Characterization of Besov-Triebel-Lizorkin spaces via approximation by Whittaker's cardinal series and related unconditional Schauder bases

Let

On boundary values of solutions of the dirichlet problem for second order elliptic equation

The paper suggests some conditions on the lower order terms, which provide that the solution of the Dirichlet problem for the general elliptic equation of the second order

Alternating Sign Matrices and Some Deformations of Weyl's Denominator Formulas

An alternating sign matrix is a square matrix whose entries are 1, 0, or –1, and which satisfies certain conditions. Permutation matrices are alternating sign matrices. In this paper, we use the (generalized) Littlewood's formulas to expand the products and 2 as sums indexed by sets of alternating sign matrices invariant under a 180° rotation. If we put t = 1, these expansion formulas reduce to the Weyl's denominator formulas for the root systems of type B _n and C _n. A similar deformation of the denominator formula for type D _n is also given.     

Some boundary-value problems for linear multidimensional second-order hyperbolic equations

For the linear hyperbolic equations

Finding numerical solution of linear partial differential equations of first order with real coefficients

Applying Bittner's operational calculus we present a method to give approximate solutions of linear partial differential equations of first order

On the uniqueness of a solution to the second initial boundary-value problem for the equation of non-newtonian polytropic filtration

The uniqueness of a nonnegative solution of the second initial boundary-value problem for the equation

AnL p Semigroup Approach to Degenerate Parabolic Boundary Value Problems

The Crandall-Liggett theorem is applied to

Singular solutions of a transmission problem in plane linear elasticity for wedge-shaped regions

In plane elasticity, when two different wedge-shaped elastic materials (isotropic, homogeneous) are bonded together along a common edge and subject to tractions on the boundary, the stress field will become infinite at the apex. In fact, asymptotically, the displacementu satisfies

Almost sure invariance principles when EX 1 2 =∞

Summary Let {Y _i} be iid with EY ₁=0, EY ₁ ² =1. Let {X_i} be iid normal mean zero, variance one random variables. According to Strassen's first almost sure invariance principle {X _i} and {Y _i} can be reconstructed on a new probability space without changing the distribution of each sequence such that a.s., thus improving on the trivial bound obtainable from the law of the iterated logarithm: a.s. In this work we establish analogous improvements for symmetric {Y _i} in the domain of normal attraction to a symmetric stable law with index 0<<2. (We make this assumption of symmetry in order to avoid messy details concerning centering constants.) Let {X _i} be iid symmetric stable random variables with index 0<<2. Then, for example, hypotheses are stated which imply for a given satisfying 2> that a.s., thus improving on the trivial bound: a.s., >0.This research was supported in part by a National Science Foundation grant, USA     

Volume Formulas in Lp-Spaces

We extend classical volume formulas for ellipsoids and zonoids to p-sums of segments $${vol}\left( {\sum\limits_{i=1}^m { \oplus_p } [ -x_i ,x_i ]} \right)^{1/n} \sim_{c_p} n^{ - \frac{1}{{p'}}} \left( {\sum\limits_{card(I) = n} {|\det (x_i)_i |^p}} \right)^{\frac{1}{{pn}}}$$ where x1,...,xm are m vectors in $\mathbb{R}^n ,\frac{1}{p} + \frac{1}{{p\prime }} = 1$ . According to the definition of Firey, the Minkowski p-sum of segments is given by $$\sum\limits_{i = 1}^m { \oplus _p [ - x_{i,} x_i ]} = \left\{ {\sum\limits_{i = 1}^m {\alpha _i } x_i \left| {\left( {\sum\limits_{i = 1}^m {|\alpha _i |^{p^\prime } } } \right)} \right.^{\frac{1}{{p^\prime }}} \leqslant 1} \right\}.$$ We describe related geometric properties of the Lewis maps associated to classical operator norms.     

An Elementary Approach to an Eigenvalue Estimate for Matrices

A celebrated result of Johnson, Maurey, König and Retherford from 1977 states that for every complex matrix satisfies the following eigenvalue estimate:

Laplace approximations for sums of independent random vectors

Summary LetX _i,iN, be i.i.d.B-valued random variables whereB is a real separable Banach space, and a mappingB R. Under some conditions an asymptotic evaluation of is possible, up to a factor (1+o(1)). This also leads to a limit theorem for the appropriately normalized sums under the law transformed by the density exp .     

Construction of a solution of a mixed problem for the generalized heat conduction equation by the fourier method

By the Fourier method a solution of the equation

The Law of the Iterated Logarithm for Functionals of Harris Recurrent Markov Chains: Self Normalization

Let {X _n } _n0 be a Harris recurrent Markov chain with state space E, transition probability P(x, A) and invariant measure , and let f be a real measurable function on E. We prove that with probability one,

Onextensions of the Gale-Berlekamp switching problem and constants ofl q —spaces

For positive integersn, m and realp≥1, let Upper and lower bounds for this quantity are derived, extending results of Brown and Spencer forB ₁(n,n), corresponding to the Gale-Berlekamp switching problem. For a Minkowski spaceM of dimensionm, define a quantity investigated by Dvoretzky and Rogers.     

Uniform convergence of sums of order statistics to stable laws

Let X ₁, X ₂,... denote an i.i.d. sequence of real valued random variables which ly in the domain of attraction of a stable law Q with index 0<1. under=" a=" von=" mises=" condition=" we=" show=" that=" the=" sum=" of=" order=" statistics=">

Solvability of the Dirichlet problem for degenerate quasilinear elliptic equations

In a bounded domain of the n -dimensional (n?2) space one considers a class of degenerate quasilinear elliptic equations, whose model is the equation $$\sum\limits_{i = 1}^n {\frac{{\partial F}}{{\partial x_i }}} (a^{\ell _i } (u)\left| {u_{x_i } } \right|^{m_i - 2} u_{x_i } ) = f(x),$$ where x =(x₁,..., x_r), l_i?0, m_i>1, the function f is summable with some power, the nonnegative continuous function a(u) vanishes at a finite number of points and satisfies \(\frac{{lim}}{{\left| u \right| \to \infty }}a(u) > 0\) . One proves the existence of bounded generalized solutions with a finite integral $$\int\limits_\Omega {\sum\limits_{i = 1}^n {a^{\ell _i } (u)\left| {u_{x_i } } \right|^{m_i } dx} }$$ of the Dirichlet problem with zero boundary conditions.     

Averaging and fluctuations for parabolic equations with rapidly oscillating random coefficients

In this paper we consider the parabolic equation with random coefficients:

On the characterization of quasiarithmetic means with weight function

In the present note we completely solve the characterization problem of quasiarithmetic means with weight function, that is, functions of the form $$M(x_1 ,...,x_n ) = f^{ - 1} \left( {\sum\limits_{i = 1}^n {p(x_i )} f(x_i )/\sum\limits_{i = 1}^n {p(x_i )} } \right)$$ (f is a strictly monotonic continuous real function andp is a positive valued real function.) The result obtained gives a partial answer to a 22-year-old problem of Aczél [1] and generalizes the characterization theorem of quasiarithmetic means which is due to Kolmogorov [8], Nagumo [9] and de Finetti [7].     

Analysis of uniform binary subdivision schemes for curve design

The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form