Let Ak, k ∈ N be a sequence of n×n complex valued matrices which converge to a matrix A. If A and each Ak is positive then the product AkAk−1...A2A1 ||AkAk−1...A2A1|| converges to a rank one matrix positive matrix uw, where u is a positive column eigenvector of A. If each Ak is nonsingular and A has exactly one simple eigenvalue λ of the maximal modulus with the corresponding eigenvector u, the...

Quantum multiplications on the cohomology of symplectic manifolds were first proposed by the physicist Vafa [Va2] based on Witten’s topological sigma models [Wi1]. In [RuTi], Ruan and the second named author gave a mathematical construction of quantum multiplications on cohomology groups of positive symplectic manifolds (cf. Chapter 1). The construction uses the Gromov-Ruan-Witten invariants (G...

we study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. we discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. this first part introduces the main conceps and philosophies anddiscu...

The stability of the positive fixed points of a discrete-time mathematical model for populations consisting of wild and genetically altered mosquitos proposed by Jia Li [1] is considered in this paper. The model is studied for proportional and constant mating rates. Under certain conditions the model with proportional mating rate has two positive fixed points, one unstable and the other locally...

A mathematical model of competition between two species for two growth-limiting, essential (complementary) resources in the unstirred chemostat is considered. The existence of a positive steady-state solution and some of its properties are established analytically. Techniques include the maximum principle, the fixed point index, and numerical simulations. The simulations also seem to indicate t...

* Correspondence: ss_zhangc@ujn. edu.cn School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, P. R. China Abstract This article studies the necessary and sufficient conditions for asymptotic stability of the linear positive systems with bounded time-varying delays on time scales. Using Lyapunov functions, asymptotic stability conditions for positive systems with constant...

The activity of natural killer (NK) cells is regulated by various processes including education/licensing, priming, integration of positive and negative signals through an array of activating and inhibitory receptors, and the development of memory-like functionality. These processes are often very complex due to the large number of different receptors and signaling pathways involved. Understand...

By-Domotor, Zoltan Probabilistic Relational Structures and Their Applications Stanford Univ., Calif. Inst. for Mathematical Studies in Social Science. Pub Date May 69 Note-171p; Technical Report Nc, 144 Psychology Series EDRS Price MF -10.75 HC-$8.65 Descriptors-Logic, *Mathematical Applications, *Mathematical Concepts, *Mathematics, *Probabihty, *Probability Theory The principal objects of the...

Two species predator-prey with stage structure of mature and immature mathematical models are studied over the last few decades. Xin-an Zhang et al studied a mathematical model with stage structure of two species in 2010. In this article, an attempt has been made to comprehend the coupled predator-prey dynamics with mature-immature stage structure and compare the dynamics with the existing mode...

Technology can help develop understanding of abstract mathematical concepts through visualisation and graphic representation. The teaching and learning of calculus can be challenging as it involves abstract and complex ideas. The purpose of this study was to investigate how students and teachers attempt to use TINspire, the latest graphing calculator from Texas Instruments, in teaching and lear...