Essential pure monomorphisms of sheaves of group actions

Nowadays purity plays a role in at least four branches of mathematics: Module Theory, Theory of Acts over semigroups, Model Theory, and Category Theory. Adámek and Rosciky have studied these notions categorically, and Rothmaler model-theoretically. Some authors including Banaschewski, Gould, and Normak have studied purity on G-acts, acts over a monoid or a group G.     

Short proofs for two theorems of Chien,Hell and Zhu

In (J Graph Theory 33 (2000), 14–24), Hell and Zhu proved that if a series–parallel graph G has girth at least 2?(3k?1)/2?, then χ_c(G)≤4k/(2k?1). In (J Graph Theory 33 (2000), 185–198), Chien and Zhu proved that the girth condition given in (J Graph Theory 33 (2000), 14–24) is sharp. Short proofs of both results are given in this note. © 2010 Wiley Periodicals, Inc. J Graph 66: 83‐88, 2010 Theory     

GDDP: Generalized Dual Dynamic Programming Theory

This document presents theoretical considerations about the solution of dynamic optimization problems integrating the Benders Theory, the Dynamic Programming approach and the concepts of Control Theory. The so called Generalized Dual Dynamic Programming Theory (GDDP) can be considered as an extension of two previous approaches known as Dual Dynamic Programming (DDP): The first is the work developed by Pereira and Pinto [3–5], which was revised by Velásquez and others [8,9]. The second is the work developed by Read and others [2,6,7].     

On the list decodability of rank-metric codes containing Gabidulin codes

Designs, Codes and Cryptography - Wachter-Zeh (IEEE Trans Inf Theory 59(11):7268–7276, 2013), and later together with Raviv (IEEE Trans Inf Theory 62(4):1605–1615, 2016), proved that...     

A Note on the Optimal Convergence Rate of Descent Methods with Fixed Step Sizes for Smooth Strongly Convex Functions

Journal of Optimization Theory and Applications - Based on a result by Taylor et al. (J Optim Theory Appl 178(2):455–476, 2018) on the attainable convergence rate of gradient descent for...     

纳税信誉等级评定模型

首先构建了用于评价分析的递阶层次系统 ,然后介绍模糊决策理论及灰色系统理论在数据处理方面的应用 ,最后用两种不同的方法对模拟数据进行了分析 ,得到了企业的综合评分 .     

Hilbert series of invariants, constant terms and Kostka-Foulkes polynomials

A problem that arose in the study of the mass of the neutrino led us to the evaluation of a constant term with a variety of ramifications into several areas from Invariant Theory, Representation Theory, the Theory of Symmetric Functions and Combinatorics. A significant by-product of our evaluation is the construction of a trigraded Cohen Macaulay basis for the Invariants under an action of SL_n(C) on a space of 2n+n² variables.     

A General Fredholm Theory II: Implicit Function Theorems

This is the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. In general, these spaces are not locally homeomorphic to open sets in Banach spaces. The current paper develops the Fredholm theory in M-polyfold bundles. It consists of a transversality and a perturbation theory. In upcoming papers the generalized Fredholm theory will be applied to the Floer Theory, the Gromov–Witten Theory and the Symplectic Field Theory H.H.’s research partially supported by NSF grant DMS-0603957. K.W.’s research partially supported by NSF grant DMS-0606588.     

基于Copula和极值理论的在险价值度量

针对传统孤立使用GJR模型、极值理论、Copula理论进行风险分析的不足,把GJR模型、极值理论和Copula理论有机的结合起来,给出了基于Copula和极值理论的投资组合VaR的测度方法.首先利用GJR模型刻画单个资产收益率中的自相关和异方差现象,获得近似独立同分布的新息序列,再分别应用高斯核估计的方法、极值理论拟合新息序列的分布函数的内部和两尾,利用Copula函数有效捕抓了市场之间的波动溢出效应,最后使用Monte Carlo模拟法,计算出投资组合的VaR值.实证结果表明,基于Copula和极值理论的VaR度量方法比历史模拟法更有效.     

Existence and Uniqueness for Some 3rd Order Dissipative Problems with Various Boundary Conditions

We briefly present new results on the existence and uniqueness of solutions u of a large class of initial-boundary-value problems characterized by a quasi-linear third order equation on a finite space interval with Dirichlet, Neumann or pseudoperiodic boundary conditions. The class includes equations arising in Superconductor Theory and in the Theory of Viscoelastic Materials.     

Amalgamating players,symmetry, and the Banzhaf value

We suggest new characterizations of the Banzhaf value without the symmetry axiom, which reveal that the characterizations by Lehrer (Int J Game Theory 17:89–99, 1988) and Nowak (Int J Game Theory 26:137–141, 1997) as well as most of the characterizations by Casajus (Theory Decis 71:365–372, 2011b) are redundant. Further, we explore symmetry implications of Lehrer’s 2-efficiency axiom.     

Construction of cyclotomic codebooks nearly meeting the Welch bound

Ding and Feng (IEEE Trans Inform Theory 52(9):4229–4235, 2006, IEEE Trans Inform Theory 53(11):4245–4250, 2007) constructed series of (N, K) codebooks which meet or nearly meet the Welch bound \({\sqrt{\frac{N-K}{(N-1)K}}}\) by using difference set (DS) or almost difference set (ADS) in certain finite abelian group respectively. In this paper, we generalize the cyclotomic constructions considered in (IEEE Trans Inform Theory 52(9):4229–4235, 2006, IEEE Trans Inform Theory 53(11):4245–4250, 2007) and (IEEE Trans Inform Theory 52(5), 2052–2061, 2006) to present more series of codebooks which nearly meet the Welch bound under looser conditions than ones required by DS and ADS.     

Book Reviews

Book reviewed in this article: Managing Toxic Wastes Michael Kronewetter Exploring Number Theory with Microcomputers Invitation to Number Theory with Pascal Donald D. Spencer Living in a Risky World Laurence Pringle Our World series Temperate Forests by Basil Booth Pollution & Conservation by Malcolm Penny     

Nombres de coloration de l'hypergrapheh-parti complet

Summary The chromatic index, the transversal number, the clique number, etc., have all been extensively studied in Graph Theory, and can be easily extended to Hypergraphs. The author determines these coefficients for the complete multipartite hypergraphs, which g,neralize the complete bipartite graphs, and appear also in the Theory of Designs.

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Entrata in Redazione il 16 maggio 1973.     

On the paths Hölder continuity in models of Euclidean quantum field theory

Sample paths properties of certain stochastic processes connected to models of Euclidean Quantum Field Theory are studied. In particular, the Hölder continuity of paths of the coordinate processes and trace processes is proven. The results are obtained by an application of classical probabilistic criteria together with basic estimates proven in Constructive Quantum Field Theory.     

Comments on purification in continuum games

It is pointed out that Corollary 1 in a recent paper by Khan et al. (Int J Game Theory 34:91–104, 2006), presented there as an extension of the Dvoretzky–Wald–Wolfowitz theorem, is a special case of Lyapunov’s theorem for Young measures (Balder in Rend Instit Mat Univ Trieste 31 Suppl. 1:1–69) It is also pointed out that Theorems 1–4 in Khan et al. (Int J Game Theory 34:91–104, 2006) follow from a single strong purification per se result that is already contained, as an implementation of that Lyapunov theorem for Young measures, in the proof of Theorem 2.2.1 in Balder (J Econ Theory 102:437–470, 2002).     

On the cyclomatic number of a hypergraph

This note generalizes the notion of cyclomatic number (or cycle rank) from Graph Theory to Hypergraph Theory and links it up with the concept of planarity in hypergraphs which was recently introduced by R.P. Jones. Sharp bounds are obtained for the cyclomatic number of the planar hypergraphs and, further, it is shown that the upper bound is attainable if, and only if the hypergraph satisfies Krewera's condition.     

Extending Greene's theorem to directed graphs

The purpose of this note is to prove a theorem on acyclic digraphs, conjectured by Linial (J. Combin. Theory Ser. A, 30 (1981), 331–334), which includes Greene's theorem (J. Combin. Theory Ser. A, 20 (1976), 69–79) on decompositions of a partially ordered set into antichains.     

The Euler–Lagrange theory for Schur's Algorithm: Algebraic exposed points

In this paper the ideas of Algebraic Number Theory are applied to the Theory of Orthogonal polynomials for algebraic measures. The transferring tool are Wall continued fractions. It is shown that any set of closed arcs on the circle supports a quadratic measure and that any algebraic measure is either a Szegö measure or a measure supported by a proper subset of the unit circle consisting of a finite number of closed arcs. Singular parts of algebraic measures are finite sums of point masses.