Thermodynamic stable interaction pair potentials which are not of the form “positive function + real continuous function of positive type” are presented in dimension one. Construction of such a potential in dimension two is sketched. These constructions use only elementary calculations. The mathematical background is discussed separately. PACS numbers: 05.20.-y, 02.20.-a, 02.40.Ft

In this paper, we study the asymptotic behavior of positive solutions of the nonlinear difference equation xn+1 = xnf(xn−k), where f : [0,∞)→ (0,∞) is a unimodal function, and k is a nonnegative integer. Sufficient conditions for the positive equilibrium to be a global attractor of all positive solutions are established. Our results can be applied to to some difference equations derived from ma...

A dynamical system is called positive if any solution of the system starting from nonnegative states maintains nonnegative states forever. In many applications where variables represent nonnegative quantities we often encounter positive dynamical systems as mathematical models see 1, 2 , and many researches for positive systems have been done actively; for recent developments see, for example, ...

Objective. To systematically review the international literature for mathematical equations used to predict effective pressures for positive airway pressure (PAP) devices. Methods. Google Scholar, PubMed, Scopus, Embase, Web of Science, CINAHL, and The Cochrane Library were searched through June 27, 2015. The PRISMA statement was followed. There was no language limitation. Results. 709 articles...

The intrinsic, or mitochondrial, pathway of caspase activation is essential for apoptosis induction by various stimuli including cytotoxic stress. It depends on the cellular context, whether cytochrome c released from mitochondria induces caspase activation gradually or in an all-or-none fashion, and whether caspase activation irreversibly commits cells to apoptosis. By analyzing a quantitative...

We prove that the matrix of capacitance in electrostatics is a positive matrix. We explore the physical implications of this mathematical fact, and study the eigenvalue problem for the matrix of capacitance and its physical meaning. Many properties are easily visualized by constructing a “potential space” isomorphic to the euclidian space and defining an inner product in it. The problem of mini...

This paper reviews and discusses the more recent literature and application of Positive Mathematical Programming in the context of agricultural supply models. Specifically, advances in the empirical foundation of parameter specifications as well as the economic rationalisation of PMP models – both criticized in earlier reviews – are investigated. Moreover, the paper provides an overview on a la...

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 second part continues to study the question of catecoricitytrans...