Concentration phenomena in weakly coupled elliptic systems with critical growth*

In this paper we consider the weakly coupled elliptic system with critical growth

A short proof for the sum formula and its generalization

For positive integers with a _r  = 2, the multiple zeta value or r-fold Euler sum is defined as [2]

Random k-Sat: A Tight Threshold For Moderately Growing k

We consider a random instance I of k-SAT with n variables and m clauses, where k=k(n) satisfies k—log₂ n. Let m ₀=2 ^k nln2 and let =(n)>0 be such that n. We prove that

Strictly Cyclic Algebra of Operators Acting on Banach Spaces H p(β)

Let be a sequence of positive numbers and 1 p< . We consider the space H ^p() of all power series such that . We investigate strict cyclicity of the weakly closed algebra generated by the operator of multiplication by zacting on H ^p(), and determine the maximal ideal space, the dual space and the reflexivity of the algebra . We also give a necessary condition for a composition operator to be bounded on H ^p() when is strictly cyclic.     

A Littlewood-Paley type inequality

In this note we prove the following theorem: Let u be a harmonic function in the unit ball and . Then there is a constant C = C(p, n) such that

Bounds on leaves of one-dimensional foliations

Let X be a variety over an algebraically closed field, a onedimensional singular foliation, and a projective leaf of . We prove that

Interpolation by Rational Functions with Nodes on the Unit Circle

From the Erds–Turán theorem, it is known that if f is a continuous function on and L _n (f, z) denotes the unique Laurent polynomial interpolating f at the (2 n + 1)th roots of unity, then Several years later, Walsh and Sharma produced similar result but taking into consideration a function analytic in and continuous on and making use of algebraic interpolating polynomials in the roots of unity.In this paper, the above results will be generalized in two directions. On the one hand, more general rational functions than polynomials or Laurent polynomials will be used as interpolants and, on the other hand, the interpolation points will be zeros of certain para-orthogonal functions with respect to a given measure on .     

On the riemann zeta-function and the divisor problem II

Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If E ^*(t)=E(t)-2πΔ^*(t/2π) with , then we obtain

Multiple positive solutions for a quasilinear system of Schrödinger equations

We consider the quasilinear system

A note on <Emphasis Type="Italic">q</Emphasis>-multiplicative functions

We prove the following statement. Let , and let . Suppose that, for all and , the sequence satisfies the relation

An Application of U(g)-bimodules to Representation Theory of Affine Lie Algebras

Let be the affine Lie algebra associated to the simple finite-dimensional Lie algebra . We consider the tensor product of the loop -module associated to the irreducible finite-dimensional -module V() and the irreducible highest weight -module L _k,. Then L _k, can be viewed as an irreducible module for the vertex operator algebra M _k,0. Let A(L _k,) be the corresponding -bimodule. We prove that if the -module is zero, then the -module is irreducible. As an example, we apply this result on integrable representations for affine Lie algebras.     

Inertial Iterative Process for Fixed Points of Certain Quasi-nonexpansive Mappings

This paper deals with a general formalism which consists in approximating a point in a nonempty set , in a real Hilbert space , by a sequence such that , where , are in and is a sequence included in a certain class of self-mappings on , such that every fixed point set of contains . This iteration method is inspired by an implicit discretization of the second order ‘heavy ball with friction’ dynamical system. Under suitable conditions on the parameters and the operators , we prove that this scheme generates a sequence which converges weakly to an element of . In particular, by appropriate choices of , this algorithm works for approximating common fixed points of infinite countable families of a wide class of operators which includes -averaged quasi-nonexpansive mappings for .      

Approximating periodic functions by interpolation sums of Jackson type

Let

Approximating periodic functions in the uniform metric by Jackson type polynomials

Let C be the space of continuous 2π-periodic functions f with the norm . Let , where , be the Jackson polynomials of a function f, E _n (f) be the best approximation of f in the space C by trigonometric polynomials of order n, and let , be the function trigonometrically conjugate to the primitive of f. The paper establishes results of the following types:

Efficient Estimation in a Semiparametric Autoregressive Model

This paper constructs efficient estimates of the parameter in the semiparametric auto-regression model ,with a smooth function and independent and identically distributed innovations _t with zero means and finite variances. This will be done under the assumptions that and that the errors have a density with finite Fisher information for location. The former condition guarantees that the process can be chosen to be stationary and ergodic.     

Three-dimensional sets with small sumset

We describe the structure of three dimensional sets of lattice points, having a small doubling property. Let be a finite subset of ℤ³ such that dim = 3. If and , then lies on three parallel lines. Moreover, for every three dimensional finite set that lies on three parallel lines, if , then is contained in three arithmetic progressions with the same common difference, having together no more than terms. These best possible results confirm a recent conjecture of Freiman and cannot be sharpened by reducing the quantity υ or by increasing the upper bounds for .     

Convex Embeddings and Bisections of 3-Connected Graphs1

Given two disjoint subsets T ₁ and T ₂ of nodes in an undirected 3-connected graph G = (V, E) with node set V and arc set E, where and are even numbers, we show that V can be partitioned into two sets V ₁ and V ₂ such that the graphs induced by V ₁ and V ₂ are both connected and holds for each j = 1,2. Such a partition can be found in time. Our proof relies on geometric arguments. We define a new type of convex embedding of k-connected graphs into real space R ^k-1 and prove that for k = 3 such an embedding always exists. ¹ A preliminary version of this paper with title Bisecting Two Subsets in 3-Connected Graphs appeared in the Proceedings of the 10th Annual International Symposium on Algorithms and Computation, ISAAC 99, (A. Aggarwal, C. P. Rangan, eds.), Springer LNCS 1741, 425&ndash;434, 1999.     

Solutions to nonlinear Neumann problems with an inverse square potential

Let Ω be an open bounded domain in with smooth boundary . We are concerned with the critical Neumann problem

Hilbert Space Representations of Cross Product Algebras II

In this paper, we study and classify Hilbert space representations of cross product -algebras of the quantized enveloping algebra with the coordinate algebras of the quantum motion group and of the complex plane, and of the quantized enveloping algebra with the coordinate algebras of the quantum group and of the quantum disc. Invariant positive functionals and the corresponding Heisenberg representations are explicitly described.Presented by S.L. Woronowicz.