Annihilators in Normal Autometrized Algebras

The concepts of an annihilator and a relative annihilator in an autometrized l-algebra are introduced. It is shown that every relative annihilator in a normal autometrized l-algebra is an ideal of and every principal ideal of is an annihilator of . The set of all annihilators of forms a complete lattice. The concept of an I-polar is introduced for every ideal I of . The set of all I-polars is a complete lattice which becomes a two-element chain provided I is prime. The I-polars are characterized as pseudocomplements in the lattice of all ideals of containing I.     

Continuity of Stochastic Convolutions

Let B be a Brownian motion, and let be the space of all continuous periodic functions f with period 1. It is shown that the set of all f such that the stochastic convolution does not have a modification with bounded trajectories, and consequently does not have a continuous modification, is of the second Baire category.     

On posets with isomorphic interval posets

Let be a partially ordered set, Int the system of all (nonempty) intervals of partially ordered by the set-theoretical inclusion . We are interested in partially ordered sets with Int isomorphic to Int . We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If is a directed partially ordered set, the only with Int isomorphic to Int are corresponding to direct decompositions of ( denotes the dual of . The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11].     

Asymptotic behavior of solutions of A 2nth order nonlinear differential equation

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for

A Comparison on the Commutative Neutrix Convolution of Distributions and the Exchange Formula

Let , be ultradistributions in and let and where is a sequence in which converges to the Dirac-delta function . Then the neutrix product is defined on the space of ultradistributions as the neutrix limit of the sequence provided the limit exist in the sense that

On positive solutions of quasilinear elliptic systems

In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems where –_p is the p-Laplace operator, p > 1 and is a C ^1,-domain in . We prove an analogue of [7, 16] for the eigenvalue problem with and obtain a non-existence result of positive solutions for the general systems.     

Existence of Positive Solutions for a Class of Higher Order Neutral Functional Differential Equations

The higher order neutral functional differential equation

A Canonical Directly Infinite Ring

Let be the set of nonnegative integers and the ring of integers. Let be the ring of N × N matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of yields that the subrings generated by them coincide. This subring is the sum of the ideal consisting of all matrices in with only a finite number of nonzero entries and the subring of generated by the identity matrix. Regular elements are also described. We characterize all ideals of , show that all ideals are finitely generated and that not all ideals of are principal. Some general ring theoretic properties of are also established.     

Strictly Cyclic Algebra of Operators Acting on Banach Spaces H p(β)

Let be a sequence of positive numbers and 1 p< . We consider the space H ^p() of all power series such that . We investigate strict cyclicity of the weakly closed algebra generated by the operator of multiplication by zacting on H ^p(), and determine the maximal ideal space, the dual space and the reflexivity of the algebra . We also give a necessary condition for a composition operator to be bounded on H ^p() when is strictly cyclic.     

On intervals and isometries of MV-algebras

Let Int be the lattice of all intervals of an MV-algebra . In the present paper we investigate the relations between direct product decompositions of and (i) the lattice Int , or (ii) 2-periodic isometries on , respectively.     

Rings of maps: sequential convergence and completion

The ring B(R) of all real-valued measurable functions, carrying the pointwise convergence, is a sequential ring completion of the subring C(R) of all continuous functions and, similarly, the ring of all Borel measurable subsets of R is a sequential ring completion of the subring of all finite unions of half-open intervals; the two completions are not categorical. We study -rings of maps and develop a completion theory covering the two examples. In particular, the -fields of sets form an epireflective subcategory of the category of fields of sets and, for each field of sets , the generated -field yields its epireflection. Via zero-rings the theory can be applied to completions of special commutative -groups.     

Strongly Mixing Sequences of Measure Preserving Transformations

We call a sequence (T _n ) of measure preserving transformations strongly mixing if tends to P(A)P(B) for arbitrary measurable A, B. We investigate whether one can pass to a suitable subsequence such that almost surely for all (or "many") integrable f.     

Incidence Structures of Type (p, n)

Every incidence structure (understood as a triple of sets (G, M, I), I G×M) admits for every positive integer p an incidence structure where G ^p (M ^p) consists of all independent p-element subsets in G (M) and I ^p is determined by some bijections. In the paper such incidence structures are investigated the 's of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets G and M.     

The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals

We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil, , where R is a compact interval of , and f are functions with values on L(Z,W) and Z respectively, and Z and W are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral, , as well as to unbounded intervals R.     

The third boundary value problem in potential theory for domains with a piecewise smooth boundary

The paper investigates the third boundary value problem for the Laplace equation by the means of the potential theory. The solution is sought in the form of the Newtonian potential (1), (2), where is the unknown signed measure on the boundary. The boundary condition (4) is weakly characterized by a signed measure the corresponding operator on the space of signed measures on the boundary of the investigated domain G. If there is 0 such that the essential spectral radius of is smaller than || (for example, if G R ³ is a domain with a piecewise smooth boundary and the restriction of the Newtonian potential on G is a finite continuous functions) then the third problem is uniquely solvable in the form of a single layer potential (1) with the only exception which occurs if we study the Neumann problem for a bounded domain. In this case the problem is solvable for the boundary condition for which (G) = 0.     

Hypersurfaces in ℝn and critical points in their external region

In this paper we study the hypersurfaces given as connected compact regular fibers of a differentiable map , in the cases in which has finitely many nondegenerate critical points in the unbounded component of .     

Description of Simple Exceptional Sets in the Unit Ball

For z B ⁿ, the boundary of the unit ball in . If the exceptional set for f. In this note we give a tool for describing such sets. Moreover we prove that if Eis a G and F subset of the projective (n– 1)-dimensional space then there exists a holomorphic function fin the unit ball B ⁿso that E(f) = E.     

A Completion of \mathbb{Z} is a Field

We define various ring sequential convergences on and . We describe their properties and properties of their convergence completions. In particular, we define a convergence on by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields Further, we show that is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.     

Determinants of Matrices Associated with Incidence Functions on Posets

Let S = x ₁,...,x _n} be a finite subset of a partially ordered set P. Let f be an incidence function of P. Let denote the n × n matrix having f evaluated at the meet of x _i and x _j as its i, j-entry and denote the n × n matrix having f evaluated at the join of x _i and x _j as its i, j-entry. The set S is said to be meet-closed if for all 1 i, j n. In this paper we get explicit combinatorial formulas for the determinants of matrices and on any meet-closed set S. We also obtain necessary and sufficient conditions for the matrices and on any meet-closed set S to be nonsingular. Finally, we give some number-theoretic applications.     

On solutions of quasilinear wave equations with nonlinear damping terms

In this paper we consider the existence and asymptotic behavior of solutions of the following problem: