银行对抗住房抵押贷款提前还贷的合同设计

本文首先分析了贷款人采用每月等本金还款方式下,贷款人提前还贷行为发生时银行的损失.在这样的背景下设计了银行通过收取违约金对抗住房抵押贷款提前还贷行为的合同,并且给出了违约金收取方案的数学模型.     

提前还贷及其隐含期权的分析

可提前还款的定期贷款是隐含着期权的利率衍生物，本文建立CIR利率模型下可提前还款的定期贷款的数学模型，通过离散偏微分方程，建立了模型的计算方法，讨论了随机利率对提前还贷的影响．     

供应商的相关违约对供应链的收益影响分析

本文研究包含一个零售商和两个供应商的供应链模型。首先分析了零售商的支付方式问题,得出当供应商适当的选择交货付款价格和提前支付价格时,零售商采取提前支付或交货付款的预期收益相同;其次,违约事件比较少的情况下,供应商的违约概率很大程度上取决于供应商违约的相关系数,且随着供应商违约相关性从高度正相关到高度负相关变化时,零售商的收益逐渐减小,供应商收益逐渐增加,整个供应链的收益逐渐增加。     

最大期望收益与最小期望损失决策一致性条件

本首先建立了条件收益值与条件损失值之间的关系，其次在理想期望概念的基础上建立了期望收益与期望损失之间的关系。然后给出了依据最大期望收益准则与最小期望损失准则决策一致性条件。     

RFID对供应链提前期压缩的影响及协调研究

提前期压缩是基于时间竞争的供应链管理的核心,是供应链竞争优势的有力来源。RFID技术通过提高供应链中信息共享、加速物流操作,进而缩短提前期。在市场需求预测精度随提前期变化的假设下,研究由生产商和零售商组成的两阶段供应链中,生产商承担压缩成本采用RFID技术压缩提前期对供应链及其成员收益的影响。确定了可使供应链收益提高的标签成本约束条件,并提出了相应的收益协调机制。研究结果表明:供应链成员的收益随服务水平和标签成本变化而变化,通过引入收益协调机制,可以实现供应链成员收益的Pareto改进。最后通过数值算例对结论进行了验证。     

基于收益损失的装配式建筑经济补偿研究

装配式建筑的发展已经步入了崭新的时代,但在发展过程中依然面临着成本偏高的挑战,而目前的经济补偿研究大多是针对的增量成本,忽略了在市场竞争中更加重要的收益损失因素.以收益损失的视角,通过对两方开发者博弈分析,了解其收益损失的来源以及形成机理;利用C-D生产函数建立收益损失的测算模型,获得收益损失补偿基数;建立"政府-开发者"装配式建筑收益损失分摊模型,并对装配式建筑的综合效益进行量化分析,计算出双方的分摊系数,最后提出基于收益损失的装配式建筑分摊的经济补偿措施,为相关政策的制定提供参考.     

按揭支付的单调性分析

考虑了基于随机提前偿付的按揭支付的期望收入或损失的分析模型,模型具有和提前偿付的概率分布无关的一些单调特性,揭示了潜在的异于传统的按揭风险控制思路,可以支持新颖支付模式的研发,并构成按揭风险治理的有力补充.     

二级供应链中提前期压缩的价格协调机制

提前期压缩是形成供应链战略优势的有利来源.在市场需求预测精度随提前期变化的情况下,采用逻辑证明和数值分析的方法,研究由供应商-零售商构成的两阶段供应链中由供应商承担压缩成本的提前期压缩对供应链及其成员收益的影响,并提出了相应的供应链价格协调机制.结果表明:提前期压缩对供应链成员收益的影响随服务水平和压缩成本不同而不同,通过引入价格协调机制,可以实现供应链成员收益的Pareto改进.最后通过数值算例对结论进行了验证.     

基于存货质押的库存管理研究

针对基于存货质押的库存管理问题进行分析并构建模型,从还贷和不还贷两个角度,研究模型的最佳订货批量和质押量.模型以利润函数为目标函数,利润函数包括了销售额、缺货损失、剩余品价值、产品成本以及贷款本息和.通过对利润函数进行求解,得出最佳订购批量、存货质押量和最大期望利润,最后根据利润的大小决定是否偿还贷款.     

考虑属性关联的C-TODIM决策方法

针对属性具有关联性的多属性决策问题,考虑到决策者具有参照依赖和损失规避行为,提出一种新的C-TODIM决策方法。依据经典TODIM决策方法,考虑决策者的参照依赖行为,计算每个方案相对于其它各个方案关于各属性的收益或损失值;再考虑到决策者的损失规避行为,集成属性关联情形下方案关于所有属性的收益或损失值,得到每个方案相对于其它各个方案的个体感知优势度;在此基础上,计算每个方案的总体感知优势度,并依据总体感知优势度的大小对方案进行排序。最后通过一个风险投资的算例验证该方法的可行性和有效性。     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².