确定性需求连续生产模型下的最优保理融资策略

保理是融资机构基于供应链上下游企业之间实际发生交易而给予供应链卖方企业的一种短期融资。基于连续生产模型研究了资金约束制造商的最优保理融资策略。考虑保理时间决策对融资成本和需求损失的影响,比较了固定期保理和即时保理两种策略下制造商的利润。研究发现,固定期保理策略下的最优保理时间随着其边际利润的增加而提前,而随着保理费率上升、应收款账期延长、自有资金增加而延迟。数值研究结果发现,保理商最优保理费率随着应收账款账期延长而降低。     

The Co-Emergence of Machine Techniques, Paper-and-Pencil Techniques, and Theoretical Reflection: A Study of Cas use in Secondary School Algebra

This paper addresses the dialectical relation between theoretical thinking and technique, as they co-emerge in a combined computer algebra (CAS) and paper-and-pencil environment. The theoretical framework in this ongoing study consists of the instrumental approach to tool use and an adaptation of Chevallard’s anthropological theory. The main aim is to unravel the subtle intertwining of students’ theoretical thinking and the techniques they use in both media, within the process of instrumental genesis. Two grade 10 teaching experiments are described, the first one on equivalence, equality and equation, and the second one on generalizing and proving within factoring. Even though the two topics are quite different, findings indicate the importance of the co-emergence of theory and technique in both cases. Some further extensions of the theoretical framework are suggested, focusing on the relation between paper-and-pencil techniques and computer algebra techniques, and on the issue of language and discourse in the learning process.With the collaboration of André Boileau, Fernando Hitt, Denis Tanguay, Luis Saldanha, and José Guzmán     

Lost in Translation: Examining Translation Errors Associated With Mathematical Representations

Translation errors and conceptual misunderstandings made by students translating among graphical, tabular, and symbolic representations of linear functions were examined. The study situated student errors in the context of the “Translation‐Verification Model” developed specifically for the purpose of explaining student behavior during the process of translating relationships from one mathematical representation to another. Three distinct error types were identified to explain student performance. An examination of the error types revealed that specific translation errors tend to occur at different stages of the translation process. Translation errors are also related to “attribute density,” the amount of information inherently encoded in a given representation. The findings of the study have implications for teaching linear relationships—student weaknesses and strengths are identified.     

存在破产成本时保理授信下供应商赊销策略研究

在存在破产成本的前提下,构建了保理商确定授信额度的量化模型,并研究了供应商如何在保理授信下确定赊销量的问题。研究结果表明,保理商的授信以保理费率不低于临界值为前提。当保理费率高于一定水平时,授信额度较高,供应商将在额度内进行赊销交易。否则,供应商将超出授信额度进行赊销交易,并且此时,若固定破产成本高于阈值,供应商最优赊销量存在上限,保理对供应链的作用主要体现在其风险分担功能上;若固定破产成本低于阈值,供应商最优赊销量存在下限,保理对供应链的作用主要体现在其融资功能上。     

Factoring 111 ... 11 — A stimulating problem

The problem of factoring numbers like 111, 111, 111, 111 is a very productive one. It is beguiling, for in spite of its trivial appearance, this factoring problem leads immediately to considerations of the algebra of polynomials, ring homomorphisms, roots of unity, programming, repeating decimals, and recreational mathematics. This article shows how a pre‐calculus class can be introduced naturally to such ideas. Many of these applications are traditionally considered advanced, and will reappear in a student's curriculum.

A table of 56 factorizations is presented ; the largest is R45 =111, 111, ..., ..., 111. The article follows with an annotated list of applications of the factoring problem (focusing on 111, 111, 111, 111), which have been used successfully with pre‐calculus students. The techniques and comments are geared to the teacher of such a course.     

The black-box Niederreiter algorithm and its implementation over the binary field

The most time-consuming part of the Niederreiter algorithm for factoring univariate polynomials over finite fields is the computation of elements of the nullspace of a certain matrix. This paper describes the so-called ``black-box' Niederreiter algorithm, in which these elements are found by using a method developed by Wiedemann. The main advantages over an approach based on Gaussian elimination are that the matrix does not have to be stored in memory and that the computational complexity of this approach is lower. The black-box Niederreiter algorithm for factoring polynomials over the binary field was implemented in the C programming language, and benchmarks for factoring high-degree polynomials over this field are presented. These benchmarks include timings for both a sequential implementation and a parallel implementation running on a small cluster of workstations. In addition, the Wan algorithm, which was recently introduced, is described, and connections between (implementation aspects of) Wan's and Niederreiter's algorithm are given.

     

矩阵多项式空间的进一步研究

设A为数域F上的n级矩阵,记F[A]={f(A)|f(x)∈F[x]},它显然是F~(n×n)的子空间.讨论了F[A]的基和维数,引入了f(A)的坐标和F[A]的因式子空间的概念,给出了用因式子空间表示F[A]的几个定理,刻画了F[A]的结构.     

Factoring matrices into the product of two matrices

Linear algebra of factoring a matrix into the product of two matrices with special properties is developed. This is accomplished in terms of the so-called inverse of a matrix subspace which yields an extended notion for the invertibility of a matrix. The product of two matrix subspaces gives rise to a natural generalization of the concept of matrix subspace. Extensions of these ideas are outlined. Several examples on factoring are presented. AMS subject classification (2000)  15A23, 65F30     

A study of the difficulties experienced with mathematics by engineering students in higher education

This paper describes a study undertaken to investigate the problem of the lack of mathematical expertise demonstrated by polytechnic engineering students. The study is based on a multiple‐choice diagnostic mathematics test, designed for the purpose, which was taken by incoming engineering students over a period of five years. The test aims to identify particular areas of difficulty. These difficulties are analysed and suggestions are made regarding their cause and alleviation. It has been confirmed that there is cause for concern at the overall mathematical ability of the students and it has been possible to identify certain areas of mathematics which appear to be difficult to a large proportion of students. It has also been possible to identify some of the common errors made by students in certain topic areas. Some suggestions have been made regarding the implications for teaching.     

整系数多元多项式快速分解（1）——初始化算法

对于一般形式的整系数多元多项式Ｆ（ｘ１，ｘ２，…，ｘｔ）进行因式分解，通常总是首先选定一个变量，比如Ｘｔ，作为主变量，将下的因式分解转化为对关子Ｘｔ首１的，并使Ｆ＊（０，…，０，Ｘｔ）无重因式的多元多项式Ｆ＊进行分解．本文给出了这种转化的一个新算法．由此算法而得到的Ｆ＊之规模要明显地小于以前的方法的结果，从而使得进一步分解Ｆ＊以得到Ｆ的因式分解的计算时间复杂可以大大地降低．     

Factoring and recognition of read-once functions using cographs and normality and the readability of functions associated with partial k-trees

An approach for factoring general boolean functions was described in Golumbic and Mintz [Factoring logic functions using graph partitioning, in: Proceedings of IEEE/ACM International Conference on Computer Aided Design, November 1999, pp. 195-198] and Mintz and Golumbic [Factoring Boolean functions using graph partitioning, Discrete Appl. Math. 149 (2005) 131-153] which is based on graph partitioning algorithms. In this paper, we present a very fast algorithm for recognizing and factoring read-once functions which is needed as a dedicated factoring subroutine to handle the lower levels of that factoring process. The algorithm is based on algorithms for cograph recognition and on checking normality.For non-read-once functions, we investigate their factoring based on their corresponding graph classes. In particular, we show that if a function F is normal and its corresponding graph is a partial k-tree, then F is a read 2^k function and a read 2^k formula for F can be obtained in polynomial time.     

A factored implicit scheme for numerical weather prediction

The nonlinear partial differential equations of atmospheric dynamics govern motion on two time scales, a fast one and a slow one. Only the slow-scale motions are relevant in predicting the evolution of large weather patterns. Implicit numerical methods are therefore attractive for weather prediction, since they permit a large time step chosen to resolve only the slow motions. To develop an implicit method which is efficient for problems in more than one spatial dimension, one must approximate the problem by smaller, usually one-dimensional problems. A popular way to do so is to approximately factor the multidimensional implicit operator into one-dimensional operators. The factorization error incurred in such methods, however, is often unacceptably large for problems with multiple time scales. We propose a new factorization method for numerical weather prediction which is based on factoring separately the fast and slow parts of the implicit operator. We show analytically that the new method has small factorization error, which is comparable to other discretization errors of the overall scheme. The analysis is based on properties of the shallow water equations, a simple two-dimensional version of the fully three-dimensional equations of atmospheric dynamics.     

Factoring functions of Maurey’s factorization theorem

It is proved that the best possible factoring functions of Maurey’s factorization theorem are unique up to multiplication by constant-modular functions.     

The isomorphism problem for quantum affine spaces,homogenized quantized Weyl algebras,and quantum matrix algebras

Bell and Zhang have shown that if A and B are two connected graded algebras finitely generated in degree one that are isomorphic as ungraded algebras, then they are isomorphic as graded algebras. We exploit this result to solve the isomorphism problem in the cases of quantum affine spaces, quantum matrix algebras, and homogenized multiparameter quantized Weyl algebras. Our result involves determining the degree one normal elements, factoring out, and then repeating. This creates an iterative process that allows one to determine relationships between relative parameters.     

Language,Intellectual Structures and Common Mathematical Errors: A Call for Research

This article illustrates several typical mathematical errors made by high school and lower division college students. These illustrations are then categorized and analyzed from the points of view of mathematics, developmental psychology, and learning theory. It is concluded from the analysis that research is needed in the area and that a multifacted approach might at least result in progress toward resolving the problem of common logico-mathematical errors. The article suggests at least three theoretical bases which could support such a research-oriented approach.     

How to Choose Secret Parameters for RSA-Type Cryptosystems over Elliptic Curves

Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA-type cryptosystems over elliptic curves. The analysis is more difficult because the underlying groups are not always cyclic. Previous papers suggested the use of strong primes in order to prevent factoring attacks and cycling attacks. In this paper, we only focus on cycling attacks because for both RSA and its elliptic curve-based analogues, the length of the RSA-modulus n is typically the same. Therefore, a factoring attack will succeed with equal probability against all RSA-type cryptosystems. We also prove that cycling attacks reduce to find fixed points, and derive a factorization algorithm which (most probably) completely breaks RSA-type systems over elliptic curves if a fixed point is found.     

n次单位根在代数问题中的应用

主要论述n次单位根在一些组合数求和、多项式的整除、因式分解中的应用,说明了n次单位根法可拓宽解题思路,是一种方便、快捷的数学解题方法.     

RETRACTED ARTICLE: Blockchain-based intelligent contract for factoring business in supply chains

Factoring business, an important aspect in the supply chain finance field, has significant potential in adopting blockchain-based intelligent contract technology. Based on the existing theories of factoring business in supply chains, this paper conducts a coupling analysis between blockchain technology and supply chain factoring business. Specifically, we propose the application scenarios of blockchain-based intelligent contract technology in the supply chain factoring business from three aspects: the division and transfer of creditors’ rights certificate, the factoring financing of upstream suppliers, and the due payment of core enterprises, and elaborate their implementation processes. Furthermore, from a game theoretical perspective, we analyze the mechanism of the key technology implementation of the intelligent contract to verify whether the nodes on the blockchains will follow the relevant protocols to automatically execute them. Finally, we conduct a three-way game analysis of the supply chain factor financing process and obtain an equilibrium solution based on the principle of utility maximization, which highlights the optimization effect of the intelligent contract technology on the decision-making behavior of individual entities in the supply chain.

     

Security of meta-He digital signature scheme based on factoring and discrete logarithms

To enhance the security of signature schemes, Pon et al., recently, investigated all eight variants of the He’s digital signature scheme. The security of the proposed schemes is based on the difficulties of simultaneously solving the factoring and discrete logarithm problems with almost the same sizes of arithmetic modulus. This paper shows that the all eight variants of the He’s digital signature scheme, as well as two more variants, are not secure if attackers can solve discrete logarithm problems. Moreover, the attackers can easily forge signatures of the most optimal signature schemes of the generalized He’ signature schemes even though they can solve neither discrete logarithm problems nor factoring.     

二元整系数多项式因式分解的一种理论和算法

我们发现可以把二元多项式盾成系数为一元多项式的一元多项式来进行分解，据此，本文建立了二元整系数多项式因式分解的一种理论，提出了一个完整的分解二元整系数多项式的算法。这个算法还能很自然地推广成分解多元整系数多项式的算法。