The radius of convexity of particular functions and applications to the study of a second order differential inequality

In this paper we determine the radius of convexity of particular functions. The obtained results are used to deduce sharp estimates regarding functions which satisfy a second order differential subordination. A lemma regarding starlikeness that involves the notion of convolution is established, and is used in order to obtain a sharp starlikeness condition.     

On automorphism groups of quasiprimitive 2-arc transitive graphs

We characterize the automorphism groups of quasiprimitive 2-arc-transitive graphs of twisted wreath product type. This is a partial solution for a problem of Praeger regarding quasiprimitive 2-arc transitive graphs. The solution stimulates several further research problems regarding automorphism groups of edge-transitive Cayley graphs and digraphs. This work forms part of an ARC grant project and is supported by a QEII Fellowship.     

The frequency transfer function corresponding to hand-arm system

The paper presents a study regarding the frequency transfer function corresponding to hand-arm system. Theoretical the frequency transfer function obtains applying the Laplace function for the differential equations of moving system. This is a part of the study regarding the mechanical vibrations action over the hand-arm system. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Principal minors, Part II: The principal minor assignment problem

The inverse problem of finding a matrix with prescribed principal minors is considered. A condition that implies a constructive algorithm for solving this problem will always succeed is presented. The algorithm is based on reconstructing matrices from their principal submatrices and Schur complements in a recursive manner. Consequences regarding the overdeterminancy of this inverse problem are examined, leading to a faster (polynomial time) version of the algorithmic construction. Care is given in the MATLAB^® implementation of the algorithms regarding numerical stability and accuracy.     

Cost Uncertainty in Competitive Bidding Models

In this paper a number of issues will be examined regarding uncertainty about cost estimates in competitive bidding models. First, the value of information is derived when the relevant parameters are known. Next, it is shown how the usual procedure for finding the optimal price can be improved by taking into account information regarding the relation between the ratio of estimated cost to real cost for winning bids, and markup. Finally, a trial-and-error procedure is presented for determining the parameters needed to estimate the value of information.     

Moving Beyond “Those Kids”: Addressing Teacher Beliefs Regarding the Role of Culture Within Effective Science Pedagogy for Diverse Learners

This study focused on intensive work within a large, urban, low‐performing middle school in the southwest to address and transform teacher beliefs regarding the role of culture within their science pedagogy. Given the recent, rapid growth of numbers of students from Hispanic/Latino(a) backgrounds in the United States, it is critical that a paradigm shift takes place within schools and existing beliefs of science teachers to address the needs of a much changed classroom. This study details the journey of middle‐school teachers who were provided support and experiences targeted at addressing their existing beliefs regarding the role of culture and the growth and change that were achieved through a science education reform effort. Implications for further research will be discussed, including the need for attention to beliefs regarding culture are shared.     

Bivalent and other solutions of fuzzy relational equations via linguistic hedges

We show that the well-known results regarding solutions of fuzzy relational equations and their systems can easily be generalized to obtain criteria regarding constrained solutions such as solutions which are crisp relations. When the constraint is empty, constrained solutions are ordinary solutions. The generalization is obtained by employing intensifying and relaxing linguistic hedges, conceived in this paper as certain unary functions on the scale of truth degrees. One aim of the paper is to highlight the problem of constrained solutions and to demonstrate that this problem naturally appears when identifying unknown relations. The other is to emphasize the role of linguistic hedges as constraints.     

Applications of classification based on similarities and dissimilarities

In this paper, we first review some definitions and propositions regarding similarities between two objects (2-similarity), or among three or more objects (3-similarity/n-similarity). Then the notion of 3-dissimilarity is introduced and the relationships and connections between 2-dissimilarities and 3-dissimilarities are studied. Through some examples, the applications regarding the concepts of 3-similarity, 4-similarity, and dissimilarity relations will be brought out.     

A simulation approach for handling uncertainty in the analytic hierarchy process

Uncertainty considerations are introduced into the analytic hierarchy process (AHP). The rank order of decision alternatives depends on two types of related uncertainties: (1) uncertainty regarding the future characteristics of the decision making environment described by a set of scenarios, and (2) uncertainty associated with the decision making judgment regarding each pairwise comparison. A simulation approach for handling both types of related uncertainties in the AHP is described. The example introduced by Saaty and Kearns (1985) is extended here to include uncertainty considerations.     

Recurrence and decay properties of a star-typed queueing model with refusal

We consider a multiclass service system with refusal and bulk-arrival. The properties regarding recurrence, ergodicity, and decay properties of such model are discussed. The explicit criteria regarding recurrence and ergodicity are obtained. The stationary distribution is given in the ergodic case. Then, the exact value of the decay parameter, denoted by λ_E, is obtained in the transient case. The criteria for the λ_E-recurrence are also obtained. Finally, the corresponding λ_E-invariant vector/measure is considered.     

Studies Regarding the Alternate Simulation Techniques for Machine Toolsand Industrial Robots

In the paper are presented results regarding the design, simulation and testing of some robotized structures with parallel kinematics in order to identify appropriate simulation techniques and to reveal the properties of particular studied characteristics. The paper is structured in three parts: introduction regarding the tasks of the simulations techniques and the developed applications, comparison of the results obtained in simulations, considering the working space modelling accuracy and the speed of workspace identification and the last part conclusions. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey

This paper is concerned with a mathematical model dealing with a predator–prey system with disease in the prey. Mathematical analysis of the model regarding stability has been performed. The effect of delay on the above system is studied. By regarding the time delay as the bifurcation parameter, the stability of the positive equilibrium and Hopf bifurcations are investigated. Furthermore, the direction of Hopf bifurcations and the stability of bifurcated periodic solutions are determined by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, to verify our theoretical predictions, some numerical simulations are also included.     

Statistical tests involving several independent gamma distributions

Statistical tests are developed regarding linear combinations of the parameters of several independent gamma populations. The tests are based on a generalized minimum chi-square procedure. On utilizing these, one can test hypotheses regarding the means or the scale parameters when the shape parameters are unknown. In these tests there is no need to assume the equality of the shape parameters of the underlying populations. Tests for comparing coefficients of variation of several gamma populations have also been developed. For the two population case, a power comparison of these tests with some existing tests is also presented. Two examples are provided to explain the procedure.     

The Development of an Instrument to Measure Preservice Teachers' Attitudes about Discourse in the Mathematics Classroom

This study explored the themes that comprise preservice teachers' attitudes regarding discourse in the K‐12 mathematics classroom. The initial development of the theory underlying preservice teachers' attitudes regarding mathematical discourse is documented through the development of a 5‐point Likert instrument. Analysis of the Preservice Teachers' Attitudes About Discourse in the Mathematics Classroom (PADM) Instrument (N – 277) resulted in three reliable factors: Promoting Mathematical Reasoning (α₁= .85), Examining Complex Mathematical Concepts (α₂= .81), and Valuing Students' Mathematical Ideas (α₃= .85). These results suggest a framework that mathematics educators can employ to address preservice teachers' attitudes regarding discourse in an effort to support their implementation of reform‐based discourse in the teaching of mathematics in their future classrooms.     

Markovian bulk-arrival and bulk-service queues with general state-dependent control

We study a modified Markovian bulk-arrival and bulk-service queue incorporating general state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated, and the relationship between this stopped queue and the full queueing model is examined and exploited. Using this relationship, the equilibrium behaviour for the full queueing process is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined, and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting times and busy period distributions are answered in detail, and the Laplace transforms of these distributions are presented. Further properties regarding the busy period distributions including expectation and conditional expectation of busy periods are also explored.

     

B-transform and its application to a fish-hyacinth model

A new transform proposed by Oyelami and Ale for impulsive systems is applied to an impulsive fish-hyacinth model. A biological policy regarding the growth of the fish and the hyacinth populations is formulated.     

Hilbert–Pachpatte type general integral inequalities

In this article we present very general weighted Hilbert–Pachpatte type integral inequalities. These are regarding ordinary derivatives and fractional derivatives of Riemann–Liouiville and Canavati types. Also regarding general derivatives of Widder type and linear differential operators. Our results apply to continuous functions and some to integrable functions.     

Impact of uncertainty in the quality of returns on the profitability of a single-period refurbishing operation

This paper investigates how the profitability of reuse activities is affected by uncertainty regarding the quality of returned products. Specifically, we examine a reverse supply chain consisting of two collection sites and a refurbishing site, which faces stochastic demand for refurbished products in a single-period setting. The quality of returns (refurbishing yield) becomes known only after the transportation of the products to the refurbishing site. We prove that the expected profit function has a unique optimal solution (procurement and production quantities) and we derive the conditions under which it is optimal to use only one of the collection sites. The analysis is supported by numerical results which provide insights regarding the effect of the uncertain yields at the two collection sites and their correlation on optimal decisions and system profitability.     

A uniqueness theorem for a generalized solution of a system of two quasilinear equations in the class of bounded,measurable functions

A theorem is formulated and proved regarding the uniqueness of a generalized solution of Cauchy's for a hyperbolic system consisting of two first-order quasilinear equations with one spatial variable. Admissible solutions are bounded, measurable functions satisfying an additional condition of entropy type.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 69, pp. 3–18, 1977.It is the author's pleasure to thank O. A. Ladyzhenskaya for her attention to this work and for her valuable remarks and suggestions and also A. I. Koshelev and G. I. Natanson for useful consultations regarding sources in the literature.     

Generalized discrete autoregressive moving‐average models

This article proposes the generalized discrete autoregressive moving‐average (GDARMA) model as a parsimonious and universally applicable approach for stationary univariate or multivariate time series. The GDARMA model can be applied to any type of quantitative time series. It allows to compute moment properties in a unique way, and it exhibits the autocorrelation structure of the traditional ARMA model. This great flexibility is obtained by using data‐specific variation operators, which is illustrated for the most common types of time series data, such as counts, integers, reals, and compositional data. The practical potential of the GDARMA approach is demonstrated by considering a time series of integers regarding votes for a change of the interest rate, and a time series of compositional data regarding television market shares.