ATM network design for corporate networks

Asynchronous transfer mode (ATM) networks play an important role in support of distributed applications and modern corporate systems. The applications that use these architectures transfer high volumes of data in high-speed bursts and have stringent delay requirements. To address these needs, network managers seek cost efficient network solutions that provide network capacity sufficient to support high-speed applications.In this paper we present a new formulation and solution procedure for designing ATM networks to support corporate applications. Given the locations of the application servers and multiple clients we would like to design a minimum cost ATM network by which the clients can access the servers. Most of the previous work done in this area separates the problem into a routing problem (virtual circuit routing) and an assignment (virtual path assignment) problem. Thus, the solutions tend to be sub-optimal in the combined problem. This research optimizes virtual path (VP) assignment and virtual circuit (VC) routing simultaneously. We formulate the combined problem explicitly and develop an effective solution method. The solution method provides the designer with virtual paths and virtual circuits over which the actual communication takes place. Computational results are provided.     

On the core of network synthesis games

We use polynomial formulations to show that several rational and discrete network synthesis games, including the minimum cost spanning tree game, satisfy the assumptions of Owen's linear production game model. We also discuss computational issues related to finding and recognizing core points for these classes of games.     

The effectiveness of corporate governance: board structure and business technical efficiency in Spain

This study seeks to determine the effectiveness of corporate governance by analyzing the impact of board structure on firm technical efficiency. Resampling methods and bootstrapping techniques applied in Data Envelopment Analysis are used to evaluate firm performance. Truncated regressions are estimated to determine the effect of five board characteristics—board size, board independence, board reputation, board diversity and board activity—on efficiency. The result of this empirical study shows that business technical efficiency increases with a heterogeneous board with a limited number of directorships per director and with a limited activity specified in a reduced number of annual board meetings with a higher number of specialized committees.     

The convex hull of two core capacitated network design problems

The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated facility. We can load any number of units of the facility on each of the arcs at a specified arc dependent cost. The problem is to determine the number of facilities to be loaded on the arcs that will satisfy the given demand at minimum cost.This paper studies two core subproblems of the NLP. The first problem, motivated by a Lagrangian relaxation approach for solving the problem, considers a multiple commodity, single arc capacitated network design problem. The second problem is a three node network; this specialized network arises in larger networks if we aggregate nodes. In both cases, we develop families of facets and completely characterize the convex hull of feasible solutions to the integer programming formulation of the problems. These results in turn strengthen the formulation of the NLP.Research of this author was supported in part by a Faculty Grant from the Katz Graduate School of Business, University of Pittsburgh.     

The uniqueness of the core

Simple proofs are given for two theorems of Duffus and Rival: If a finite poset is dismantled by irreducibles as much as possible, the subposet one finally obtains is unique up to isomorphism. If one dismantles by doubly irreducibles, the subposet is unique.     

The design of corporate tax structures

We consider the corporate tax structuring problem (TaxSP), a combinatorial optimization problem faced by firms with multinational operations. The problem objective is nonlinear and involves the minimization of the firm's overall tax payments i.e. the maximization of shareholder returns. We give a dynamic programming (DP) formulation of this problem including all existing schemes of tax-relief and income-pooling. We apply state space relaxation and state space descent to the DP recursions and obtain an upper bound to the value of optimal TaxSP solutions. This bound is imbedded in a B&B tree search to provide another exact solution procedure. Computational results from DP and B&B are given for problems up to 22 subsidiaries. For larger size TaxSPs we develop a heuristic referred to as the Bionomic Algorithm (BA). This heuristic is also used to provide an initial lower bound to the B&B algorithm. We test the performance of BA firstly against the exact solutions of TaxSPs solvable by the B&B algorithm and secondly against results obtained for large-size TaxSPs by Simulated Annealing (SA) and Genetic Algorithms (GA). We report results for problems of up to 150 subsidiaries, including some real-world problems for corporations based in the US and the UK. Support for this work was provided by the IST Framework 5 Programme of the European Union, Contract IST2000-29405, Eurosignal ProjectMathematics Subject Classification (2000): 90C39, 91B28     

The maximality of the core model

Our main results are: 1) every countably certified extender that coheres with the core model is on the extender sequence of , 2) computes successors of weakly compact cardinals correctly, 3) every model on the maximal 1-small construction is an iterate of , 4) (joint with W. J. Mitchell) is universal for mice of height whenever , 5) if there is a such that is either a singular countably closed cardinal or a weakly compact cardinal, and fails, then there are inner models with Woodin cardinals, and 6) an -Erdös cardinal suffices to develop the basic theory of .

     

Open core and small groups in dense pairs of topological structures

Dense pairs of geometric topological fields have tame open core, that is, every definable open subset in the pair is already definable in the reduct. We fix a minor gap in the published version of van den Dries's seminal work on dense pairs of o-minimal groups, and show that every definable unary function in a dense pair of geometric topological fields agrees with a definable function in the reduct, off a small definable subset, that is, a definable set internal to the predicate.For certain dense pairs of geometric topological fields without the independence property, whenever the underlying set of a definable group is contained in the dense-codense predicate, the group law is locally definable in the reduct as a geometric topological field. If the reduct has elimination of imaginaries, we extend this result, up to interdefinability, to all groups internal to the predicate.     

The structure of the core of ideals

The core of an R-ideal I is the intersection of all reductions of I. This object was introduced by D. Rees and J. Sally and later studied by C. Huneke and I. Swanson, who showed in particular its connection to J. Lipman's notion of adjoint of an ideal. Being an a priori infinite intersection of ideals, the core is difficult to describe explicitly. We prove in a broad setting that: core(I) is a finite intersection of minimal reductions; core(I) is a finite intersection of general minimal reductions; core(I) is the contraction to R of a ‘universal’ ideal; core(I) behaves well under flat extensions. The proofs are based on general multiplicity estimates for certain modules. Received: 16 May 2000 / Revised version: 11 December 2000 / Published online: 17 August 2001     

The extreme core

For a Siegel modular cusp formf of weightk letv(f) be the closure of the convex ray hull of the support of the Fourier series inside the cone of semidefinite forms. We show the existence of the extreme core,C _ext, which satisfiesv(f) ⊇k C_ext for all cusp forms. This is a generalization of the Valence Inequality to Siegel modular cusp forms. We give estimations of the extreme core for general n. For n ≤5 we use noble forms to improve these estimates. Forn = 2 we almost specify the extreme core but fall short. We supply improved estimates for all relevant constants and show optimality in some cases. The techniques are mainly from the geometry of numbers but we also use IGUSA’s generators for the ring of Siegel modular forms in degree two.     

The structures of German mathematics textbooks

From a socio-cultural perspective it is argued that the modality of artefacts has, structuring effects on the activities in which the artefact is involved. The mathematics textbook is an artefact that has a major influence on the activity of learning mathematics. Against this setting, the structures of the units in German mathematics textbooks for different grades and ability levels have been analysed. Firstly, the different structural elements have been examined with regard to: characteristics in terms of content; linguistic characteristics; visual characteristics; their pedagogical functions within the learning process; and situative conditions. Secondly, the orders of the structural elements within the units of the different textbooks have been compared. The findings reveal that the structure of the units is very similar in different mathematics textbooks. The units are not only composed of analogous structural elements, but these elements are also arranged in almost the same sequence. In order to develop a deeper understanding of these findings the structure of the units has been compared to the influential learning theories of J. F. Herbart and H. Roth. On this basis it is argued that the structure of the units seems to reflect the phases of idealised learning processes in general. The issue is raised if this is an appropriate structure in order to provide opportunities to learn mathematics.     

Cost-based pricing model with value-added tax and corporate income tax for a supply chain network

This article aims to propose the short-term cost-based pricing method of supply chain network with the consideration of value-added tax (VAT) and corporate income tax. First, the average cost function of each business unit in supply chain network is given, and the average cost function is taken as the monotone mapping in n-dimensional space. According to Kantorovich theorem, the existence and uniqueness of equilibrium point where the cost equals the income is discussed. When the demand function satisfies certain conditions, there generally exist many equilibrium points for cost-based pricing. Moreover, the iteration method for finding one of the equilibrium solutions is given. Then, tax burden of producers and consumers is described and illustrated with an example.     

The core of discontinuous games

The traditional design of cooperative games implicitly assumes that preferences are continuous. However, if agents implement tie breaking procedures, preferences are effectively lexicographic and thus discontinuous. This rouses concern over whether classic core nonemptiness theorems apply in such settings. We show that balanced NTU games may have empty cores when agents have discontinuous preferences. Moreover, exchange economies may lack coalitionally rational trades when consumers implement tie breaking rules, even if these rules are themselves continuous and convex as are all first order preferences. Results are more positive when “utility” is transferable. We prove that balancedness is necessary and sufficient to ensure a nonempty core in lexicographic TU games.     

A dynamic analysis of corporate investments and emission tax policy in an oligopoly market with network externality

We investigate the product innovation, green R&D investments and the emission tax policy in an oligopoly market with network externality. It is shown that an appropriate tax policy should be deployed to effectively control pollution and motivate innovation. At the early stage of the market, the emission tax should gradually reduce to motivate firms to achieve optimal investments. Later at the mature stage, the emission tax policy should carefully consider both the market competition and green technology levels.     

The structure of the core of a numerical contraction

A bounded linear operatorT is a numerical contraction if and only if there exists a selfadjoint contractionZ such that . The aim of the present paper is to study the structure of the coreZ(T) of all selfadjoint contractions satisfying the above inequality. Especially we consider several conditions for thatZ(T) is a single-point set. By using this argument we shall characterize extreme points of the set of all numerical contractions. Moreover we shall give effective sufficient conditions for extreme points.