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.     

On Some Isomorphism on the Category of b-Spaces

Given a nuclear b-space N, we show that if is a finite or -finite measure space and 1p, then the functors L _loc ^p (,N.) and NL ^p (,.) are isomorphic on the category of b-spaces of L. Waelbroeck.     

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.     

An intelligent decision support system for assisting industrial wastewater management

Sustainable economic development requires the inclusion of environmental factors in the decision making procedure. The generic objective of the Environmentally Sensitive Investment System (ESIS) Project is to provide industry and governmental departments or agencies with a tool to assess the technical and economic implications of capital-intensive projects, in response to stated environmental policies. More specifically, the ESIS prototype helps to find wastewater management alternatives that meet given environmental regulatory standards in a technologically sound and cost-efficient manner. The use of this decision support system will enhance the ability of managers and planners to explore the quantitative implications of a wide range of options. ESIS incorporates a combination of artificial intelligence and operations research techniques, database management and visualization tools, integrated under a graphical user interface. The ESIS prototype runs on top-of-the-line personal computers.     

A Characterization of Markov Property for Semigroups with Invariant Measure

The positivity of the carré du champ operator is a direct consequence of the positivity of the associated Markov semigroup. We show in this note that the reciprocal implication holds in invariant measure, under minimal hypotheses of continuity and stability.     

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.     

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.     

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.     

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.     

A successive quadratic programming method for a class of constrained nonsmooth optimization problems

In this paper we present an algorithm for solving nonlinear programming problems where the objective function contains a possibly nonsmooth convex term. The algorithm successively solves direction finding subproblems which are quadratic programming problems constructed by exploiting the special feature of the objective function. An exact penalty function is used to determine a step-size, once a search direction thus obtained is judged to yield a sufficient reduction in the penalty function value. The penalty parameter is adjusted to a suitable value automatically. Under appropriate assumptions, the algorithm is shown to produce an approximate optimal solution to the problem with any desirable accuracy in a finite number of iterations.     

Hulls for Various Kinds of α-Completeness in Archimedean Lattice-Ordered Groups

Within Archimedean -groups, and with an infinite cardinal or , we consider X-hulls where X stands for any of the following classes of -groups: -projectable; laterally -complete; boundedly laterally -complete; conditionally -complete; combinations of the preceding, together with divisibility and/or relative uniform completeness. All these hulls exist, and may be obtained by iterated adjunction of the required extra elements, within the essential hull. When the -groups is relatively -complemented one step in the iteration suffices for several crucial properties. We derive from the above a considerable number of equations involving combinations of these hull operators.     

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     

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.     

Almost π-Lattices

In this paper we establish some conditions for an almost -domain to be a -domain. Next -lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for -rings.     

Uniform probability

A general theory of uniform probability is developed for compact metric spaces, which agrees with Lebesgue measure, Haar measure, and various fractal measures in specific cases.     

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.     

Non-commutative extrapolation algorithms

This paper contains two general results. The first is an extension of the theory of general linear extrapolation methods to a non-commutative field (or even a non-commutative unitary ring). The second one, by exploiting these new results, is to solve an old conjecture about Wynn's vector -algorithm. Then, by using designants and Clifford algebras, we show how the vectors _k ⁽ⁿ⁾ can be written as a ratio of two designants.This result allow us to find, as a particular case, some well-known results and some others which are new.     

On <Emphasis Type="Italic">L</Emphasis><Subscript>α,ω</Subscript> complete extensions of complete theories of Boolean algebras

For a complete first order theory of Boolean algebras T which has nonisomorphic countable models, we determine the first limit ordinal = (T) such that We show that for some and for all other Ts, A nonprincipal ideal I of B is almost principal, if a is a principal ideal of B} is a maximal ideal of B. We show that the theory of Boolean algebras with an almost principal ideal has complete extensions and characterize them by invariants similar to the Tarskis invariants.Mathematics Subject Classification (2000): Primary 03C15, Secondary 03C35, 06E05Revised version: 2 February 2004