On the lattice of deductive systems of a BL-algebra

For a BL-algebra A we denote by Ds(A) the lattice of all deductive systems of A. The aim of this paper is to put in evidence new characterizations for the meet-irreducible elements on Ds(A). Hyperarchimedean BL-algebras, too, are characterized.     

A geometric theory of harmonic and semi-conformal maps

We describe for any Riemannian manifold M a certain scheme M _L , lying in between the first and second neighbourhood of the diagonal of M. Semi-conformal maps between Riemannian manifolds are then analyzed as those maps that preserve M _L ; harmonic maps are analyzed as those that preserve the (Levi-Civita-) mirror image formation inside M _L .     

On the best linear approximation methods and the widths of certain classes of analytic functions

We discuss the best linear approximation methods in the Hardy spaceH _q q≥1, for classes of analytic functions studied by N. Ainulloev; these are generalizations (in a certain sense) of function sets introduced by L. V. Taikov. The exact values of their linear and Gelfandn-widths are obtained. The exact values of the Kolmogorov and Bernsteinn-widths of classes of analytic (in |z|<1) functions whose boundaryK-functionals are majorized by a prescribed functions are also obtained. Translated fromMatermaticheskie Zametki, Vol. 65, No. 2, pp. 186–193, February, 1999.     

Nonadaptive search problem with sets of equal sum

Consider the set A={1,2,3,…,2 ⁿ }, n≥3 and let x∈ A be unknown element. For given natural number S we are allowed to ask whether x belongs to a subset B of A such that the sum of the elements of B equals S. We investigate for which S it is possible to find x using a nonadaptive search.     

On Macbeath-Singerman symmetries of Belyi surfaces with PSL(2,p) as a group of automorphisms

The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called Belyi surfaces. The groups PSL(2,q),q=p ⁿ are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied in the literature. In this paper, we deal with symmetries. Singerman showed, using acertain result of Macbeath, that such surfaces admit a symmetry which we shall call in this paper the Macbeath-Singerman symmetry. A classical theorem by Harnack states that the set of fixed points of a symmetry of a Riemann surface X of genus g consists of k disjoint Jordan curves called ovals for some k ranging between 0 and g+1. In this paper we show that given an odd prime p, a Macbetah-Singerman symmetry of Belyi surface with PSL(2,p) as a group of automorphisms has at most     

The Algebraic K-Theory of Operator Algebras

We the study the algebraic K-theory of C *-algebras, forgetting the topology. The main results include a proof that commutative C*-algebras are K-regular in all degrees (that is, all theirN ^T K _iand extensions of the Fischer-Prasolov Theorem comparing algebraic and topological K-theory with finite coefficients.     

Monadic <Emphasis Type="Italic">GMV</Emphasis>-algebras

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed. The first author was supported by the Council of Czech Government, MSM 6198959214.     

The L p -curvature images of convex bodies and L p -projection bodies

Associated with the L _p -curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L _p -projection bodies are established. As a natural extension of a result due to Lutwak, an L _p -type affine isoperimetric inequality, whose special cases are L _p -Busemann-Petty centroid inequality and L _p -affine projection inequality, respectively, is established. Some L _p -mixed volume inequalities involving L _p -projection bodies are also established.     

On k-primitivity of two classes of digraphs

In this paper, we study two classes of primitive digraphs, and show that there are k-colorings that are k-primitive.     

Flatness properties of diagonal acts over monoids

If S is a monoid, the right S-act S×S, equipped with componentwise S-action, is called the diagonal act of S. The question of when this act is cyclic or finitely generated has been a subject of interest for many years, but so far there has been no explicit work devoted to flatness properties of diagonal acts. Considered as a right S-act, the monoid S is free, and thus is also projective, flat, weakly flat, and so on. In 1991, Bulman-Fleming gave conditions on S under which all right acts S ^I (for I a non-empty set) are projective (or, equivalently, when all products of projective right S-acts are projective). At approximately the same time, Victoria Gould solved the corresponding problem for strong flatness. Implicitly, Gould’s result also answers the question for condition (P) and condition (E). For products of flats, weakly flats, etc. to again have the same property, there are some published results as well. The specific questions of when S×S has certain flatness properties have so far not been considered. In this paper, we will address these problems. S. Bulman-Fleming research supported by Natural Sciences and Engineering Research Council of Canada Research Grant A4494. Some of the results in this article are contained in the M.Math. thesis of A. Gilmour, University of Waterloo (2007).     

Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point

In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R ^k →Y is a C ²-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R ¹ that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ₀)∈X×R ^k and we describe the solution set of the studied equation in a small neighbourhood of this point.     

On some properties of the functions from Sobolev-Morrey type spaces

In this paper the spaces of type Sobolev-Morrey-W _p,a,г,τ ^l (Q,G)-are constructed, the differential properties are studied and it is proved that the functions from these spaces satisfy Holder's condition, in the case, if the domain G∋R ⁿ satisfies the flexible λ-horn condition.     

Reliability formula &; limit law of the failure time of “<Emphasis Type="Italic">m</Emphasis>-consecutive-<Emphasis Type="Italic">k</Emphasis>-out-of-<Emphasis Type="Italic">n</Emphasis>:<Emphasis Type="Italic">F</Emphasis> system”

An “m-consecutive-k-out-of-n:F system” consists of n components ordered on a line; the system fails if and only if there are at least m nonoverlapping runs of k consecutive failed components. In this paper, we give a recursive formula to compute the reliability of such a system. Thereafter, we state two asymptotic results concerning the failure time Z _n of the system. The first result concerns a limit theorem for Z _n when the failure times of components are not necessarily with identical failure distributions. In the second one, we prove that, for an arbitrary common failure distribution of components, the limit system failure distribution is always of the Poisson class.      

On the topology of spherically symmetric space-times

Spherically symmetric space-times have attained considerable attention ever since the early beginnings of the theory of general relativity. In fact, they have appeared already in the papers of K. Schwarzschild [12] and W. De Sitter [5] which were published in 1916 and 1917 respectively soon after Einstein's epoch-making work [7] in 1915. The present survey is concerned mainly with recent results pertainig to the toplogy of spherically symmetric space-times. Definition. By space-time a connected time-oriented 4-dimensional Lorentz manifold is meant. If (M,<,>) is a space-time, and Φ: SO(3)×M→M an isometric action such that the maximal dimension of its orbits is equal to 2, then the action Φ is said to be spherical and the space-time is said to be spherically symmetric [8]; [11]. Likewise, isometric actions Ψ: O(3)×M→M are also considered ([10], p. 365; [4]) which will be called quasi-spherical if the maximal dimension of its orbits is 2 and then the space-time is said to be quasi-spherically symmetric here. Each quasi-spherical action yields a spherical one by restricting it to the action of SO(3); the converse of this statement will be considered elsewhere. The main results concerning spherically symmetric space-times are generally either of local character or pertaining to topologically restricted simple situations [14], and earlier results of global character are scarce [1], [4], [6], [13]. A report on recent results concerning the global geometry of spherically symmetric space-times [16] is presented below.     

k-systems, k-networks and k-covers

The concepts of k-systems, k-networks and k-covers were defined by A. Arhangel’skii in 1964, P. O’Meara in 1971 and R. McCoy, I. Ntantu in 1985, respectively. In this paper the relationships among k-systems, k-networks and k-covers are further discussed and are established by mk-systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given by means of mk-systems.     

A Method of Deducing L-Polyhedra for n-Lattices

We suggest a method for selecting an L-simplex in an L-polyhedron of an n-lattice in Euclidean space. By taking into account the specific form of the condition that a simplex in the lattice is an L-simplex and by considering a simplex selected from an L-polyhedron, we present a new method for describing all types of L-polyhedra in lattices of given dimension n. We apply the method to deduce all types of L-polyhedra in n-dimensional lattices for n=2,3,4, which are already known from previous results.     

I-convergence theorems for a class of k-positive linear operators

In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.      

The minimizing of the Nielsen root classes

Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M ₂)−χ(M ₁0/(1−χ(M ₂)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M ₂)−χ(M ₂)/(1−χ(M ₂)). Also we construct, for each integer n≥3, an example of a map f: K _n →N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time.     

A Note on Geometric Structures of Linear Ordered Orthogonal Arrays and (T,M,S)-Nets of Low Strength

The equivalent geometrical configurations of linear ordered orthogonal arrays are determined when their strengths are 3 and 4. Existence of such geometrical configurations is investigated. They are also useful in the study of (T, M, S)-nets.