit exist in the sense that

A Completion of \mathbb{Z} is a Field

We define various ring sequential convergences on and . We describe their properties and properties of their convergence completions. In particular, we define a convergence on by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields Further, we show that is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.     

On Large Deviations of Vector-Valued Additive Functions of a Markov Gaussian Field

We prove a local limit theorem for large deviations of the sums , where , is a Markov Gaussian random field, is a bounded vector-valued function, and . This paper generalizes the paper [13].     

One-Dimensional Topologically Nontrivial Solutions in the Skyrme Model

We consider the Skyrme model using the explicit parameterization of the rotation group through elements of its algebra. Topologically nontrivial solutions already arise in the one-dimensional case because the fundamental group of is . We explicitly find and analyze one-dimensional static solutions. Among them, there are topologically nontrivial solutions with finite energy. We propose a new class of projective models whose target spaces are arbitrary real projective spaces .     

Spin Models and Strongly Hyper-Self-Dual Bose-Mesner Algebras

We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let and denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of with respect to p. By a hyper-duality of , we mean an automorphism of such that for all ; and is a duality of . is said to be hyper-self-dual whenever there exists a hyper-duality of . We say that is strongly hyper-self-dual whenever there exists a hyper-duality of which can be expressed as conjugation by an invertible element of . We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra.     

Equational Theories for Classes of Finite Semigroups

It is proved that there exists an infinite sequence of finitely based semigroup varieties such that, for all i, an equational theory for and for the class of all finite semigroups in is undecidable while an equational theory for and for the class of all finite semigroups in is decidable. An infinite sequence of finitely based semigroup varieties is constructed so that, for all i, an equational theory for and for the class of all finite semigroups in is decidable whicle an equational theory for and for the class of all finite semigroups in is not.     

On the Spectrum of Degenerate Operator Equations

We study the distribution in the complex plane of the spectrum of the operator , generated by the closure in of the operation originally defined on smooth functions with values in a Hilbert space satisfying the Dirichlet conditions . Here and A is a model operator acting in . Criterial conditions on the parameter for the eigenfunctions of the operator to form a complete and minimal system as well as a Riesz basis in the Hilbert space H are given.     

Bernstein-Type Theorems and Uniqueness Theorems

Let be an entire function of finite type with respect to finite order and let be a subset of an open cone in a certain n-dimensional subspace (the smaller , the sparser ). We assume that this cone contains a ray 0} \right\}$$ " align="middle" border="0"> . It is shown that the radial indicator of at any point may be evaluated in terms of function values at points of the discrete subset . Moreover, if tends to zero fast enough as over , then this function vanishes identically. To prove these results, a special approximation technique is developed. In the last part of the paper, it is proved that, under certain conditions on and , which are close to exact conditions, the function bounded on is bounded on the ray.     

Existence of Positive Solutions for a Class of Higher Order Neutral Functional Differential Equations

The higher order neutral functional differential equation

Sharp Conditions for the CLT of Linear Processes in a Hilbert Space

In this paper we study the behavior of sums of a linear process associated to a strictly stationary sequence with values in a real separable Hilbert space and are linear operators from H to H. One of the results is that satisfies the CLT provided are i.i.d. centered having finite second moments and . We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables under minimal conditions.     

Imprimitive Q-polynomial Association Schemes

It is well known that imprimitive P-polynomial association schemes with are either bipartite or antipodal, i.e., intersection numbers satisfy either for all for all . In this paper, we show that imprimitive -polynomial association schemes with are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either .     

K-Theory for the Banach Algebra of Operators on James's Quasi-reflexive Banach Spaces

We prove that the K-groups of the Banach algebra of bounded, linear operators on the pth James space , where 1 < p < , are given by and . Moreover, for each Banach space and each non-zero, closed ideal contained in the ideal of inessential operators, we show that and . This enables us to calculate the K-groups of for each Banach space which is a direct sum of finitely many James spaces and -spaces.     

Hypersurfaces in ℝn and critical points in their external region

In this paper we study the hypersurfaces given as connected compact regular fibers of a differentiable map , in the cases in which has finitely many nondegenerate critical points in the unbounded component of .     

The type set for some measures on \mathbb{R}^{2n} with n-dimensional support

Let be realhomogeneous functions in ofdegree and let bethe Borel measure on given by