On a double boundary layer in a nonlinear boundary value problem

The question of the isotopy of a quasiconformal mapping and its special aspects in dimension greater than 2 are considered. It is shown that an arbitrary quasiconformal mapping of a ball has an isotopy to the identity map such that the coefficient of quasiconformality (dilatation) of the mapping varies continuously and monotonically. In contrast to the planar case, in dimension higher than 2 such an isotopy is not possible in an arbitrary domain. Examples showing specific features of the multidimensional case are given. In particular, they show that even when such an isotopy exists, it is not always possible to perform an isotopy so that the coefficient of quasiconformality approaches 1 monotonically at each point in the source domain.     

Linking the individual forgetting context with customer capital from a seller's perspective

Customer capital is a result of interaction between an organization and its customers. Customers change their characteristics, including addresses, behaviour and preferences; but as the customer requirements change, basic beliefs or processes that is, things that individuals take for granted at an implicit and an explicit level of knowledge, must also change. This paper aims to identify the role of an individual forgetting context on customer capital in today's organization through an empirical study of 229 sellers (front-line contact people) in the Spanish optometry industry. Two structural equation models have been used, resulting in the conclusion that before obtaining an up-to-date memory, it is necessary to identify new ways of doing and interpreting things, which in turn result in a shift in relations that favour the customers.     

Outerplanar Thrackles

We show that a graph drawing is an outerplanar thrackle if and only if, up to an inversion in the plane, it is Reidemeister equivalent to an odd musquash. This establishes Conway’s thrackle conjecture for outerplanar thrackles. We also extend this result in two directions. First, we show that no pair of vertices of an outerplanar thrackle can be joined by an edge in such a way that the resulting graph drawing is a thrackle. Secondly, we introduce the notion of crossing rank; drawings with crossing rank 0 are generalizations of outerplanar drawings. We show that all thrackles of crossing rank 0 are outerplanar. We also introduce the notion of an alternating cycle drawing, and we show that a thrackled cycle is alternating if and only if it is outerplanar.     

Scheduling continuous casting of aluminum using a multiple objective ant colony optimization metaheuristic

This paper presents an ant colony optimization metaheuristic for the solution of an industrial scheduling problem in an aluminum casting center. We present an efficient representation of a continuous horizontal casting process which takes account of a number of objectives that are important to the scheduler. We have incorporated the methods proposed in software that has been implemented in the plant.     

An automorphism group of an ω‐stable structure that is not locally (OB)

We observe that there is an example of an automorphism group of a model of an ω‐stable theory—in fact, the prime model of an uncountably categorical theory—that is not locally (OB), answering a question of Rosendal.     

Composition of matrix products and categorical equivalence

First, we prove two finite algebras are categorically equivalent if and only if the matrix products of their irredundant non-refinable covers are isomorphic. Second, we characterize families of irreducible algebras such that there exists an algebra whose neighbourhoods in an irredundant non-refinable cover are isomorphic to the respective irreducible algebra in the given family. Finally, we exhibit two facts by constructing examples. The first one is that there is a family of irreducible algebras such that there are many algebraic structures whose neighbourhoods in an irredundant non-refinable cover are isomorphic to the respective irreducible algebra in the given family. The second example is an algebra such that the matrix product of an irredundant non-refinable cover is bigger than the given algebra.     

The index for Fredholm elements in a Banach algebra via a trace II

We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index.     

Geometry of isometric reflection vectors

In this paper we study the geometry of isometric reflection vectors. In particular, we generalize known results by proving that the minimal face that contains an isometric reflection vector must be an exposed face. We also solve an open question by showing that there are isometric reflection vectors in any two dimensional subspace that are not isometric reflection vectors in the whole space. Finally, we prove that the previous situation does not hold in smooth spaces, and study the orthogonality properties of isometric reflection vectors in those spaces.     

静态条件下SLK交货期完工时间的离差平方和最小问题

本文考察n(n≥2)个独立工件在单台机器上加工的排序问题,工件的交货期按SLK方法设置。目标是求最优加工顺序S~*和最优SLK因子K~*,使完上时间与交货期的离差平方和最小,对此,我们不仅给出了SLK交货期下对任意给定顺序S的最优SLK因子K~*(S)证明了按SPT(Shortest Processing Time)规则排序得到的就是最优顺序S~*而且证明了多个最优加工顺序下最优SLK因子相等。最后,给出了一个示例。     

Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

Semiring and Semimodule Issues in MV-Algebras

It is known that an atomic right LCM domain need not be a UFD but is a projectivity-UFD if it is also modular. This paper studies a slightly weaker and easier condition, the RAMP (acronym for the property in the title) , which also ensures that an atomic right LCM domain will be a projectivity-UFD. Among other things it is shown that in an atomic LCM domain, modularity is equivalent to the pair RAMP and LAMP (the left-right analog of RAMP). This result is then used to show that an atomic LCM domain with conjugation is modular. An example is given of an atomic LCM domain that has neither the RAMP nor the LAMP. All rings are not-necessarily commutative integral domains. Recall that an atomic ring is one in which every nonzero nonunit is a product of atoms (i.e. irreducibles) . A ring R is a right LCM domain if for any two elements a and b in R, aR ∩ bR is a principal right ideal. A right LCM domain need not be a left LCM domain [3] . If a ring has both properties it is called an LCM domain. It Is known (see Example 2 below) that, unlike the commutative case, an atomic right LCM domain need not be a UFD (unique factorization domain). In [1] it is shown that if the ring is also modular then it is a projectivity-UFD (definition of the latter recalled below)     

MONOPOLY,POTENTIAL COMPETITION AND PRIVATE STOCK INFORMATION IN EXHAUSTIBLE RESOURCE MARKETS

ABSTRACT. This paper develops an exhaustible resource model with an incumbent monopolist that faces future potential entry of a single rival or backstop technology. The model is characterized by private stock information in the sense that firms do not know with certainty the size and/or quality of their rival's reserve stock. Results indicate that if such information is private, the strategic response of the monopolist to an entry threat is to extract reserves in the pre‐entry era at a rate faster than would a pure monopolist in an uncontested market, and thus could lead to an improvement in economic welfare relative to the situation where entry is restricted.     

Approximation of Planar Convex Sets from Hyperplane Probes

This paper studies a geometric probing problem. Suppose that an unknown convex set in R ² can be probed by an oracle which, when given a unit vector, will return the position of the supporting hyperplane of the convex set that has the given vector as an outward normal. We present an on-line algorithm for choosing probing directions so that, after n probes, an inner and an outer estimate of the convex set are obtained that are within of each other in Hausdorff distance. This is optimal since there exist convex sets that, even if visible, cannot be approximated better than with n-sided polygons, for example, a circle. Received April 18, 1995, and in revised form March 28, 1996.     

An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevskiĭ 3-space

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevskiĭ 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron is not stationary under the flex.     

An efficient algorithm for allocating paged,drum-like storage

Cody and Coffman have studied the problem of distributing a set of a equal-size records among the sectors of a drum-like storage device so as to minimize the average rotational latency cost. This paper is an extension of that work. We employ the same model but a different latency delay function. Motivated by the NP-completeness of the general problem and the fact that an arbitrary assignment can have an expected latency cost almost twice that of an optimal assignment, we propose and analyze a fast heuristic whose performance compares favorably with that of an optimal algorithm.This research was supported in part by the National Science Foundation under Grant no. 28290.     

Determination of the insulated inclusion in conductivity problem and related Eshelby conjecture

In the study of composites, it is important to determine the shape of inclusions. There is an interesting case in conductivity problem that the inclusion is insulated. In present paper, we first obtain the representation formula of the solution to an exterior problem, and then prove that for any uniform loading such solution can be extended into the inclusion as an affine function if and only if the insulated inclusion is an ellipse or an ellipsoid. We also show that an analogous result holds for the elasticity problem, which is related to Eshelby conjecture. The main results in this paper are motivated by Ammari, Kang, Kim and Lee (2013), Ammari, Kang and Lim (2005), Kang and Milton (2008), and Liu (2008).     

Optimal boundedness criteria for extended-real-valued functions

The notion of genuinely bounded below function is introduced and characterized by means of the concept of co-equilibrated function. As an application, we state two boundedness criteria for extended-real-valued functions, both optimal in a clearly defined sense. The first one says that an extended-real-valued function minorized by an affine map and coinciding from some value up with a co-equilibrated function is bounded below. The second criterion states that an extended-real-valued function minorized by an affine map is bounded below provided that one of its sub-level sets is co-equilibrated.     

Probing interactions in exploratory teaching: a case study

This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students’ competence in justifying an ellipse. We analyse the complex interactions between student, content, and teacher, and discuss explicit pedagogical strategies that help students develop a higher level of geometric reasoning. The findings indicate that students engaged in guided explorations by the teacher and in group discussions with peers were able to identify an ellipse and justify their reasoning.     

L-Fuzzy拟序集的理想完备化

建立[4]中定义的L-fuzzy拟序集的一种理想完备化,即证明了L-fuzzy拟序集上的所有L-fuzzy理想组成的集合,赋以合适的程度映射构成L-fuzzydomain,任意从L-fuzzy拟序集到L-fuzzydomain的L-fuzzy单调映射都可以扩张成为一个L-fuzzyScott连续映射。     

The degree of the E-characteristic polynomial of an even order tensor

The E-characteristic polynomial of an even order supersymmetric tensor is a useful tool in determining the positive definiteness of an even degree multivariate form. In this paper, for an even order tensor, we first establish the formula of its E-characteristic polynomial by using the classical Macaulay formula of resultants, then give an upper bound for the degree of that E-characteristic polynomial. Examples illustrate that this bound is attainable in some low order and dimensional cases.