On regular rings and annihilators

Let F_n stand for the distribution of a normalized sum of n independent random variables with common distribution H. In [6] we assumed the restricted convergence. and obtain an analogous result. The method of proof is considerably different, in particular a very recent continuation theorem (lemma 3.2) for infinitely divisible distributions is needed.     

Existence and stability of stationary profiles of the lw scheme

In this paper we study the behavior of difference schemes approximating solutions with shocks of scalar conservation laws When a difference scheme introduces artificial numerical diffusion, for example the Lax-Friedrichs scheme, we experience smearing of the shocks, whereas when a scheme introduces numerical dispersion, for example the Lax-Wendroff scheme, we experience oscillations which decay exponentially fast on both sides of the shock. In his dissertation. Gray Jennings studied approximation by monotone schemes. These contain artificial viscosity and are first-order accurate; they are known to be contractive in the sense of any l^p norm. Jennings showed existence and l¹ stability of traveling discrete smeared shocks for such schemes. Here we study similar questions for the Lax-Wendroff scheme without artificial viscosity; this is a nonmonotone, second-order accurate scheme. We prove existence of a one-parameter family of stationary profiles. We also prove stability of these profiles for small perturbations in the sense of a suitably weighted l² norm. The proof relies on studying the linearized Lax-Wendroff scheme.     

Constructions of covering triangulations with folds

Let G be a graph with a known triangular embedding in a surface S, and consider G_(m), the composition of G with an independant set of order m. The purpose of this paper is to construct a triangular embedding of G_(m) into a surface by using a covering triangulation with folds. We make the construction for three cases. One of them is used for proving that G_(m) can be triangularly embedded into a surface if G is an Eulerian graph which can be triangularly embedded into a surface S with the same orientability characteristic as .     

Growth of a PSL2R Manifold Group

The purpose of this paper is to present characterizations of the inhomogeneous Hardy-Bessel potential spaces F^p_α (K) over the 2-series field K defined by Littlewood-Paley type function, where Δ₀(x) = 1(|x|≥1), = 0(other), Δ_j(x) = 2^j ≥, = 0(other) (j ≥ 1). These characterizations are given by difference of functions, ball means of difference and atoms. As applications of these results we shall determine when F^p_α(K) is a multiplication algebra, and prove the lower majorant property, the uniform localization property and the equivalence of Fourier multipliers.     

Numerical solution of a time-like Cauchy problem for the wave equation

Let D ? ?ⁿ be a bounded domain with piecewise-smooth boundary, and q(x,t) a smooth function on D × [0, T]. Consider the time-like Cauchy problem Given g, h for which the equation has a solution, we show how to approximate u(x,t) by solving a well posed fourth-order elliptic partial differential equation (PDE). We use the method of quasi-reversibility to construct the approximating PDE. We derive error estimates and present numerical results.     

Gevrey Asymptotic Representation of the Solutions of Equations with One Turning Point

An ordinary differential equation of the type with parameterξ ? IRⁿ and smooth coefficients a_j,a ? C^∞([-T,T]) is studied. It is assumed that all the characteristic roots of the equation vanish at t = 0 while for t ≠ 0 they are real and distinct. The constructions of real-valued phase functions ?pH_kl (k,l = 1., m) and of amplitude functions A_jkl such that for a given s ? [-T, T] every solution u(t, ξ) of the equation can be represented as where Ψ_j(s, ξ)= D^j_tu(s,ξ), j = 0,m-1 are given.     

The eigenvalues and eigenfunctions of a spherically symmetric anharmonic oscillator

We show that the operator H_s has a complete set of eigenfunctions and eigenvalues , which satisfy [2l(l + 1) - (3n² + 3n + 1)]s + o(s) and lim_s→0 = 0. The functions are given in spherical coordinates as a product of generalized Laguerre functions and spherical harmonics.     

A power law for connectedness of some random graphs at the critical point

We consider P(G is connected) when G is a graph with vertex set Z⁺ = {1,2, …}, and the edge between i and j is present with probability p(i, j) = min(λ h(i, j), 1) for certain functions h(i, j) homogeneous of degree -1. It is known that there is a critical value λ_c of λ such that . We show that the probability, at the critical point λ_c, that n₁, and n₂ are connected satisfies a power law, in the sense that for n₂ ≧ n_t ≧ 1 for any δ > 0 and certain constants c₁ and c₂.     

A semi-discrete convergent scheme for a quasilinear hyperbolic equation

We establish here the convergence (thereby proving the existence) of a semi-discrete scheme for the quasilinear hyperbolic equation where x ∈ Rⁿ, t ∈ [0,T], and ? ∈ L^∞ (Rⁿ). It is well known that the above problem does not necessarily have global classical solutions and the usual concepts of weak solution. do not lead to a unique solution The existence of a unique solution to the above problem in a suitable sense was established in [3], where a parabolic problem obtained by introducing the term ??Δu was studied and then the behavior as ? → 0 was discussed. A difference scheme approach to a problem of the above type where ?_i does not depend on x and t and Ψ does not depend on u was also studied in [2]. The aim of this paper is to present a proof for the case when ? depends on x, Ψ depends on u, and the technical complications in this case are nontrivial. The discussions in this paper my be considered as continuation of the ideas in the above papers.     

Half-Linear Eigenvalue Problems

We consider the eigenvalue problem for t ? [0, b], where aⁿ = |a|ⁿ sgna, a ? ?, λ ? ?, the constants μ, v are real such that 0 ≤ μ < n and derive asymptotic estimates for solutions of the differential equation in the definite case q(t)> 0 which corresponds to the well-known WKB-approximation in the linear case n = 1, μ = 0. In the second part we investigate the asymptotic distribution of the eigenvalues in the general case of two -point boundary conditions and refine these results for the so called separated boundary conditions.     

Weighted (LF)-spaces of Continuous Functions

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Analysis of the thermoelastic model of a plate with non-linear shape memory alloy reinforcements

In this paper we study the questions of the existence and uniqueness of the solutions for a thermoelastic system of equations in a two-dimensional domain, where both the viscosity v and the rigidity D are positive. It seems that such a system has up to now been considered in a one-dimensional setting only. The change of dimensions enforces the growth conditions with respect to θ and the additional regularity of the data. The existence of solutions in the case of the Neumann boundary conditions for θ and some weak regularity of data is proved. Under stronger regularity conditions the uniqueness is also established. The system has an interpretation as a plate reinforced by a shape memory alloy (SMA) wire mesh.     

Spectral Decomposition of Symmetric Operator Matrices

The authors study symmetric operator matrices in the product of Hilbert spaces H = H₁×H₂, where the entries are not necessarily bounded operators. Under suitable assumptions the closure L_o exists and is a selfadjoint operator in H. With L_o, the closure of the transfer function is considered. Under the assumption that there exists a real number β < inf p(A) such that M(β)<< 0, it follows that β ε p(L_o). Applying a factorization result of A.I. Virozub and V.I. Matsaev [VM] to the holomorphic operator function M(λ, the_spectral subspaces of L_o corresponding to the intervals ] — ∞, β] and [β, ∞[ and the restrictions of L_o to these subspaces are characterized. Similar results are proved for operator matrices which are symmetric in a Krein space.     

The variance of a partial match retrieval in a multidimensional symmetric trie

Let N records be stored in an M-dimensional trie (M-d trie). It is shown that under the symmetric Bernoulli model the variance of the cost C_N^ω of a partial match retrieval is with continuous periodic function τ_ω, where u is the number of unspecified components in a query ω of size M. This confirms in quantitative manner a conjecture by Kirschenhofer, Prodinger, and Szpankowski [Int. J. Found. Comput. Sci., 4 , 69–84 (1993)], who presented a detailed analysis of Var C_N^ω in the M = 2, u = 1-case, but used in their proof a transformation formula of Ramanujan, which does not seem to have an analogue for M > 2. Our analysis is based on exponential approximations and Mellin inversion.     

Spatially localized free vibrations for a non-linear string model

We prove the existence of infinitely many non-zero time-periodic solutions (breathers) to the dispersive wave equation of the form which are localized in the spatial variable, that is The main tool employed is the concentration compactness principle of P. L. Lions.     

On critical exponents for some quasilinear parabolic equations

We study the Cauchy problem for the quasilinear parabolic equation where p > 1 is a parameter and ψ is a smooth, bounded function on (1, ∞) with ? ? sψ′(s)/ψ(s) ? θ for some θ > 0. If 1 < p < 1 + 2/N, there are no global positive solutions, whereas if p > 1 + 2/N, there are global, positive solutions for small initial data.     

Maximum Bandwidth Under Edge Addition

We determine how much the bandwidth B(G) of a graph G can increase when a single edge is added. Let g(b,n) be the maximum possible value of B(G + e) when G has n vertices and bandwidth b. The problem of studying when B(G + e) ≦ B (G) + 1 was originally possed by Erdos. We determine © 1996 John Wiley & Sons, Inc.     

Generalized herglotz domains

Let F(θ k, α) be the far field pattern arising from the scattering of a time harmonic plane acoustic wave of wave number k and direction a by a sound-soft cylinder of cross section D. Suppose F has the Fourier expansion where a_n = a_n(k, . Then if ?² is a Dirichlet eigenvalue for D, sufficient conditions are given on D for the existence of a nontrivial sequence |b_n| where the b_n are independent of such that for all directions Domains for which this is true are called generalized Herglotz domains. The conditions for a domain to be a generalized Herglotz domain are given either in terms of the Schwarz function for the analytic boundary ?D or in terms of the Rayleigh hypothesis in acoustic scattering theory and examples are given showing the applicability of these conditions.     

On a free boundary problem in electrostatics

Let Ω_i ? ?^N, i = 0, 1, be two bounded separately star-shaped domains such that $ \Omega _0 \supset \bar \Omega _1 $. We consider the electrostatic potential u defined in $ \Omega : = \Omega _0 \backslash \bar \Omega _1 $: The geometry of the two boundary components Γ₀ and Γ₁ is not given, but instead the electrostatic potential u is supposed to satisfy the further boundary conditions Using a best possible maximum principle, we show that this free boundary problem has a unique solution which is radially symmetric.     

Stabilization and regularization for solutions of an ill posed problem for the wave equation

In this paper we study the problem of finding u: [O, T] → D(A), D(A) ? H, H a Hibert space such that: Is a linear positive, self-adjoint operator with a compact inverse. The problem is well known to be illposed because uniqueness and existence generally fail. We restore the stability with an a priori bound on ∥ du(0)/dt ∥ for some particular values of T.