Product line selection and pricing analysis: Impact of genetic relaxations

A model for the product line selection and pricing problem (PLSP) is presented andthree solution procedures based on a genetic algorithm are developed to analyze the results based on consumer preference patterns. Since the PLSP model is nonlinear and integer, two of the solution procedures use genetic encoding to “relax” the NP hard model. The relaxations result in linear integer and shortest path models for the fitness evaluation which are solved using branch and bound and labeling algorithms, respectively. Performance of the quality of solutions generated by the procedures is evaluated for various problem sizes and customer preference structures. The results show that the genetic relaxations provide efficient and effective solution methodologies for the problem, when compared to the pure artificial intelligence technique of genetic search. The impact of the preference structure on the product line and the managerial implications of the solution characteristics generated by the genetic relaxations are also discussed. The models can be used to explicitly consider tradeoffs between marketing and operations concerns in designing a product line.     

Some insights into proportional lot sizing and scheduling

This paper deals with proportional lot sizing and scheduling (PLSP) and gives some insights into the properties of this problem. Such insights may be useful for developing heuristic and/or exact solution procedures. The emphasis of this paper is on the multi-level, multi-machine case. We provide a mixed-integer programming model, relate it to other models that can be found in the literature, and discuss characteristics which make solving instances of the PLSP-model a hard task.     

Lattices of equivalence relations closed under the operations of relation algebras

One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as lattices of equivalence relations on finite sets closed under certain first-order formulas. We generalize this question to a different collection of first-order formulas, giving examples to demonstrate that our new question is distinct. We then note that every lattice M _n can be represented in this new way.     

Flat Modules over Group Rings of Finite Groups

Let k be a commutative ring of coefficients and G be a finite group. Does there exist a flat k G-module which is projective as a k-module but not as a k G-module? We relate this question to the question of existence of a k-module which is flat and periodic but not projective. For either question to have a positive answer, it is at least necessary to have |k| ≥ ?_ω. There can be no such example if k is Noetherian of finite Krull dimension, or if k is perfect.     

钻井布局模型

本文的关键思想是找出在变化中的不变量 .对于第一小题 ,作者发现可以把所有的点“移到”一个方格中 ,而它们相对网格结点的距离不变 ,这样问题就得到了大大的简化 .对于第二题 ,本文发现坐标变换时各点之间的欧氏距离不变 ,利用各点的距离关系 ,给出一系列的判定条件 ,最后用优化算法 (充要条件 )判定 .第二题的算法对于第三题也是通用的 ,因此第三题应用第二题的方法来解决     

线代教学中如何发挥例题的作用

由同济大学编《线性代数》的一个典型例题入手,拓展到多个典型例题,引导学生步步深入,得到行列式计算的解题方法,提高学生分析问题,综合问题,解决问题的能力．     

Isoperimetric Inequalities for Soluble Groups

We approach the question of which soluble groups are automatic. We describe a class of nilpotent-by-Abelian groups which need to be studied in order to answer this question. We show that the nilpotent-by-cyclic groups in this class have exponential isoperimetric inequality and so cannot be automatic.     

Where can we really prove instances of the Paris-Harrington principle?

A fundamental question in mathematical logic asks: What are the minimal assumptions and deduction principles required to prove a particular theorem? Now consider the special case of a theorem that can be established by checking a finite number of decidable cases — think of a single instance of the finite Ramsey theorem. In this particular situation the answer to our question is trivial: The theorem can be demonstrated by an explicit verification, thus without the use of any “strong” proof principles. This answer, however, is not very satisfying: An explicit verification may be unfeasible if there is an enormous number of cases to check. At the same time there might be a short and meaningful proof using stronger proof methods. Such a situation suggests a modified question: What are the minimal assumptions and deduction principles required for a reasonably short proof of the given theorem? Our contribution explores this question for instances of the Paris-Harrington principle. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

概率与直觉

通过“免费抽奖问题”、“生日问题”、“肇事车认定问题”一个例子说明:在求某个事件的概率时,如果不经过认真分析,常常会被直觉误导。并分析了导致错觉的原因是错误地选择了样本空间,进而说明正确选择样本空间的重要性。     

A compact HL-space need not have a monolithic hyperspace

We show that Kunen's example of a compact L-space, constructed under CH, can be modified so that it has a non-monolithic hyperspace. This answers a question of Bell's. This example is also relevant to a question of Arhangel'skii's.

     

On a question of Zariski on Zariski surfaces

We give a new method to construct unirational surfaces which may be applied to the following question posed by Zariski in his studies on unirational surfaces. Is any Zariski surface with geometric genus zero rational? Our main result is a negative answer to this question in any characteristic case.     

Radical Ideals of Dedekind Domains and their Extensions

The question of whether or not an ideal of a ring can be a radical is studied, and a characterisation of the ideals which can be radical is obtained for Dedekind domains and their polynomial and matrix rings. Some partial results on this question are given for other extension rings of Dedekind domains.     

An elementary proof of Schmüdgen's theorem on the moment problem of closed semi-algebraic sets

We prove the main result from Schmüdgen's 2003 article in a more elementary way. The result states that the question of whether a finitely generated preordering has the so-called strong moment property can be reduced to the same question for preorderings corresponding to fiber sets of bounded polynomials.

     

Coverings over Tori and topological approach to Klein’s resolvent problem

This paper answers the question: what coverings over a topological torus can be induced from a covering over a space of dimension k? The answer to this question is then applied in algebro-geometric context to present obstructions to transforming an algebraic equation depending on several parameters to an equation depending on fewer parameters by means of a rational transformation.     

Criteria for testing Wall’s question

In this paper we find certain equivalent formulations of Wall’s question and derive two interesting criteria that can be used to resolve this question for particular primes.     

On the complexity of sequentially lifting cover inequalities for the knapsack polytope

The well-known sequentially lifted cover inequality is widely employed in solving mixed integer programs.However,it is still an open question whether a sequentially lifted cover inequality can be computed in polynomial time for a given minimal cover(Gu et al.(1999)).We show that this problem is N P-hard,thus giving a negative answer to the question.     

Rigid actions of amenable groups

Given a countable discrete amenable group G, does there exist a free action of G on a Lebesgue probability space which is both rigid and weakly mixing? The answer to this question is positive if G is abelian. An affirmative answer is given in this paper, in the case that G is solvable or residually finite. For a locally finite group, the question is reduced to an algebraic one. It is exemplified how the algebraic question can be positively resolved for some groups, whereas for others the algebraic viewpoint suggests the answer may be negative.     

Real polynomial iterative roots in the case of nonmonotonicity height ≥ 2

It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question.     

Reduction of homomorphisms mod p and algebraicity

Let A be an abelian variety over a number field K. Let φ be an endomorphism of A(K) into itself which reduces modulo v for almost all finite places v of K. The question we discuss in this paper is whether φ arises from an endomorphism of the abelian variety A. We answer this question in the affirmative for many cases. The question is inspired by a work of C. Corrales and R. Schoof, and uses a recent work of Larsen. We also look at the analogue of this question for linear algebraic groups.