Performance evaluation of a multi-echelon production,transportation and distribution system: A matrix analytical approach

This study proposes an originative method to evaluate complex supply chains. A tentative multi-echelon production, transportation and distribution system with stochastic factors built-in is employed as a test bed for the proposed method. The supply subsystem formulated in this study is a two-stage production facility with constant probability of feedback and stochastic breakdowns. The transportation subsystem is a service facility with one server. The distribution subsystem under study is a single central warehouse with M retailers. All the participants of the supply chain use base-stock policies and single-server settings. We investigated both the make-to-order (MTO) and make-to-stock (MTS) policies for different base-stock levels, as adopted at different sites. Applying quasi-birth-and-death (QBD) processes as decomposed building blocks and then using the existing matrix analytical computing approach for the performance evaluation of a tandem queue constitutes the main procedure of this study. We also discuss the possibilities of extending the current model to account for other inventory control policies as well as for multi-server case. Numerical study shows our proposed analytical model is robust for practical use.     

A note on the spatial behavior for the generalized Tricomi equation

This short note is devoted to the study of the spatial decay estimates for the solutions of the generalized Tricomi equation. The relevance of this kind of study is that we obtain the decay for an equation which can be elliptic, parabolic and hyperbolic depending on the different points of the region. This equation is relevant in the study of fluids as well as for the anti-plane deformations of prestressed functionally graded linear elastic solids.     

Effect of auto-correlations on the optimum allocations in two phase stratified sampling—A bayesian approach

In this paper we study the problem of optimal allocation when the model for generation of observations in a particular stratum permits for auto-correlations. The object of the study is assumed to be the estimation of the population mean as precisely as possible.     

Spectral analysis of operator polynomials and higher-order difference operators

The study of the spectral properties of operator polynomials is reduced to the study of the spectral properties of the operator specified by the operator matrix. The results obtained are applied to higher-order difference operators. Conditions for their invertibility and for them to be Fredholm, as well as the asymptotic representation for bounded solutions of homogeneous difference equations are obtained.     

Reading mathematics for understanding—From novice to expert

As students progress through the college mathematics curriculum, enter graduate school and eventually become practicing mathematicians, reading mathematics textbooks and journal articles appears to become easier and leads to increased proficiency and understanding. This study was designed to begin to understand how mathematically more advanced readers read for understanding in mathematical exposition as it appears in textbooks compared to first-year undergraduate students. Three faculty members and three graduate students participated in this study and read from a first-year graduate textbook in an area of mathematics unfamiliar to each of them. The observed reading strategies of these more mathematically advanced readers are compared to observed reading strategies of first-year undergraduate students from an earlier study. The reading methods of the faculty level mathematicians were all quite similar and were markedly different from those that have been identified for undergraduate students, as well as from those used by the graduate students in this study. A Mathematics Reading Framework is proposed based on this study and previous research documenting the strategies that first-year undergraduate students use for reading exposition in their mathematics textbooks.     

Mathematical creativity in generally gifted and mathematically excelling adolescents: what makes the difference?

Due to uncertainty regarding the relationship between mathematical creativity, mathematical expertise and general giftedness, we have conducted a large-scale study that explores the relationship between mathematical creativity and mathematical ability. We distinguish between relative and absolute creativity in order to address personal creativity as a characteristic that can be developed in schoolchildren. This paper presents part of a study that focuses on the power of multiple solution tasks (MSTs) as a tool for the evaluation of relative creativity. We discuss relationships between mathematical creativity, mathematical ability and general giftedness as reflected in the present empirical study of senior high school students in Israel which implemented the MST tool. The study demonstrates that between-group differences are task dependent and are a function of mathematical insight as it is integrated in the mathematical task. Thus, we conclude that different types of MSTs can be used for different research purposes, which we discuss at the end of this paper.     

Nonparametric estimation of quantiles for a class of stationary processes

We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk(Va R) and applied to many time series which have important applications in econometrics.     

Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary.     

A Case History of Nuclear Power Plant Site Selection

This paper discusses a multidisciplinary study conducted to select a site for a nuclear power plant. A series of screening steps was carried out to identify candidate sites for the plant, as well as candidate water sources. Multiobjective decision analysis methods were used to evaluate and rank these candidate sites and water sources; a risk analysis was carried out to determine the effects of major uncertainties. The evaluation concerns considered in the study are discussed, as well as the scales used to measure impacts with regard to these concerns.     

Measurement of Returns to Scale and Damages to Scale for DEA-based operational and environmental assessment: How to manage desirable (good) and undesirable (bad) outputs?

Environmental assessment is increasingly important in preventing various types of pollutions. Data Envelopment Analysis (DEA) has been long used as an operational performance measure, but we have insufficiently explored the use of DEA for environmental assessment. This study explores a new use of DEA for the environmental assessment in which outputs are classified into desirable (good) and undesirable (bad) outputs. Such an output separation is important in the DEA-based environmental assessment. This study extends the use of DEA to the measurement of both Returns to Scale (RTS) for desirable outputs and Damages to Scale (DTS) for undesirable outputs. A Range-Adjusted Measure (RAM) is used as a DEA model for this study because the non-radial model can easily combine the two types of outputs in a unified treatment. All the mathematical features regarding the RAM-based RTS/DTS measurement are first discussed from the operational and environmental performance in a separate treatment. Then, this study combines the two performance measures as a unified measure. The RAM-based RTS/DTS is mathematically explored from the unified measure for operational and environmental performance.     

Changes of Working Styles in a Computer Algebra Environment – The Case of Functions

This study is an empirical investigation of 11th graders at a German high school (Gymnasium). Working over a 24-hour period in a computer lab, we investigated students' use of quadratic functions with `Derive', and trigonometric functions with `Mathplus' (or `Theorist' for Macintosh). We were particularly interested in the working styles of students while they solved problems and looked for changes in these styles, as compared to traditional paper and pencil activities. While students worked on the computer, their activities (such as inputs from the keyboard, menu choices or mouse movements) were saved by a special program, which ran in the `background'. We are interested in the possibilities of developing a research method based on these `computer protocols'. The study should be seen as an exploratory study for developing hypotheses for further empirical investigations.This revised version was published online in September 2005 with corrections to the Cover Date.     

Recurrent Linear Operators

We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication operators on classical Banach spaces. We show that on separable complex Hilbert spaces the study of recurrent operators reduces, in many cases, to the study of unitary operators. Finally, we study the notion of product recurrence and state some relevant open questions.     

Hermite–Padé approximation and simultaneous quadrature formulas

We study Hermite–Padé approximation of the so-called Nikishin systems of functions. In particular, the set of multi-indices for which normality is known to take place is considerably enlarged as well as the sequences of multi-indices for which convergence of the corresponding simultaneous rational approximants takes place. These results are applied to the study of the convergence properties of simultaneous quadrature rules of a given function with respect to different weights.     

A Nonlinear Scalarization Function and Generalized Quasi-vector Equilibrium Problems

Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions for generalized quasi-vector equilibrium problems. This paper is dedicated to Professor Franco Giannessi for his 68th birthday     

On the Existence and Uniqueness of Solution of MRE and Applications

In this paper, we study the existence and uniqueness of the solution for Markov renewal equation (MRE) of a semi-Markov process with countable state space. This method and its proof are based on an iterative scheme. A numerical solution is also given as well as a case study on system reliability assessment.     

A frequency-domain analysis of inexact gradient methods

Mathematical Programming - We study robustness properties of some iterative gradient-based methods for strongly convex functions, as well as for the larger class of functions with sector-bounded...     

The Effectiveness of Substituting Locally Available Materials in Teaching Chemistry in Nigeria: A Case for Science Education in Developing Countries

This article investigates the effectiveness of improvising locally available materials for teaching chemistry in Nigeria, as a case for a culture of improvisation for teaching the sciences in developing countries. The scarcity and cost of imported materials for teaching science has remained a major challenge to teaching sciences in developing countries, and the fact that many teachers from developing countries tend to wait for these imported materials before they can teach continues to present a set‐back for science education in many non‐Western nations. In this experimental study, second year students in 3 Nigerian Senior Secondary schools in the state of Lagos, Nigeria, were sampled to determine whether there will be a significant difference in their performance when taught using imported materials compared to when taught using local substitutes. The study reveals that whereas their attitudes towards local materials may not be as positive as their attitudes towards imported materials, their performances did not differ when taught with either, as long as they were unaware of which material was local or imported. The result of this study proved that science education will flourish if teachers in Nigeria, and probably other developing countries, can begin to improvise local materials for science instruction.     

Static and Dynamic Theories of Liquid Crystals

The study of liquid crystals gives rise to many fascinating but difficult mathematical problems. The purpose of this paper is to briefly summarize some recent advances, as well as to describe the present state of art of the theory of liquid crystals. For the static theory, we emphasis on the theory of defects and the theory of Smectic A materials. We will also study the Ericksen-Leslie theory for the liquid crystal flow. The well-posedness as well as the motion of the defects will be discussed.     

On the solvability of a boundary value problem for a fourth-order ordinary differential equation

We study the existence and multiplicity of nontrivial periodic solutions for a semilinear fourth-order ordinary differential equation arising in the study of spatial patterns for bistable systems. Variational tools such as the Brezis–Nirenberg theorem and Clark theorem are used in the proofs of the main results.     

A simulation analysis of arrest costs

This paper presents results from a study that incorporates an activity based costing (ABC) analysis within a stochastic discrete-event simulation model. The study involves building a model of the arrest and custody process for a Police Force within the UK. The study outlines the use of simulation and ABC in enabling the cost of each arrest type to be estimated as well as a tool for resource deployment under a scenario of a change in the law regarding ‘late drinking’. The use of stochastic simulation ensures that variation in activity is considered during the analysis and resources are therefore deployed over time to ensure that service quality levels are maintained.