Representability of Analytic Functions in Terms of Their Boundary Values

Suppose that is an arbitrary finite complex Borel measure on the interval is its Poisson integral, and are the conjugate harmonics of , and is the nontangential limiting value of the analytic function as . In this paper, we consider the problem of representing the analytic function in terms of its boundary values .     

Two Splittings of a Square Matrix

In this note it is shown that any square matrix AC ^n×n can be represented as the sum A= , where is complex symmetric and rank . The corresponding persymmetric result can be used in finding the terms of a small rank perturbed Toeplitz matrix via an O(n ²) computation. This allows one to perform fast matrix–vector products in case n is large.     

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.     

Extremal Decomposition Problems in the Space of Riemann Surfaces

An extension of a theorem on extremal decomposition of a Riemann surface is obtained. The problem of extremal decomposition is extended from the case of a Riemann surface with a prescribed set of distinguished points to the case of the Teichmüller space corresponding to under quasiconformal homeomorphisms f. For the functional of our problem on extremal decomposition of a surface , we consider a function expressing the dependence of the extremal value of on a point . Differentiation formulas for the function are derived. These formulas are different and depend on the genus g of the surface . The case where the function is pluriharmonic is considered. Bibliography: 8 titles.     

Second-Order Subexponential Behavior of Subordinated Sequences

Suppose that , , and are three discrete probability distributions related by the equation (E): , where denotes the k-fold convolution of In this paper, we investigate the relation between the asymptotic behaviors of and . It turns out that, for wide classes of sequences and , relation (E) implies that , where is the mean of . The main object of this paper is to discuss the rate of convergence in this result. In our main results, we obtain O-estimates and exact asymptotic estimates for the difference .     

The First-Order Nonholonomic Connections with the Galilean Groups of Local Transformations

In the canonical smooth fiber bundles : ^{n+1 n} endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups and construct -invariant generalizations of differentiable connections. In both regular and special cases of the representations of the relevant groups , we found all the affine nonholonomic ₁-, ₂-, and _{1, 2}-connections of the first order (see [4]) possessing the local Lie groups of transformations and also described the respective -invariant planar connections.     

On Some Rings of Arithmetical Functions

In this paper, we consider several constructions which from a given B-product * _B lead to another one We shall be interested in finding what algebraic properties of the ring are shared also by the ring . In particular, for some constructions the rings R _B and will be isomorphic and therefore have the same algebraic properties.     

A New Critical Behavior for Nonlinear Wave Equations

We study the inhomogeneous semilinear wave equations on with initial values and ,where is a noncompact, complete manifold. We founda new critical behavior in the following sense. There exists ap* > 0. When 1 < p p*, the above problem hasno global solution for any nonnegative not identicallyzero and for any and ; when the problem has a global solution for some and some and . If , which is equipped with the Euclideanmetric, then . If we show that belongs to the blow upcase. Although homogeneous semilinear wave equations are known to exhibit acritical behavior for a long time, this seems to be the first result oninhomogeneous ones.     

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 .     

Strong topologies on vector-valued function spaces

Let be a real Banach space and let E be an ideal of L ⁰ over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function , defined by , belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.     

Curves on Quasi-Schemes

This paper concerns curves on noncommutative schemes, hereafter called quasi-schemes. Aquasi-scheme X is identified with the category ofquasi-coherent sheaves on it. Let X be a quasi-scheme having a regularly embeddedhypersurface Y. Let C be a curve on X which is in good position withrespect to Y (see Definition 5.1) – this definition includes a requirement that Xbe far from commutative in a certain sense. Then C is isomorphic to , where n is the number of points of intersection of Cwith Y. Here , or rather , is the quotient category -graded modules over the commutative polynomial ring, modulo the subcategory ofmodules having Krull dimension n – 2. This is a hereditary category whichbehaves rather like , the category of quasi-coherentsheaves on .     

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.     

Direct Theorem about Approximation on a Family of Two Segments

Introduce the notation: , is the union of two segments [-1,1] and [-1 + ,1+ ], is a noninteger number, is the Hölder class with exponent on The following result announced by the authors in [J. Math. Sci. 117 (2003), No. 3] is proved. There exist numbers a ₁ ( ) , b ₁ ( ) 0 depending only on such that for any there exists a polynomial , such that . Bibliography: 11 titles.     

On the Additive D-Stability of Matrices on the Basis of the Kharitonov Criterion

On the basis of the Kharitonov theorem, sufficient conditions on an matrix A are presented for the matrix to be stable for arbitrary , .     

The Fourier Formula for Discontinuous Functions of Several Variables

An analog of the classical Fourier formula for the characteristic function of a convex compact set is considered:

Strong Positivity in Right-Invariant Order on Braid Groups and Quasipositivity

Dehornoy constructed a right invariant order on the braid group B _n uniquely defined by the condition 1{\text{ if }}\beta _0 ,\beta _1$$ " align="middle" border="0"> are words in . A braid is called strongly positive if 1$$ " align="middle" border="0"> for any . In the present paper it is proved that the braid is strongly positive if the word does not contain . We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity.     

Absolute Continuity of the Spectrum of a Periodic Schrödinger Operator

We prove the absolute continuity of the spectrum of the Schrödinger operator in , , with periodic (with a common period lattice ) scalar and vector potentials for which either , , or the Fourier series of the vector potential converges absolutely, , where is an elementary cell of the lattice , for , and for , and the value of is sufficiently small, where and otherwise, , and .     

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.     

Spectral-Null Codes and Null Spaces of Hadamard Submatrices

Codes of length 2 ^m over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of all have an rth order spectral null at zero frequency. Establishing the connection between and the parity-check matrix of Reed-Muller codes, the minimum distance of is obtained along with upper bounds on the redundancy of . An efficient algorithm is presented for encoding unconstrained binary sequences into .     

On Plane Maximal Curves

The number N of rational points on an algebraic curve of genus g over a finite field satisfies the Hasse–Weil bound . A curve that attains this bound is called maximal. With and , it is known that maximalcurves have . Maximal curves with have been characterized up to isomorphism. A natural genus to be studied is and for this genus there are two non-isomorphic maximal curves known when . Here, a maximal curve with genus g ₂ and a non-singular plane model is characterized as a Fermat curve of degree .