Constructing orthogonal pandiagonal Latin squares and panmagic squares from modular n‐queens solutions

In this article, we show how to construct pairs of orthogonal pandiagonal Latin squares and panmagic squares from certain types of modular n‐queens solutions. We prove that when these modular n‐queens solutions are symmetric, the panmagic squares thus constructed will be associative, where for an n × n associative magic square A = (a_ij), for all i and j it holds that a_ij + an?i?1,n?j?1 = c for a fixed c. We further show how to construct orthogonal Latin squares whose modular difference diagonals are Latin from any modular n‐queens solution. As well, we analyze constructing orthogonal pandiagonal Latin squares from particular classes of non‐linear modular n‐queens solutions. These pandiagonal Latin squares are not row cyclic, giving a partial solution to a problem of Hedayat. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 221–234, 2007     

Latin squares with bounded size of row prefix intersections

A latin square is a matrix of size n×n with entries from the set {1,…,n}, such that each row and each column is a permutation on {1,…,n}. We show how to construct a latin square such that for any two distinct rows, the prefixes of length h of the two rows share at most about h²/n elements. This upper bound is close to optimal when contrasted with a lower bound derived from the Second Johnson bound [6].     

A partial plane of order 6 constructed from the icosahedron

We show that a maximal partial plane of order 6 with 31 lines and a maximal pure partial plane of order 6 with 25 lines can be constructed from the icosahedron and the Petersen graph. To Daniel R. Hughes, to commemorate his 80th birthday, August 7th, 2007.     

Spectral rigidity of group actions: Applications to the case gr

We apply a technique to study the notion of spectral rigidity of group actions to a group gr. As an application, we prove that there exist rank one weakly mixing transformations conjugate to its square, thereby giving a positive answer to a well-known question.

     

On the analysis of optimization problems in arc-dependent networks

This paper is concerned with the design and analysis of algorithms for optimization problems in arc-dependent networks. A network is said to be arc-dependent if the cost of an arc $a$ depends upon the arc taken to enter $a$. These networks are fundamentally different from traditional networks in which the cost associated with an arc is a fixed constant and part of the input. We first study the arc-dependent shortest path (ADSP) problem, which is also known as the suffix-1 path-dependent shortest path problem in the literature. This problem has a polynomial time solution if the shortest paths are not required to be simple. The ADSP problem finds applications in a number of domains, including highway engineering, turn penalties and prohibitions, and fare rebates. In this paper, we are interested in the ADSP problem when restricted to simple paths. We call this restricted version the simple arc-dependent shortest path (SADSP) problem. We show that the SADSP problem is NP-complete. We present inapproximability results and an exact exponential algorithm for this problem. We also extend our results for the longest path problem in arc-dependent networks. Additionally, we explore the problem of detecting negative cycles in arc-dependent networks and discuss its computational complexity. Our results include variants of the negative cycle detection problem such as longest, shortest, heaviest, and lightest negative simple cycles.²     

Research problems from the Aveiro Workshop on Graph Spectra

This is a collection of open problems presented at the Aveiro Workshop on Graph Spectra held at the University of Aveiro, Portugal from April 10-12, 2006.     

Variational problems on multiply connected thin strips III: Integration of the Ginzburg-Landau equations over graphs

We analyze the one-dimensional Ginzburg-Landau functional of superconductivity on a planar graph. In the Euler-Lagrange equations, the equation for the phase can be integrated, provided that the order parameter does not vanish at the vertices; in this case, the minimization of the Ginzburg-Landau functional is equivalent to the minimization of another functional, whose unknowns are a real-valued function on the graph and a finite set of integers.

     

Unfair allocation of gains under the Equal Price allocation method in purchasing groups

Certain purchasing groups do not flourish. A supposed reason for this is a creeping dissatisfaction among various members of a group with the allocation of the cooperative gains. In this paper, we analyze unfairness resulting from using the commonly used Equal Price (EP) method for allocating gains under the assumption of continuous quantity discounts. We demonstrate that this unfairness is caused by neglecting a particular component of the added value of individual group members. Next, we develop two fairness ratios and tie these to fairness properties from cooperative game theory. The ratios show among other things that being too-big a player in a purchasing group can lead to decreasing gains. They can be used to assess if EP is an unfair method in specific situations. Finally, we discuss measures a purchasing group could consider in order to attenuate perceived unfairness. Thereby, the group may improve its stability and prosperity.     

On the weighting method for mixed least squares–total least squares problems

It is well known that the standard algorithm for the mixed least squares–total least squares (MTLS) problem uses the QR factorization to reduce the original problem into a standard total least squares problem with smaller size, which can be solved based on the singular value decomposition (SVD). In this paper, the MTLS problem is proven to be closely related to a weighted total least squares problem with its error‐free columns multiplied by a large weighting factor. A criterion for choosing the weighting factor is given; and for the sake of stability in solving the MTLS problem, the Cholesky factorization‐based inverse (Cho‐INV) iteration and Rayleigh quotient iteration are also considered. For large‐scale MTLS problems, numerical tests show that Cho‐INV is superior to the standard QR‐SVD method, especially for the case with big gap between the desired and undesired singular values and the case when the coefficient matrix has much more error‐contaminated columns. Rayleigh quotient iteration behaves more efficient than QR‐SVD for most cases and fails occasionally, and in some cases, it converges much faster than Cho‐INV but still less efficient due to its higher computation cost.     

不确定环境下的投标方报价模型研究

在传统投标报价模型的基础上引入风险因子,提出报价要在收益与风险之间进行权衡.放宽了所有投标方的最高成本与最低成本是相同的这一前提假设,并借助Mathematica 5.0推导出投标方的报价模型.最后利用仿真对上述关系进行了分析.     

On sampling theory associated with the resolvents of singular Sturm-Liouville problems

This paper is concerned with the sampling theory associated with resolvents of eigenvalue problems. We introduce sampling representations for integral transforms whose kernels are Green's functions of singular Sturm-Liouville problems provided that the singular points are in the limit-circle situation, extending the results obtained in the regular problems.

     

前景理论视角下专利代理服务模式优化研究

专利代理服务是知识产权服务体系中的重要组成,利用预期收益分配契约激励专利代理服务参与者,引导双方采取共赢的行为策略,是提高合作效率、提升专利代理服务效果的重要方向。在考虑决策者有限理性的基础上,提出一种专利代理服务预期收益分配方案,引入前景理论衡量心理因素对专利代理服务参与主体的影响,建立收益感知矩阵,构建演化博弈模型,刻画更贴近现实的认知决策过程,进而探讨技术发明人与专利代理机构之间的博弈关系和稳定策略,最后通过数值仿真揭示影响稳定策略的关键变量。结果表明:这种预期收益分配方案具有可行性,区别设置预期收益分配模式的违约处罚水平以及减小预期收益分成比重是避免违约、维持长期稳定合作的最佳途径。     

Sufficient conditions for the existence of multipliers and Lagrangian duality in abstract optimization problems

We consider the following optimization problem: in an abstract setX, find and elementx that minimizes a real functionf subject to the constraintsg(x)0 andh(x)=0, whereg andh are functions fromX into normed vector spaces. Assumptions concerning an overall convex structure for the problem in the image space, the existence of interior points in certain sets, and the normality of the constraints are formulated. A theorem of the alternative is proved for systems of equalities and inequalities, and an intrinsic multiplier rule and a Lagrangian saddle-point theorem (strong duality theorem) are obtained as consequences.     

On the robustness of least squares procedures in regression models

The criterion robustness of the standard likelihood ratio test (LRT) under the multivariate normal regression model and also the inference robustness of the same test under the univariate set up are established for certain nonnormal distributions of errors. Restricting attention to the normal distribution of errors in the context of univariate regression models, conditions on the design matrix are established under which the usual LRT of a linear hypothesis (under homoscedasticity of errors) remains valid if the errors have an intraclass covariance structure. The conditions hold in the case of some standard designs. The relevance of C. R. Rao's (1967 In Proceedings Fifth Berkeley Symposium on Math. Stat. and Prob., Vol. 1, pp. 355–372) and G. Zyskind's (1967, Ann. Math. Statist.38 1092–1110) conditions in this context is discussed.     

A partial adjustment valuation approach with stochastic and dynamic speeds of partial adjustment to measuring and evaluating the business value of information technology

This paper extends previous studies to develop a partial adjustment valuation (PAV) approach in which the speeds of partial adjustment are assumed to be stochastic and dynamic over time in measuring and evaluating the values of information technology and others (e.g., e-commerce or EC, brand name, etc.). A practical application is presented to demonstrate the application of the proposed PAV approach and it is compared to the other two existing PAV approaches.     

基于多任务委托—代理理论的高校教师激励机制研究

对高校教师的激励是高等教育中一个非常重要的环节,对高校教师合理的激励机制设计是提高高等教育水平的制度保证.从教师激励工作中高校管理者作为委托人与高校教师作为代理人二者信息不对称的角度出发,运用博弈论与委托代理理论,将高校教师工作进行教学努力和科研努力的划分,运用多任务委托代理理论对教师激励机制进行研究,建立模型进行分析,并结合西安科技大学现实提出合理化建议,以求达到既提高教学质量又提高科研产出水平的目的.     

A class of one-dimensional geometric variational problems with energy involving the curvature and its derivatives: a geometric measure-theoretic approach

The notions of Legendrian and Gaussian towers are defined and investigated. Then applications in the context of one-dimensional geometric variational problems with the energy involving the curvature and its derivatives are provided. Particular attention is paid to the case when the functional is defined on smooth boundaries of plane sets.