Estimates of the dilatation function of Beurling-Ahlfors extension

In this paper we estimate the dilatation function of the Beurling-Ahlfors extension in the most general case. By introducing ?h,m-function, we obtain an inequality which is sharp up to a constant.     

An improved randomized approximation algorithm for maximum triangle packing

This paper deals with the maximum triangle packing problem. For this problem, Hassin and Rubinstein gave a randomized polynomial-time approximation algorithm that achieves an expected ratio of for any constant ?>0. By modifying their algorithm, we obtain a new randomized polynomial-time approximation algorithm for the problem which achieves an expected ratio of 0.5257(1−?) for any constant ?>0.     

Identities for the Widder transform and transforms with Bessel function kernels

In the present paper, we consider the classical Widder transform, the H_ν-transform, the K_ν-transform, and the Y_ν-transform. Some identities involving these transforms and many others are given. By making use of these identities, a number of new Parseval-Goldstein type identities are obtained for these and other well-known integral transforms.     

Sample-based polynomial approximation of rational Bézier curves

We present an iteration method for the polynomial approximation of rational Bézier curves. Starting with an initial Bézier curve, we adjust its control points gradually by the scheme of weighted progressive iteration approximations. The L_p-error calculated by the trapezoidal rule using sampled points is used to guide the iteration approximation. We reduce the L_p-error by a predefined factor at every iteration so as to obtain the best approximation with a minimum error. Numerical examples demonstrate the fast convergence of our method and indicate that results obtained using the L₁-error criterion are better than those obtained using the L₂-error and L_∞-error criteria.     

A short note on the overpartition function

In this brief note, we give a combinatorial proof of a variation of Gauss’s q-binomial theorem, and we determine arithmetic properties of the overpartition function modulo 8.     

Remark on uniqueness of mild solutions to the Navier-Stokes equations

We investigate a limiting uniqueness criterion to the Navier-Stokes equations. We prove that the mild solution is unique under the class , where bmo^-1 is the “critical” space including Lⁿ. As an application of uniqueness theorem, we also consider the local well-posedness of Navier-Stokes equations in bmo^-1.     

Hardness of lazy packing and covering

We prove APX-hardness for the two problems maximum resource bin packing and lazy bin covering. Simple algorithms matching the best absolute bounds under the assumption P≠NP are also derived.     

On the approximation of spectra of linear operators on Hilbert spaces

We present several new techniques for approximating spectra of linear operators (not necessarily bounded) on an infinite-dimensional, separable Hilbert space. Our approach is to take well-known techniques from finite-dimensional matrix analysis and show how they can be generalized to an infinite-dimensional setting to provide approximations of spectra of elements in a large class of operators. We conclude by proposing a solution to the general problem of approximating the spectrum of an arbitrary bounded operator by introducing the n-pseudospectrum and argue how that can be used as an approximation to the spectrum.     

Colorings of k-balanced matrices and integer decomposition property of related polyhedra

We show that a class of polyhedra, arising from certain 0,1 matrices introduced by Truemper and Chandrasekaran, has the integer decomposition property. This is accomplished by proving certain coloring properties of these matrices.     

A note on the rank parity function

We provide some further theorems on the partitions generated by the rank parity function. New Bailey pairs are established, which are of independent interest.     

Convergence of a stochastic particle approximation for fractional scalar conservation laws

We are interested in a probabilistic approximation of the solution to scalar conservation laws with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation is based on a stochastic differential equation driven by an α-stable Lévy process and involving a nonlinear drift. The approximation is constructed using a system of particles following a time-discretized version of this stochastic differential equation, with nonlinearity replaced by interaction. We prove convergence of the particle approximation to the solution of the conservation law as the number of particles tends to infinity whereas the discretization step tends to 0 in some precise asymptotics.     

Absolutely convergent Fourier series and function classes

We study the smoothness property of a function f with absolutely convergent Fourier series, and give best possible sufficient conditions in terms of its Fourier coefficients to ensure that f belongs either to one of the Lipschitz classes Lip(α) and lip(α) for some 0<α?1, or to one of the Zygmund classes Λ_∗(1) and λ_∗(1). Our theorems generalize some of those by Boas [R.P. Boas Jr., Fourier series with positive coefficients, J. Math. Anal. Appl. 17 (1967) 463-483] and one by Németh [J. Németh, Fourier series with positive coefficients and generalized Lipschitz classes, Acta Sci. Math. (Szeged) 54 (1990) 291-304]. We also prove a localized version of a theorem by Paley [R.E.A.C. Paley, On Fourier series with positive coefficients, J. London Math. Soc. 7 (1932) 205-208] on the existence and continuity of the derivative of f.     

Twisted first homology groups of the automorphism group of a free group

The automorphism group and outer automorphism group of a free group F_n of rank n act on the abelianized group H of F_n and the dual group H^* of H. The twisted first homology groups of and with coefficients in H and H^* are calculated.     

On the 3-restricted edge connectivity of permutation graphs

An edge cut W of a connected graph G is a k-restricted edge cut if G−W is disconnected, and every component of G−W has at least k vertices. The k-restricted edge connectivity is defined as the minimum cardinality over all k-restricted edge cuts. A permutation graph is obtained by taking two disjoint copies of a graph and adding a perfect matching between the two copies. The k-restricted edge connectivity of a permutation graph is upper bounded by the so-called minimum k-edge degree. In this paper some sufficient conditions guaranteeing optimal k-restricted edge connectivity and super k-restricted edge connectivity for permutation graphs are presented for k=2,3.     

Waiting times in queues with relative priorities

This paper determines the mean waiting times for a single server multi-class queueing model with Poisson arrivals and relative priorities. If the server becomes idle, the probability that the next job is from class-i is proportional to the product between the number of class-i jobs present and their priority parameter.     

An extension of the Vu-Sine theorem and compact-supercyclicity

If (Tt)_t?0 is a bounded C₀-semigroup in a Banach space X and there exists a compact subset K⊆X such that

     

Zeros of orthogonal Laurent polynomials and solutions of strong Stieltjes moment problems

The strong Stieltjes moment problem for a bisequence consists of finding positive measures μ with support in [0,∞) such that

     

Conservation laws for some compacton equations using the multiplier approach

This paper is an application of the variational derivative method to the derivation of the conservation laws for partial differential equations. The conservation laws for (1+1) dimensional compacton k(2,2) and compacton k(3,3) equations are studied via multiplier approach. Also the conservation laws for (2+1) dimensional compacton Zk(2,2) equation are established by first computing the multipliers.     

Convergence of SSOR methods for linear complementarity problems

In this paper, by applying the SSOR splitting, we propose two new iterative methods for solving the linear complementarity problem LCP (M,q). Convergence results for these two methods are presented when M is an H-matrix (and also an M-matrix). Finally, two numerical examples are given to show the efficiency of the presented methods.