Coupled-expanding maps and one-sided symbolic dynamical systems

This paper studies relationships between coupled-expanding maps and one-sided symbolic dynamical systems. The concept of coupled-expanding map is extended to a more general one: coupled-expansion for a transitive matrix. It is found that the subshift for a transitive matrix is strictly coupled-expanding for the matrix in certain disjoint compact subsets; the topological conjugacy of a continuous map in its compact invariant set of a metric space to a subshift for a transitive matrix has a close relationship with that the map is strictly coupled-expanding for the matrix in some disjoint compact subsets. A certain relationship between strictly coupled-expanding maps for a transitive matrix in disjoint bounded and closed subsets of a complete metric space and their topological conjugacy to the subshift for the matrix is also obtained. Dynamical behaviors of subshifts for irreducible matrices are then studied and several equivalent statements to chaos are obtained; especially, chaos in the sense of Li–Yorke is equivalent to chaos in the sense of Devaney for the subshift, and is also equivalent to that the domain of the subshift is infinite. Based on these results, several new criteria of chaos for maps are finally established via strict coupled-expansions for irreducible transitive matrices in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, respectively, where their conditions are weaker than those existing in the literature.     

Numerical modelling of the plane problem of the stress state of a tube immersed in a liquid

A numerical method for solving the plane problem of determining the stress state of a tube of arbitrary section immersed in a homogeneous incompressible liquid is proposed. The change from the boundary conditions for this problem to the boundary conditions for a biharmonic stress function is carried out, which enables the algorithm for solving boundary value problems in the case of a polyharmonic function developed earlier to be used to solve the problem under consideration. It is shown that the boundary conditions for doubly-connected domains contain three unknown constants. The conditions for finding these constants in a form that is convenient for the implementation of a numerical algorithm are obtained. Tubes with sections in the form of concentric, eccentric and elliptic rings are considered as examples.     

The Statistical Analysis of a Disparity Test

A market research survey was conducted using a Disparity test to measure the change in preference for four consumer products, as the products became progressively "worn" through use. The results were analysed to see if the deterioration in average preference for a product was uniformly less than for another product, in order to see if "longer lasting" claims for this product could be made for one of the dimensions measured in the test. By fitting a suitable statistical model to the data using weighted least squares estimation it was possible to infer that it was reasonable to make such a claim for one of the products.     

A committed delivery strategy with fixed frequency and quantity

We analyze a supply chain environment in which a distributor facing price-sensitive demand has the opportunity to contractually commit to a delivery quantity at regular intervals over a finite horizon in exchange for a per-unit cost reduction for units acquired via committed delivery. Supplemental orders needed to meet demand are purchased at an additional unit cost. For normally distributed demand, we use a simulation-based approximation to develop models yielding closed-form solutions for the optimal order quantity and resell price for the distributor. Inventory, ordering and pricing implications for this “committed delivery strategy” are investigated.     

A methodology for knowledge discovery to support product family design

This paper introduces a methodology for knowledge discovery related to product family design that integrates an ontology with data mining techniques. In the proposed methodology, the ontology represents attributes for the components of products in functional hierarchies. Fuzzy clustering is employed for data mining to first partition product functions into subsets for identifying modules in a given product family and then identify the similarity level of components in a module. Module categorization is introduced to support association rule mining for knowledge discovery related to platform design. We apply the proposed methodology to first develop and then utilize design knowledge for a family of power tools. Based on the developed design knowledge, a new platform is suggested to improve commonality in the power tool family.     

On the general nonlinear self-adjoint spectral problem for differential-algebraic systems

We consider a general self-adjoint spectral problem, nonlinear with respect to the spectral parameter, for linear differential-algebraic systems of equations. Under some assumptions, we present a method for reducing such a problem to a general self-adjoint nonlinear spectral problem for a system of differential equations. In turn, this permits one to pass to a problem for a Hamiltonian system of ordinary differential equations. In particular, in this way, one can obtain a method for computing the number of eigenvalues of the original problem lying in a given range of the spectral parameter.     

A Characterization for Geodsic Spheres in Space Forms

We use the maximum principle for second-order elliptic operators to establish a sufficient condition for a compact hypersurface in a space form to be a geodesic sphere in terms of a pinching for the s-mean curvature.     

An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem

Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear global optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, such as in generating surrogate constraints, scatter search uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we present a scatter search implementation designed to find high quality solutions for the NP-hard linear ordering problem, which has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics. Our implementation incorporates innovative mechanisms to combine solutions and to create a balance between quality and diversification in the reference set. We also use a tracking process that generates solution statistics disclosing the nature of combinations and the ranks of antecedent solutions that produced the best final solutions. Extensive computational experiments with more than 300 instances establishes the effectiveness of our procedure in relation to approaches previously identified to be best.     

A continuous time,deterministic, nonstationary model of economic ordering

The paper considers the problem of economic ordering for a deterministic, nonstationary environment in continuous time. Previous work on the topic is reviewed. The specification of the cost criterion common in inventory theory is called in question for nonstationary situations as far as interest cost is concerned. It is proposed to account for interest by discounting rather than in a holding cost expression. The main interest of the paper is in three versions of the problem: First an unconstrained version, for which inventory is allowed to become negative (backlogging model), second a model in which inventory is constrained to be nonnegative (non-backlogging model), and third a nonbacklogging model with a storage space constraint. For the first two problems necessary optimality conditions are derived which are based on control theory for continuous time systems with jumps in the state trajectories, especially on Blaquière's impulsive maximum principle. These conditions reduce the problem of finding an optimal ordering plan, i.e. an unknown number of optimal ordering times and for each of them an optimal order size to a one parameter search problem. Due to the possibility of multiple solutions of the optimality conditions for each ordering time, one cannot in general identify a unique candidate ordering plan for each value of the search parameter, but only a tree-structured set of such plans. The optimality conditions for the first two problem versions and for a fourth one with a storage space constraint but without a non-backlogging constraint are eventually combined to yield a solution of the storage space constrained non-backlogging version.     

Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics

The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions.     

Optimal Control and Stabilization for Some Fisher-Like Models

This article concerns optimal control and stabilization for some Fisher-like models with control acting in a subdomain ω. We investigate the optimal position of ω for some optimal harvesting problems. First, we refer to a logistic model with diffusion. We remember the necessary optimality conditions, and then obtain an iterative method to improve the position of ω for the optimal harvesting effort (for a simplified model without logistic term). Next, we consider the null stabilization for a controlled Fisher model and obtain a descent method to improve the position of ω in order to get a faster stabilization to zero. Numerical tests illustrating the effect of the last method are given. We also studied the null stabilization for a prey-predator system and have reduced it to the study of the null stabilizability for a related Fisher model.     

A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications

The purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a Banach space. As applications, we utilize our results to obtain some new results for finding a solution of an equilibrium problem, a fixed point problem and a common zero-point problem for maximal monotone mappings in Banach spaces.     

A systematic approximation for the equations governing convection–diffusion in a porous medium

In order to take into account thermal effects in flows through porous media, one makes ad hoc modifications to Darcy’s equation by appending a term that is similar to the one that is obtained in the Oberbeck–Boussinesq approximation for a fluid. In this short paper we outline a systematic procedure for obtaining an Oberbeck–Boussinesq type of approximation for the flow of a fluid through a porous medium. In addition to establishing the appropriate equation for a flow governed by Darcy’s equation, we proceed to obtain the approximations for flows governed by equations due to Forchheimer and Brinkman.     

On the energy flux vector for bending vibrations of a plate : PMM vol. 40, n 6, 1976, pp. 1131–1135

An expression for the energy flux vector of plate bending vibrations is obtained in invariant form. The derivation of expressions for the transverse force, bending and twisting moments in an arbitrary orthogonal coordinate system and the derivation of an orthogonality type condition for normal waves being propagated in a thin elastic strip with free edges are considered as applications.In a number of cases it turns out to be useful to consider the energy flux vector in analyzing the vibrations in systems with distributed parameters. The expressions for the Umov-Poynting vector in electrodynamics and for the energy flux vector in acoustics are well-known. An analogous vector for the bending Vibrations of a plate was mentioned only in [1 – 3], This vector is used in [1] to prove a uniqueness theorem for a two-component acoustic model consisting of an ideal compressible fluid and elastic plates in contact with it. However, the expression for the energy flux in [1] (it was later cited in [2, 3] with a reference to [1]) is erroneous. An exact expression (within the framework of the applicability of the Kirchhoff equation) is found below for the energy flux vector of the bending vibrations of a plate and some applications of the formulas obtained are mentioned.     

Patterns generated by mth-order Markov chains

We derive an expression for the expected time for a pattern to appear in higher-order Markov chains with and without a starting sequence. This yields a result for directly calculating, the first time one of a collection of patterns appears, in addition to the probability, for each pattern, that it is the first to appear.     

On Primitive Cellular Algebras

First we define and study the exponentiation of a cellular algebra by a permutation group that is similar to the corresponding operation (the wreath product in primitive action) in permutation group theory. Necessary and sufficient conditions for the resulting cellular algebra to be primitive and Schurian are given. This enables us to construct infinite series of primitive non-Schurian algebras. Also we define and study, for cellular algebras, the notion of a base, which is similar to that for permutation groups. We present an upper bound for the size of an irredundant base of a primitive cellular algebra in terms of the parameters of its standard representation. This produces new upper bounds for the order of the automorphism group of such an algebra and in particular for the order of a primitive permutation group. Finally, we generalize to 2-closed primitive algebras some classical theorems for primitive groups and show that the hypothesis for a primitive algebra to be 2-closed is essential. Bibliography: 16 titles.     

Development of utility function for life insurance buyers in the Indian market

Insurance as a financial instrument has been used for a long time. The dramatic increase in competition within the insurance sector (in terms of providers coupled with awareness for the need for insurance) has concomitantly resulted in more policy options being available in the market. The insurance seller needs to know the buyer's preference for an insurance product accurately. Based on such multi-criterion decision-making, we use a logarithmic goal programming method to develop a linear utility model. The model is then used to develop a ready reckoner for policies that will aid investors in comparing them across various attributes.     

Decision making in stock trading: An application of PROMETHEE

The key issue for decision making in stock trading is selection of the right stock at the right time. In order to select the superior stocks (alternatives) for investment, a finite number of alternatives have to be ranked considering several and sometimes conflicting criteria. Therefore, we are faced with a special multicriteria decision-making problem. The purpose of this paper is to develop a decision-making model for selecting superior stocks in stock exchange and a model is provided in order to structure this problem. The proposed model is structured around two pillars: Industry evaluation and Company evaluation. The preference ranking organization method for enrichment evaluation (PROMETHEE) has been used for solving the problem. The model has been applied at Tehran Stock Exchange (TSE) as a real case and a survey from the experts in order to determine the effective criteria for industry evaluation and company evaluation has been conducted.     

A necessary and sufficient condition for Pareto-optimal security strategies in multicriteria matrix games

In this paper, a scalar game is derived from a zero-sum multicriteria matrix game, and it is proved that the solution of the new game with strictly positive scalarization is a necessary and sufficient condition for a strategy to be a Pareto-optimal security strategy (POSS) for one of the players in the original game. This is done by proving that a certain set, which is the extension of the set of security level vectors in the criterion function space, is convex and polyhedral. It is also established that only a finite number of scalarizations are necessary to obtain all the POSS for a player. An example is included to illustrate the main steps in the proof.This work was done while the author was a Research Associate in the Department of Electrical Engineering at the Indian Institute of Science and was financially supported by the Council of Scientific and Industrial Research, Delhi, India.The author wishes to express his gratefulness to Professor U. R. Prasad for helpful discussions and to two anonymous referees for suggestions which led to an improved presentation.