On Generalizations of Ostrowski Inequality and Some Related Results

Some generalizations of the Ostrowski inequality, the Milovanovi-Peari-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.     

Topological existence and stability for stackelberg problems

The aim of this paper is to study, in a topological framework, existence and stability for the solutions to a parametrized Stackelberg problem. To this end, approximate solutions are used, more precisely, -solutions and strict -solutions. The results given are of minimal character and the standard types of constraints are considered, that is, constant constraints, constraints defined by a finite number of inequalities, and more generally constraints defined by an arbitrary multifunction.     

ε-solutions in vector minimization problems

This paper presents some properties of -solutions for vector minimization problems where the function to be optimized takes its values in the Euclidean space ^p . The results obtained generalize the classical ones for exact Pareto solutions.     

Some topological properties of ω-covering sets

We prove the following theorems:1. There exists an -covering with the property s ₀.2. Under cov there exists X such that is not an -covering orX \ B is not an -covering].3. Also we characterize the property of being an -covering.     

Approximation and Prediction of the Numerical Solution of Some Burgers Problems

The Aitken's ²-prediction of Brezinski has already been used by Morandi Cecchi et al. in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's ²-process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of ²-prediction, the so-called -prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method.     

Un théorème de finitude (A Theorem of Finitude)

We prove that, for an inner form of GL _n , the number of classes of cuspidal automorphic representations with fixed central character and fixed factor at almost every place is finite. We also prove, in the local situation, relations between the level and the -factor of an irreducible smooth representation.     

Some Properties of Isologism of Groups and Baer-Invariants

Let be a variety of groups defined by the set of laws V. In this paper we study the concept of -isologism of groups in terms of -extensions and their connections with the Baer-invariant of groups are also discussed.AMS Subject Classification (2000): primary 20F14, 20F19, secondary 20E10     

Study of Noetherian Γ-Semirings via Operator Semirings

In this paper we study Noetherian -semirings and obtain Cohens theorem for a special class of -semirings. Weak primary decomposition theorem for a particular type of -semirings is also obtained.Presently Lecturer in Mathematics, University of Burdwan, GOLAPBAG, W.B. INDIA.     

A Note on π-Engel Conditions

In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20     

Epsilon-Eigenvalues of Multivalued Operators

Landau's theory of -eigenvalues for bounded linear operators is well suited to cope with difficulties arising from the lack of usual eigenvalues. The notion of -eigenvalue is studied here in the general setting of positively homogeneous multivalued operators. Besides containing a number of new results, the paper sheds a fresh light on many features of the original theory.     

On the variational convergence of non-coercive quadratic integral functionals and semicontinuity problems

In this paper we give some results about convergence of non coercive quadratic integral functionals by examining the behaviour of coefficients. We apply our results to semicontinuity problems and we illustrate them by some examples.AMS Subject Classification: 40A10, 49J45.     

On the Representation of Approximate Subdifferentials for a Class of Generalized Convex Functions

Given a family of real-valued functions defined in a normed vector space X, we study a class of -convex functions having a simpler representation for the --subdifferential. The case =X^* with X being a Banach space (the Fenchel case) is particularly analysed, and we find that the sublinear lower semicontinuous functions satisfy the simpler representation with respect to X^*. As a side result, we provide various new subdifferential-type charaterizations of positively homogeneous functions among those which are lower semicontinuous and convex. In addition, we also discuss that family related to the the so-called prox-bounded functions. In this more general framework our simpler representation may give rise to a new notion of enlargement of the subdifferential.Mathematics Subject Classifications (2000) 47H05, 46B99, 47H17.This work is based on research material supported in part by CONICYT-Chile through FONDECYT 101-0116 and FONDAP-Matemáticas Aplicadas II.     

An algebraic approach to the vector ε-algorithm

The vector -algorithm is obtained from the scalar -algorithm by taking the pseudo-inverse of a vector instead of the inverse of a scalar. Thus the vector -algorithm is known only through its rules contrarily to the scalar -algorithm and some other extrapolation algorithms.The aim of this paper is to provide an algebraic approach to the vector -algorithm.     

Convergence of a generalized subgradient method for nondifferentiable convex optimization

A generalized subgradient method is considered which uses the subgradients at previous iterations as well as the subgradient at current point. This method is a direct generalization of the usual subgradient method. We provide two sets of convergence conditions of the generalized subgradient method. Our results provide a larger class of sequences which converge to a minimum point and more freedom of adjustment to accelerate the speed of convergence.Most of this research was performed when the first author was visiting Decision and Information Systems Department, College of Business, Arizona State University.     

Generalizations of Perfect, Semiperfect, and Semiregular Rings

For a ring R and a right R-module M, a submodule N of M is said to be -small in M if, whenever N + X = M with M/X singular, we have X = M. If there exists an epimorphism p: P M such that P is projective and Ker(p) is -small in P, then we say that P is a projective -cover of M. A ring R is called -perfect (resp., -semiperfect, -semiregular) if every R-module (resp., simple R-module, cyclically presented R-module) has a projective -cover. The class of all -perfect (resp., -semiperfect, -semiregular) rings contains properly the class of all right perfect (resp., semiperfect, semiregular) rings. This paper is devoted to various properties and characterizations of -perfect, -semiperfect, and -semiregular rings. We define (R) by (R)/Soc(R_R) = Jac(R/Soc(R_R)) and show, among others, the following results:

On the Operator Semirings of a Γ-Semiring

In this paper we introduce the notion of operator semirings of a -semiring to study -semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a -semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various -semirings.AMS Subject Classification (2000): 16Y60, 16Y99     

The ε-algorithm for the identification of a transfer-function model: some applications

The aim of this paper is to apply an algorithm related to the rational approximation for the identification of the lag structure in a transfer-function model. In fact, we apply the -algorithm proposed by Berlinet [3–5] to determine the polynomial orders in univariate and multivariate ARMA models. Furthermore, it has been proposed by Berlinet [5], González and Cano [13, 14] and González et al. [15] for a transfer-function model with one input and multiple inputs, respectively.The main contribution in this paper concerns the study of the relative significance of the elements in the -algorithm table, in the same way as that given by Berlinet and Francq [7] for ARMA models, to confirm the pattern used to specify the model. Two examples will be considered, namely, the sales series M [8] and a simulated model [20].A comparison is also made between the results of the -algorithm and the corner method generally used in the econometric literature. Although the -algorithm requires a more advanced theory in Numerical Analysis, it can be applied in a more simple way than the corner method.     

On Some Generalizations and Refinements of a Ky Fan Inequality

In this paper, a Ky Fan inequality and an inequality by Wu and Wang [10] will be generalized. Some new and improved refinements of the Ky Fan inequality will be put forward.AMS Subject Classification (2000) 26D15     

On Connectedness via Closure Operators

This paper describes a convenient modification of the approach presented in the paper Closure operators and connectedness by G. Castellini and D. Hajek, which is shown to give a suitable generalization of left- and right-constant subcategories, both at the object and the morphism levels. We show in particular that the framework we introduce here allows the simultaneous study of the classes of connected topological spaces, of concordant continuous maps and of monotone continuous maps.     

Almost flat locally finite coverings of the sphere

For any subset A of the unit sphere of a Banach space X and for [0,2) the notion of -flatness is introduced as a measure of non-flatness of A. For any positive , construction of locally finite tilings of the unit sphere by -flat sets is carried out under suitable -renormings of X in a quite general context; moreover, a characterization of spaces having separable dual is provided in terms of the existence of such tilings. Finally, relationships between the possibility of getting such tilings of the unit sphere in the given norm and smoothness properties of the norm are discussed.