A note on the hardness of Skolem-type sequences

The purpose of this note is to give upper bounds (assuming different from ) on how far the generalizations of Skolem sequences can be taken while still hoping to resolve the existence question. We prove that the existence questions for both multi-Skolem sequences and generalized Skolem sequences are strongly -complete. These results are significant strengthenings and simplifications of the recent -completeness result for generalized multi-Skolem sequences.     

The polynomial dichotomy for three nonempty part sandwich problems

We classify into polynomial time or -complete all three nonempty part sandwich problems. This solves the polynomial dichotomy into polynomial time and -complete for this class of graph partition problems.     

Combinatorial constructions of fault-tolerant routings with levelled minimum optical indices

The design of fault-tolerant routings with levelled minimum optical indices plays an important role in the context of optical networks. However, not much is known about the existence of optimal routings with levelled minimum optical indices besides the results established by Dinitz, Ling and Stinson via the partitionable Steiner quadruple systems approach. In this paper, we introduce a new concept of a large set of even levelled -design of order v and index 2, denoted by -LELD, which is equivalent to an optimal, levelled (v−2)-fault-tolerant routing with levelled minimum optical indices of the complete network with v nodes. On the basis of the theory of three-wise balanced designs and partitionable candelabra systems, several infinite classes of -LELDs are constructed. As a consequence, the existence problem for optimal routings with levelled minimum optical indices is solved for nearly a third of the cases.     

Majorization of regular measures and weights with finite and positive critical exponent

For the sets , 1?p<∞, of positive finite Borel measures μ on the real axis with the set of algebraic polynomials P dense in Lp(R,dμ), we establish a majorization principle of their “boundaries,” i.e. for every there exists such that dμ/dν?1. A corresponding principle holds for the sets , p>0, of non-negative upper semi-continuous on R functions (weights) w such that P is dense in the space : For every there exists such that w?ω.     

Descriptive properties of families of autohomeomorphisms of the unit interval

Let H⊂C[0,1] stand for the Polish space of all increasing autohomeomorphisms of [0,1]. We show that the family of all strictly singular autohomeomorphisms is -complete. This confirms a suggestion of Graf, Mauldin and Williams. Some related results are also included.     

Continuity and Schatten-von Neumann p-class membership of Hankel operators with anti-holomorphic symbols on (generalized) Fock spaces

In this paper we investigate Hankel operators with anti-holomorphic symbols ∈L²(C,m|z|), where are general Fock spaces. We will show that is not continuous if the corresponding symbol is not a polynomial . For polynomial symbols we will give necessary and sufficient conditions for continuity and compactness in terms of N and m. For monomials we will give a complete characterization of the Schatten-von Neumann p-class membership for p>0. Namely in case 2k<m the Hankel operators are in the Schatten-von Neumann p-class iff p>2m/(m−2k); and in case 2k?m they are not in the Schatten-von Neumann p-class.     

On the commutator of the Marcinkiewicz integral

boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the and the boundedness for the commutator of the Marcinkiewicz integral are obtained.     

On multicolour noncomplete Ramsey graphs of star graphs

Given graphs , where k≥2, the notation

     

Remarks on the formula for γ-interior

The paper presents a formula for the γ-interior of a set under special conditions for , more general than those in the previous paper [Acta Math. Hungar. 80 (1998) 89-93]. There are also some applications.     

Well-posedness and regularity of generalized Navier-Stokes equations in some critical Q-spaces

We study the well-posedness and regularity of the generalized Navier-Stokes equations with initial data in a new critical space , , which is larger than some known critical homogeneous Besov spaces. Here is a space defined as the set of all measurable functions with

     

Multiple solutions for elliptic problems with asymmetric nonlinearity

In this paper we establish the existence of multiple solutions for the semilinear elliptic problem

     

Weighted estimates for a class of multilinear fractional type operators

In this paper, a class of multiple fractional type weights is defined as

     

A new construction of vertex algebras and quasi-modules for vertex algebras

In this paper, a new construction of vertex algebras from more general vertex operators is given and a notion of quasimodule for vertex algebras is introduced and studied. More specifically, a notion of quasilocal subset(space) of for any vector space W is introduced and studied, generalizing the notion of usual locality in the most possible way, and it is proved that on any maximal quasilocal subspace there exists a natural vertex algebra structure and that any quasilocal subset of generates a vertex algebra. Furthermore, it is proved that W is a quasimodule for each of the vertex algebras generated by quasilocal subsets of . A notion of Γ-vertex algebra is also introduced and studied, where Γ is a subgroup of the multiplicative group C^× of nonzero complex numbers. It is proved that any maximal quasilocal subspace of is naturally a Γ-vertex algebra and that any quasilocal subset of generates a Γ-vertex algebra. It is also proved that a Γ-vertex algebra exactly amounts to a vertex algebra equipped with a Γ-module structure which satisfies a certain compatibility condition. Finally, two families of examples are given, involving twisted affine Lie algebras and certain quantum torus Lie algebras.     

Generalized Navier-Stokes equations with initial data in local Q-type spaces

In this paper, we establish a link between Leray mollified solutions of the three-dimensional generalized Navier-Stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of . This result applies to the usual incompressible Navier-Stokes equations.     

A note on exact complex travelling wave solutions for (2+1)-dimensional B-type Kadomtsev-Petviashvili equation

The -expansion method can be used for constructing exact travelling wave solutions of real nonlinear evolution equations. In this paper, we improve the -expansion method and explore new application of this method to (2+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation. New types of exact complex travelling wave solutions of (2+1)-dimensional BKP equation are found. Some exact solutions of (2+1)-dimensional BKP equation obtained before are special cases of our results in this paper.     

Derivations as square roots of Dirichlet forms

The aim of this work is to analyze the structure of a tracially symmetric Dirichlet form on a -algebra, in terms of a killing weight and a closable derivation taking values in a Hilbert space with a bimodule structure. It is shown that the generator of the associate Markovian semigroup always appears, in a natural way, as the divergence of a closable derivation. Applications are shown to the decomposition of Dirichlet forms and to the construction of differential calculus on metric spaces.     

Two new transformation formulas of basic hypergeometric series

By means of a modified version of Cauchy's method for obtaining bilateral series identities, two new transformation formulas for bilateral basic hypergeometric series are derived. These contain several important identities for basic hypergeometric series as special cases, including the nonterminating q-Saalschütz summation, Bailey's very well-poised summation and the nonterminating Watson transformation.