Some characterizations of φ-Lagrangian dual problems

We give some characterizations of the Lagrangian dual objective function λ_φdefined with respect to a coupling function φ, namely, conditions for the existence of a φ, and characterizations when q> is given. In particular, when φ is the so-called “natural coupling function”, one of these characterizations reduces to the main result of [6].     

Some characterizations of appell andℊ-appell polynomials

Summary Several characterizations are given for the wellknown Appell polynomials and for their basic analogues: the -Appell polynomials defined by Equation (3.3)below. The main results contained in Theorems 1, 2and 3of the present paper, and the applications considered in Section 2,are believed to be new. Some interesting connections with earlier results are also indicated.Supported, in part, by NSERC (Canada) grant A-7353.     

Mod-retractable strongly π-regular rings and group algebras

Abstract

In this work, we show that a two-sided mod-retractable and strongly π-regular ring is two-sided semiartinian. On the other hand, a strongly π-regular von Neumann regular ring is left mod-retractable if and only if it is a left semiartinian V-ring. We apply these results to group algebras and thereby we give the complete structure of groups whose group algebras are mod-retractable.

Communicated by Toma Albu     

Some characterizations of the integrable Teichmüller space

In this paper, we prove that the Bers projection of the integrable Teichmller space is holomorphic. By using the Douady-Earle extension, we obtain some characterizations of the integrable Teichmller space as well as the p-integrable asymptotic affine homeomorphism.     

On ∗-minimal ∗-ideals and ∗-biideals in involution rings

For semiprime involution rings, we determine some ∗-minimal ∗-ideals using idempotent elements. Nevertheless, ∗-minimal ∗-biideals are characterized by idempotent elements. Moreover, the involutive version of a theorem due to Steinfeld, which investigates a semiprime involution ring A if A=SocA, is given. Finally, semiprime involution rings having no proper nonzero ∗-biideals are characterized.     

Some characterizations of almost Dunford–Pettis operators and applications

This paper attempts to deal with some characterizations of almost Dunford–Pettis operators from a Banach lattice into a Banach space. It also discusses some of the consequences derived from this study. As an application, we generalize some results of Meyer-Nieberg on the duality between semi-compact operators and order weakly compact operators.     

Some remarks on the method of orienting curves ∗

This paper gives a discussion on the hypotheses (H1) – (H5) given in [10], under which the Method of Orienting Curves can be applied for solving optimal control problems with state constraints. We prove that Hypothesis (H2) can be ruled out and (H3) can be replaced by a weaker one.     

Some new Triebel-Lizorkin spaces on spaces of homogeneous type and their frame characterizations

Let(X,p,μ)d,θ be a space of homogeneous type,(?) ∈(0,θ],|s|＜(?) andmax{d/(d＋(?)),d/(d＋s＋(?))}＜q≤∞.The author introduces the new Triebel-Lizorkin spaces (?)_∞q~s(X) and establishes the framecharacterizations of these spaces by first establishing a Plancherel-P(?)lya-type inequalityrelated to the norm of the spaces (?)_∞q~s(X).The frame characterizations of the Besovspace (?)_pq~s(X) with|s|＜(?),max{d/(d＋(?)),d/(d＋s＋(?))}＜p≤∞ and 0＜q≤∞and the Triebel-Lizorkin space (?)_pq~s(X)with|s|＜(?),max{d/(d＋(?)),d/(d＋s＋(?))}＜p＜∞ and max{d/(d＋(?)),d/(d＋s＋(?))}＜q≤∞ are also presented.Moreover,the au-thor introduces the new TriebeI-Lizorkin spaces b(?)_∞q~s(X) and H(?)_∞q~s(X) associated to agiven para-accretive function b.The relation between the space b(?)_∞q~s(X) and the spaceH(?)_∞q~s(X) is also presented.The author further proves that if s＝0 and q＝2,thenH(?)_∞q~s(X)＝(?)_∞q~s(X),which also gives a new characterization of the space BMO(X),since (?)_∞q~s(X)＝BMO(X).     

Global Dynamics of Some Periodically Forced,Monotone Difference Equations ∗

We study a class of periodically forced, monotone difference equations motivated by applications from population dynamics. We give conditions under which there exists a globally attracting cycle and conditions under which the attracting cycle is attenuant     

The m-ordered real free pro-2-group. Cohomological characterizations ∗

In this paper we investigate representations of simple algebraic groups over an algebraically closed field of characteristic 2 and of their Lie algebras. For the groups of rank 4 or less, we shall determine all of the extensions of simple modules. The central theme will be the study of some intimate connections among the groups of types B_l, C _l and D_l (and F ₄ when l = 4). We also give calculations for those other groups of rank 4 or less which have not already been treated elsewhere ([1], [18]), but this is primarily for the sake of completeness.     

ℓ-Divisibility of ℓ-regular partition functions

We give exact criteria for the ℓ-divisibility of the ℓ-regular partition function b _ℓ (n) for ℓ∈{5,7,11}. These criteria are found using the theory of complex multiplication. In each case the first criterion given corresponds to the Ramanujan congruence modulo ℓ for the unrestricted partition function, and the second is a condition given by J.-P. Serre for the vanishing of the coefficients of ∏ _m=1^∞(1−q ^m ) ^ℓ−1.