Nonlocal vertex algebras generated by formal vertex operators

This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundations for this study. For any vector space W, we study what we call quasi compatible subsets of Hom (W,W((x))) and we prove that any maximal quasi compatible subspace has a natural nonlocal (namely noncommutative) vertex algebra structure with W as a natural faithful quasi module in a certain sense, and that any quasi compatible subset generates a nonlocal vertex algebra with W as a quasi module. In particular, taking W to be a highest weight module for a quantum affine algebra we obtain a nonlocal vertex algebra with W as a quasi module. We also formulate and study a notion of quantum vertex algebra and we give general constructions of nonlocal vertex algebras, quantum vertex algebras and their modules.     

Uniform non-amenability of free Burnside groups

The aim of this paper is to show that free Burnside groups of sufficiently large odd exponent are non-amenable in a certain strong sense. More precisely their left regular representations are isolated from the trivial representation uniformly on finite generating sets. It follows that free Burnside groups are of uniform exponential growth. This answers a question of de la Harpe. This work has been partially supported by the NSF grant DMS-0605093 and by the RFBR Grant # 05-01-00892. Received: 25 April 2006     

STABILITY NUMBER IN SUBCLASSES OF P5-FREE GRAPHS

Two new hereditary classes of P5-free graphs where the stability number can be found in polynomial time are proposed. They generalize several known results.     

On the 2-rainbow domination in graphs

The concept of 2-rainbow domination of a graph G coincides with the ordinary domination of the prism G□K₂. In this paper, we show that the problem of deciding if a graph has a 2-rainbow dominating function of a given weight is NP-complete even when restricted to bipartite graphs or chordal graphs. Exact values of 2-rainbow domination numbers of several classes of graphs are found, and it is shown that for the generalized Petersen graphs GP(n,k) this number is between ⌈4n/5⌉ and n with both bounds being sharp.     

Assessing performance factors in the UK banking sector: A multicriteria methodology

Further consolidation takes place not only among UK banks but also across borders, since some banks see size as a key factor in remaining competitive in international markets. Therefore, it is interesting to investigate the effectiveness and performance of UK banks. Based on their assets, banks are distinguished into small and large ones and a classification of UK banks in a multivariate environment for the period 1998–2002 takes place. The PAIRCLAS multicriteria methodology is employed to investigate the performance of UK small and large banks over multiple criteria, such as asset quality, capital adequacy, liquidity and efficiency/profitability. A comparison with discriminant analysis (DA) and logistic regression (LR) facilitates the investigation of the relative performance of PAIRCLAS against them. The results of the study determine the key factors that specify the classification of a bank as small or large and provide us with the responsible banking decision makers for future readjustments.     

有机/无机杂化复合木材的制备与性能

将硅溶胶/聚丙烯酸酯,有机/无机杂化液浸注于I-69杨木材中,制成有机/无机杂化木材。FT-IR红外光谱、扫描电子显微镜分析了复合木材的微观结构和组成,结果表明,经有机/无机杂化改性后的复合木材,既保持了木材本来的性质,又具有机/无机复合物的某些特性,其力学强度和尺寸稳定性较素材显著提高。     

Multifractal detrended fluctuation analysis of derivative and spot markets

We investigate the multifractal properties of price increments in the cases of derivative and spot markets. Through the multifractal detrended fluctuation analysis, we estimate the generalized Hurst and the Renyi exponents for price fluctuations. By deriving the singularity spectrum from the above exponents, we quantify the multifractality of a financial time series and compare the multifractal properties of two different markets. The different behavior of each agent-group in transactions is also discussed. In order to identify the nature of the underlying multifractality, we apply the method of surrogate data to both sets of financial data. It is shown that multifractality due to a fat-tailed distribution is significant.     

On pre-Λ-Sets and pre-v-Sets

We introduce the notions of a pre-69m7w4uy5v0b/xxlarge923.gif" alt="Lambda" align="BASELINE" BORDER="0">-set and a pre-V-set in a topological space. We study the fundamental properties of pre-69m7w4uy5v0b/xxlarge923.gif" alt="Lambda" align="BASELINE" BORDER="0">-sets and pre-V-sets and investigate the topologies defined by these families of sets.     

The distribution of patterns of inverses modulo a prime

We investigate the distribution of the numbers x∈[1,p] for which all lie in a subset of the set of multiplicative inverses modulo a prime p. Here the a_i are integers coprime to p and the numbers are distinct .