A Lower Bound on the Greedy Weights of Product Codes

A greedy 1-subcode is a one-dimensional subcode of minimum (support) weight. A greedy r-subcode is an r-dimensional subcode with minimum support weight under the constraint that it contain a greedy (r - 1)-subcode. The r-th greedy weight e _r is the support weight of a greedy r-subcode. The greedy weights are related to the weight hierarchy. We use recent results on the weight hierarchy of product codes to develop a lower bound on the greedy weights of product codes.     

关于Euler数一个猜想的证明

研究Euler数的猜想:对于任何素数p≡1 mod4,E(p-1)／20 mod p．根据Euler数本身的性质和Fourier级数对于Gauss和的应用,证明了这个猜想是成立的．     

Integrable structure of the field theory of open superstrings

We find asymptotic expansions in the “string mass” μ for μ-deformed Γ-functions and Neumann coefficients characterizing the three-string vertex in the light-cone gauge of the field theory of open superstrings on a maximally supersymmetric pp-wave background. Dedicated to the 80th birthday of Academician Anatolii Alekseevich Logunov __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 381–385, December, 2006.     

完全单半群上同余的两种刻画

给出了完全单半群的相容组和同余结的定义,并利用它们刻画了完全单半群上的同余.     

From Lie algebra crossed modules to tensor hierarchies

The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity rely on a pairing – the embedding tensor – between a Leibniz algebra and a Lie algebra. Two such algebras, together with their embedding tensor, form a triple called a Lie-Leibniz triple, of which Lie algebra crossed modules are particular cases. This paper is devoted to showing that any Lie-Leibniz triple induces a differential graded Lie algebra – its associated tensor hierarchy – whose restriction to the category of Lie algebra crossed modules is the canonical assignment associating to any Lie algebra crossed module its corresponding unique 2-term differential graded Lie algebra. This shows that Lie-Leibniz triples form natural generalizations of Lie algebra crossed modules and that their associated tensor hierarchies can be considered as some kind of ‘lie-ization’ of the former. We deem the present construction of such tensor hierarchies clearer and more straightforward than previous derivations. We stress that such a construction suggests the existence of further well-defined Leibniz gauge theories.     

“禁摩限电”效果综合评价模型

将交通需求级别进行划分后,通过数据包络分析法计算交通需求匹配度和交通运行效率,近乎绝对细化交通运行表现,依据具有时间轴的四维交通状况模拟建立了全新多维度的交通评价体系。此外,利用模糊层次分析法确定道路交通安全评价指标体系中各个指标的权重,同时作出基于差异驱动原理的综合评价。最后,将交通的污染指标提炼为机动车的排放指标和电动车的耗电指标来衡量交通工具对环境的影响。     

模糊AHP在电网企业员工岗前培训评估中的应用

电网企业技术密集、人员众多、架构庞大,员工岗前培训与企业健康持续发展密不可分.培训工作中最突出的问题在于对培训效果缺乏合理的评估,从而无法了解企业投资的效果,以及培训对组织的贡献.以柯氏培训四级评估模型为基础,采用模糊AHP规范化整个评估过程.最后以电力企业进行的培训项目为例验证分析,证明所提算法的有效性.     

On a difference equation of the second order with an exponential coefficient

This paper is devoted to a generalization of some previous results, as we completely solve a linear homogeneous difference equation of the second order with an exponential coefficient.     

Fuzzy logic modifications of the Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is a measurement methodology based on pair-wise comparisons that relies on judgment to derive priority scales. During its implementation, one constructs hierarchies, then makes judgments or performs measurements on pairs of elements with respect to a criterion to derive preference scales, which are then synthesized throughout the structure to select the preferred alternative.One of the areas where the AHP finds application is in the subjective phases of risk assessment (RA), where it is used to structure and prioritize diverse risk factors, including the judgments of experts. Since fuzzy logic (FL) has been shown to be an effective tool for accommodating human experts and their communication of linguistic variables, there has been research aimed at modeling the fuzziness in the AHP (FAHP), and recently the focus of some of that modeling has been with respect to RA.The literature discusses more than one FAHP model, which raises the question as to which are the prominent models and what are their characteristics. In response to this question, we examine three of the most influential FAHP models. The article proceeds as follows. It begins with a brief overview of the AHP and its limitations when confronted with a fuzzy environment. This is followed by a discussion of FL modifications of the AHP. A RA-based likelihood score example is used throughout. The article ends with a commentary on the findings.     

Recursion relations for the constrained multi-component KP hierarchy

In this paper, we define a new constrained multi-component KP(cMKP) hierarchy which contains the constrained KP(cKP) hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.