Une approche transformationnelle a l'algebre universelle

In this paper we propose an axiomatization of the notion of system of terms of a theory by means of which we obtain a representation of equational classes (or varieties) of algebras. We define analgebraic transformational system (S.T.A.) as a quadruple (T,v,S,+) satisfying the axioms, where T is a set containing the variables v(n), n, and having operators S(): TT, . In addition there are operations Q⁺ on T commuting with the operators. A notion of morphism between S.T.A. 's is defined to obtain the category which is shown to be equivalent to the dual of the category of equational classes. In the last section we establish the equivalence between and Lawvere's category of algebraic theories in which every definable constant is present.

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Extrait de la Thèse de doctorat de l'auteur, Université de Montréal, 1971.     

OnU ϕ-sets of trigonometric integrals

, (t) >0 E(–, +),E<, , ¦f(t)¦ (t) xE, f(t)=0 (–, +).     

Invariant Subspaces for Positive Operators Acting on a Banach Space with Markushevich Basis

We introduce weak quasinilpotence for operators. Then, by substituting Markushevich basis and weak quasinilpotence at a nonzero vector for Schauder basis and quasinilpotence at a nonzero vector, respectively, we answer a question on the invariant subspaces of positive operators in [3].     

Approximation of functions of several variables by trigonometric polynomials with given number of harmonics,and estimates of ε-entropy

. - . .. . . . , 340 048 . 1      

WT measure vector spaces

n- M WT- , M n–1 . . WT- . .     

On the exactness of a theorem of G.A. Fomin

, . . [1] - . .     

Асимптоический Анализ Распределения Статистики Диксона

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О лагранжевом интерполировании с узлами в корнях многочленов сонина-маркова

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Zur Vollständigkeit der Induktiven Gruppoide der Partiellen Automorphismen von Algebren

For any algebraA let(A) be the set of partial automorphisms (isomorphisms between subalgebras). With the natural multiplication it is an inductive groupoid in the sense of Ehresmann.(A) is complete iff every subset of(A) which is compatible with the semi-ordering has an upper bound. The fact, whether(A) is complete or not, depends on the defining operations ofA. For every direct familyF = (, (A ) ,()_, , of algebras such that all ,, with are one-to-one functions, the direct limit is complete iff all(A) are complete. We give some theorems on the decomposition of inductive groupoids, and employ them in proving the completeness of(A) to variousA.In particular, we obtain that, in case whenG is a finite group,(G) is complete iffG is either cyclic or direct product of a noncyclic group of order 4 and a cyclic group of odd order. For finite acyclic ringsR and finite fieldsK the inductive groupoids(R) and(K) are complete.Further we deal with the question, to what extent algebras are determined by their inductive groupoids. (An algebraA of a classS is defined by(A) iff, for any algebraB of the classS, isomorphism between(A) and(B) implies isomorphism betweenA andB.) Particular attention is paid to finite groups. In general, algebras of classesS are not defined within the classS by their inductive groupoids.

     

Interpolation and best polynomial approximation in the domain ofp-adic integers

, , . , . Lip

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The authors are indebted to Professor R. Bojanic for his valuable remarks and suggestions, especially for the simplification of the proof of Theorem 4.     

Identification of the Optimal Active Set in a Noninterior Continuation Method for LCP

This paper concerns about the possibility of identifying the active set in a noninterior continuation method for solving the standard linear complementarity problem based on the algorithm and theory presented by Burke and Xu (J. Optim. Theory Appl. 112 (2002) 53). It is shown that under the assumptions of P-matrix and nondegeneracy, the algorithm requires at most Olog(₀₀/)) iterations to find the optimal active set, where ₀ is the width of the neighborhood which depends on the initial point, ₀> 0 is the initial smoothing parameter, is a positive number which depends on the problem and the initial point, and is a small positive number which depends only on the problem.     

τ-Pseudocompact Mappings

We consider the problem of extending the notion of -pseudocompactness from spaces to continuous mappings, obtain conditions under which the product of -pseudocompact mappings is -pseudocompact. Since any space X can be considered as a continuous mapping from X into a singleton, we obtain consequences of the theorems on multiplicativity of -pseudocompactness for spaces. Thus, we study the notion of -pseudocompact mapping and some its properties similar to those of a pseudocompact space as well as consequences of the obtained assertions for spaces.     

On the admissibility of function spaces of typeB p,q s andF p,q s,and boundary value problems for non-linear partial differential equations

u=f(x)+S(u), S — , u-G(u), G — . B _p,q ^s () -F _p,q ^s (). R _n — . — . _p,q ^s F _p,q ^s .     

Convergence of splitting and Newton methods for complementarity problems: An application of some sensitivity results

This paper is concerned with two well-known families of iterative methods for solving the linear and nonlinear complementarity problems. For the linear complementarity problem, we consider the class of matrix splitting methods and establish, under a finiteness assumption on the number of solutions, a necessary and sufficient condition for the convergence of the sequence of iterates produced. A rate of convergence result for this class of methods is also derived under a stability assumption on the limit solution. For the nonlinear complementarity problem, we establish the convergence of the Newton method under the assumption of a pseudo-regular solution which generalizes Robinson's concept of a strongly regular solution. In both instances, the convergence proofs rely on a common sensitivity result of the linear complementarity problem under perturbation.This work was based on research supported by the National Science Foundation under grant ECS-8717968.     

On equivalence of rearrangements of the Haar system in dyadic Hardy and BMO spaces

H={h ₁,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H ={h _(I),I} . , , . L ^p .

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Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday

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This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153.     

On maximum entropy interpolants and maximum determinant completions of associated Pick matrices

In this paper we shall show that the value of the maximum -entropy solution of an interpolation problem of the Nevanlinna-Pick type at the point maximizes the determinant of the solution of an associated matrix completion problem. This serves to show that the solutions of two distinct extremal problems coincide.Harry Dym wishes to express his thanks to Renee' and Jay Weiss for endowing the chair which supports his research.     

A generalization of second variation

f p- , l p . p=1 . . p - , f -.     

Bounds for the nonhomogeneous GASPT equation

Summary Weighted a priori bounds for the equation u+(/y)u_y=f(>0), in the halfplane y>0, are proved. If p>1, 0<+p^–1<1+, u has bounded support and y^µu_y0 (as y0₊), then the L^p norms of uu and yD²u are bounded by the L^p norm of yf. A boundary value problem in a rectangle is also studied in the appropriate weighted Sobolev class.Lavoro eseguito nell'ambito dell'Istituto di Analisi Globale ed Applicazioni del C.N.R.Lavoro eseguito nell'ambito del Gruppo Nazionale di Analisi Funzionale ed Applicazioni del C.N.R.     

Sur la répartition des valeurs de la fonction d'Euler

Let (x) denote the number of those integers n with (n) x, where denotes the Euler function. Improving on a well-known estimate of Bateman (1972), we show that (x)-Ax R(x), where A=(2)(3)/(6) and R(x) is essentially of the size of the best available estimate for the remainder term in the prime number theorem.     

Metric Density and Quasimobius Mappings

We study the notion of -density of metric spaces which was introduced by V. Aseev and D. Trotsenko. Interrelation between -density and homogeneous density is established. We also characterize -dense spaces as arcwise connected metric spaces in which arcs are the quasimobius images of the middle-third Cantor set. Finally, we characterize quasiconformal self-mappings of ⁿ in terms of -density.