New parastatistics leading to classical thermodynamics: Physical interpretation. II

In this paper, we refine some of the original notions, such as the number of degrees of freedom, for an arbitrary temperature and an ideal Boltzmann-Maxwell gas. Using the van der Waals model, we illustrate the notion of Frenkel temperature, which separates soft and rigid liquid.     

L.P.L. a fuzzy programming language: 1. Syntactic aspects

The L.P.L. language (Linguistic oriented Programming Language) that we shall present in this paper and in a forthcoming one is a new language aiming at an implementation of the concepts of the fuzzy sets theory. In the first paper, after an introduction to the basic concepts. we shall describe the syntactic aspects of L.P.L., i.e., the data declarations structure, the statements structure, the general structure of L.P.L. models. The second paper will deal first with the basic semantic and the semantics of logical expressions, then the semantics of basic statements as well as the semantics of the control structure of programs.     

Complex classical fields: An example

We study complex, classical, scalar fields within a new framework introduced in a previous work. We replace the usual functional integral by a complex functional arising from a boosted Hamiltonian. We generalize the Feynman–Kac relation to this setting, and use it to establish the spectral condition on a cylinder. We consider also positive-temperature states.     

BiBloch-type Maps: Existence and Beyond

It is shown that for f > 0 there are two constants c 1 , c 2 > 0 and a holomorphic map f from the unit disk ${\shadD} {\rm of} {\shadC}$ into ${\shadC}^2$ such that $ c_1(1-|z|)^{-\alpha }\le |\,f'(z)|\le c_2(1-|z|)^{-\alpha } $ for all $ z\in {\shadD}$ . Moreover, this existence is effectively used in the study of invariance of the Bloch-type spaces under composition, but also in the discussion of embedding the Bloch-type spaces via derivation into the Lebesgue, mixed-norm and Coifman-Meyer-Stein tent spaces.     

Beyond Adomian polynomials: He polynomials

The Adomian decomposition method is widely used in approximate calculation. The main difficulty of the method is to calculate Adomian polynomials, the procedure is very complex. In order to overcome the demerit, this paper suggests an alternative approach to Adomian method, instead of Adomian polynomials, He polynomials are introduced based on homotopy perturbation method. The solution procedure becomes easier, simpler, and more straightforward.     

P.I. envelopes of classical simple Lie superalgebras

Let be a classical simple Lie superalgebra. We describe the prime ideals in the enveloping algebra such that satisfies a polynomial identity. If the factor algebra is not artinian, then it is an order in a matrix algebra over .     

Partial Theta Functions. I. Beyond the Lost Notebook

It is shown how many of the partial theta function identitiesin Ramanujan's lost notebook can be generalized to infinitefamilies of such identities. Key in our construction is theBailey lemma and a new generalization of the Jacobi triple productidentity. By computing residues around the poles of our identitieswe find a surprising connection between partial theta functionidentities and Garrett–Ismail–Stanton-type extensionsof multisum Rogers–Ramanujan identities. 2000 MathematicsSubject Classification 05A30, 33D15, 33D90.     

The classical moment problem: Hilbertian proofs

In view of its connection with a host of important questions, the classical moment problem deserves a central place in analysis. It is usually treated by methods striking in their virtuosity, but difficult to motivate. Here we describe an elementary approach which establishes the structural results and exposes the Hilbert space origins of the arguments.     

Two classical splitting theorems: Easy proofs

The two main splitting theorems for a division ring which is finite dimensional over its center are obtained as corollaries to:Lemma. Suppose B ? A ? D where B is a (commutative) subfield of the division ring D and A is an intermediate ring. (For any set X ? D let X′ denote the cenralizer of X in D.) If B = B″, then

$\text{A}{}_{\mathrm{?B}}\text{D}\text{→}\text{π}\text{Hom}{}_{\mathrm{A\prime }}\text{(B,D)}$

where

$\text{π(a ? d) = ab′d, a ∈ A, d ∈ D}\text{and}\text{B′ ∈ B′,}$

is injective.     

Superlinear indefinite systems: Beyond Lotka-Volterra models

This paper analyzes the dynamics of a superlinear indefinite parabolic system. As a byproduct, a number of new results related to population dynamics and economy are obtained. Among them, it is shown that the presence of refuge areas in competitive environments is an optimal mechanism to avoid extinction, and that incorporating local symbiosis in competitive environments increases productivity and allows avoiding extinction of the ‘weaker’ species. Undoubtedly, a paradigm of global markets and possibly of Earth biodiversity. Our analysis combines a series of well-known results for systems with some very recent pioneering findings within the context of superlinear indefinite equations.