Propagation of a plane wave to a materially uniform but inhomogeneous body

We produce the equations of small deformations superimposed upon large for materially uniform but inhomogeneous bodies and specialize to an isotropic material and to a homogeneous finite elastic deformation. By assuming the small deformation to be a plane wave, a set of equations for the amplitude of the wave is produced which is accompanied by an additional set of conditions. By requiring a non-trivial solution for the amplitude, we obtain the secular equation and from it a set of necessary and sufficient conditions for having a real wave speed. The second set of conditions that have to be satisfied is due to the materials inhomogeneity. Essentially, the present analysis enhances the approach of Hayes and Rivlin for materially uniform but inhomogeneous bodies. The outcome is that for such bodies the restrictions on the constitutive law for having real wave speeds for an isotropic material subjected to a pure homogeneous deformation involves the field of the inhomogeneity as well.     

Stackelberg–Nash exact controllability for the Kuramoto–Sivashinsky equation

This paper deals with a hierarchical control problem for the Kuramoto–Sivashinsky equation following a Stackelberg–Nash strategy. We assume that there is a main control, called the leader, and two secondary controls, called the followers. The leader tries to drive the solution to a prescribed target and the followers intend to be a Nash equilibrium for given functionals. It is known that this problem is equivalent to a null controllability result for an optimality system consisting of three non-linear equations. One of the novelties is a new Carleman estimate for a fourth-order equation with right-hand sides in Sobolev spaces of negative order, which allows to relax some geometric conditions for the observation sets for the followers.     

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.     

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.     

Speculative trading in mean reverting markets

Mean reversion is a feature largely recognized for the price processes of many financial securities and especially commodities. In the literature there are examples where some simple speculative strategies, before transaction costs, were devised to earn excess returns from such price processes. Actually, the gain opportunities of mean reversion must be corrected to account for transaction costs, which may represent a major issue. In this work we try to determine sufficient conditions for the parameters of a mean reverting price process as a function of transaction costs, to allow a speculative trader to have positive expectations when deciding to take a position. We estimate the mean reverting parameters for some commodities and correct them for transaction costs to assess whether the potential inefficiency is actually relevant for speculative purposes.     

Lifting Property of Direct Sums of Hollow Modules

We give necessary and sufficient conditions for a module M with a decomposition that complements maximal direct summands to be a lifting module. We apply our results to get a necessary and sufficient condition for a direct sum of modules to be a quasi-discrete (discrete) module. We also give some sufficient conditions for a lifting module to be a direct sum of indecomposables.     

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.     

Existence and uniqueness for an equation of mixed type in a rectangle

A boundary value problem is considered for an equation of mixed type in a rectangle. An energy method is used to prove uniqueness for appropriate boundary conditions. Similar considerations for the adjoint problem allow one to prove the existence of a generalized solution to the problem. It is also shown that the energy method leads naturally to a finite element method. The method is described for a special case and convergence is shown for the resulting numerical procedure.     

A conceptual pathway to confidence intervals

Finding ways for the majority of students to better understand conventional normal theory-based statistical inference seems to be an intractable problem area for researchers. In this paper we propose a conceptual pathway for developing confidence interval ideas for the one-sample situation only from an intuitive sense to bootstrapping for students from about age 14 to first-year university. We make the case that conceptual development should start early; that probability and statistical instruction should change so that both orientate students towards interconnected stochastic conceptions; and that the use of visual imagery has the potential to stimulate students towards such a perspective. We analyse our conceptual pathway based on a theoretical framework for a stochastic conception of statistical inference based on imagery and some research evidence. Our analysis suggests that the pathway has the potential for students to become conversant with the concepts underpinning inference, to view statistics probabilistically and to integrate concepts into a coherent comprehension of inference.     

Searching for a set of correlated patterns

New algorithms for searching simultaneously for a set of patterns in a text are suggested, for the special case where these patterns are correlated and have a common substring. This is then extended to the case where it could be more profitable to look for more than a single overlap, and a problem related to the generalization of this idea is shown to be NP-complete. Experimental results suggest that for this particular application, the suggested algorithm yields significant improvements over previous methods.     

有横贯的Hall-型判定定理

给出了任意集上的一个集族有横贯的一些Hall-型判定定理,回答了Welsh关于相应的无限情形的公开问题,即对于无限情况,找到一个集族有横贯的充要条件.     

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.     

Scoring by usage

This paper aims to discover whether the predictive accuracy of a new applicant scoring model for a credit card can be improved by estimating separate scoring models for applicants who are predicted to have high or low usage of the card. Two models are estimated. First we estimate a model to explain the desired usage of a card, and second we estimate separately two further scoring models, one for those applicants whose usage is predicted to be high, and one for those for whom it is predicted to be low. The desired usage model is a two-stage Heckman model to take into account the fact that the observed usage of accepted applicants is constrained by their credit limit. Thus a model of the determinants of the credit limit, and one of usage, are both estimated using Heckman's ML estimator. We find a large number of variables to be correlated with desired usage. We also find that the two stage scoring methodology gives only very marginal improvements over a single stage scoring model, that we are able to predict a greater percentage of bad payers for low users than for high users and a greater percentage of good payers for high users than for low users.     

Replacement Strategies

Components of a system function for a time and then fail. A central problem is to decide whether a strategy of scheduled replacement is preferable to the running of all components until failure. This is considered by comparing some simple strategies for component replacement. Considerations from probability theory and renewal theory are used to obtain expressions for the average cost of replacements per unit time for each strategy. After obtaining some general conditions for one strategy to be preferable to another, a detailed comparison is made when the interfailure times are independent samples from a gamma distribution.     

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.     

Necessary and Sufficient Conditions for Mcshane’s Identity and Variations

Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two generators Γ to SL(2,C), this was further generalized by the authors to obtain sufficient conditions for a generalized McShane’s identity to hold for arbitrary (not necessarily type-preserving) non-reducible representations in Tan et al. (Submitted). Here we extend the above by giving necessary and sufficient conditions for the generalized McShane identity to hold (Akiyoshi, Miyachi and Sakuma had proved it for type-preserving representations). We also give a version of Bowditch’s variation of McShane’s identity to once-punctured torus bundles, in the case where the monodromy is generated by a reducible element, and provide necessary and sufficient conditions for the variations to hold.     

Separation theorems for nonconvex sets and application in optimization

The aim of this paper is to present separation theorems for two disjoint closed sets, without convexity condition. First, a separation theorem for a given closed cone and a point outside from this cone, is proved and then it is used to prove a separation theorem for two disjoint sets. Illustrative examples are provided to highlight the important aspects of these theorems. An application to optimization is also presented to prove optimality condition for a nonconvex optimization problem.     

Modeling stochastic anomalies in an SIS system

We propose a stochastic SIS model to include both a Gaussian and Poissonian perturbation to account for noise and anomalies in the transmission rate. Conditions are given for stability to the disease free equilibrium and for positive Harris recurrence with a unique invariant measure for the endemic.     

Spurious Behaviour of Numerically Computed Fluid Flow

We investigate the stability to aliasing errors of numericalschemes for hydrodynamics, taking the viscous Burgers' equationas a model for systems with a term that is quadratic in thevelocity. Considering wavelengths equal to three times the mesh-spacing,and arbitrary mean flow, we are able to demonstrate explicitlyfor common schemes (a) a sufficient criterion for stabilityand (b) blow-up of solutions in a finite time when (a) is violated.Singular behaviour is shown to persist at all wavelengths: studiesof wavelengths up to thirty times mesh-spacing make it clearthat a profile with a single region of strong convergent flowis most conducive to instability. In contrast, spectral (Galerkin)and upwind schemes are shown to be stable for all flows andperiods.