A note on quasi-Frobenius rings

It is shown that a semiperfect ring is quasi-Frobenius if and only if every closed submodule of is non-small, where denotes the direct sum of copies of the right -module and is the first infinite ordinal.

     

Completeness of perturbed systems of trigonometric functions

The paper addresses the completeness of perturbed systems of sines and cosines with non-integer indices and, moreover, complex, in the space of Lebesgue-integrable functions. The criteria for the variation from the integer value have been found such that sine and cosine systems are complete.     

Completeness criteria for some classes of unary monotone functions in P k

Systems of unary monotone functions of multi-valued logic are considered. These functions are monotone with respect to partial orders of special form. Criteria for the completeness of these functional systems are obtained.     

Completeness of systems of functions for classes of extended superposition

The problem of realization of Boolean functions by formulas of special type is considered. The notion of the supplement of systems of Boolean functions is defined. Criteria of completeness of the considered functional systems are obtained.     

Completeness of systems of entire functions in spaces of holomorphic functions

Letf be an entire function in . For a broad class of distribution densities of the set Λ, a scale of sufficient conditions for the completeness of the system of functions {f(λ×z):λ∈Λ},z∈E, where , in the spaceH(E) of holomorphic functions onE with respect to the topology of uniform convergence on compact subsets is given in terms of the mutual indicator of the functionf and the setE. These conditions are new already forn=1 even ifE is a disk. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 603–616, October, 1999.     

Linear dynamical systems over finite rings

The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the elementary divisors of the linear function, and the problem of determining whether the system is a fixed point system can be answered by computing and factoring the system's characteristic polynomial and minimal polynomial. It has become clear recently that the study of finite linear dynamical systems must be extended to embrace finite rings. The difficulty of dealing with an arbitrary finite commutative ring is that it lacks of unique factorization. In this paper, an efficient algorithm is provided for analyzing the cycle structure of a linear dynamical system over a finite commutative ring. In particular, for a given commutative ring R such that $|R|=q$, where q is a positive integer, the algorithm determines whether a given linear system over $R^n$ is a fixed point system or not in time $O(n^3\log (n\log (q)))$.     

Completeness of systems of functions,quasianalyticity and subharmonic majorants

In the paper one investigates completeness questions for certain frequently encountered systems of entire functions (for example, the completeness of the system of all entire functions of order not exceeding a given number ) in -spaces (for example, in C(E), E being a closed subset of R). Dual problems are the problems regarding the quasianatyticity of classes of functions, having Fourier transforms supported on a thin set. These latter problems are solved with the use of potential theory technique and with the aid of the investigation of conformal mappings of the upper half-plane onto special comb-like domains.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 102–156, 1989.     

Completeness of a functional system for surjective functions

Combining modalities has proven to have interesting applications and many approaches that combine time with other types of modalities have been developed. One of these approaches uses accessibility functions between flows of time to study the basic properties of the functions, such as being total or partial, injective, surjective, etc. The completeness of certain systems expressing many of these properties, with the exception of surjectivity, has been proven. In this paper we propose a language with nominals to denote the initial and final sets of each function in a model in order to obtain a complete system for reasoning about surjective partial functions.     

Completeness theory for finite partial algebras

LetA be a finite universe of cardinality ¦A¦ >- 3. We characterize the non quasi-diagonai strongly reflexive relations that determine maximal partial clones onA. Combining this with some known results, we deduce a general completeness criterion for finite partial algebras.Presented by J. Berman.Research partially supported by NSERC Canada.     

Polynomial functions and permutation polynomials over some finite commutative rings

We extend some classical results on polynomial functions . We prove all results in algebraic methods avoiding any combinatorial calculation. As applications of our methods, we obtain some interesting new results on permutation polynomials in several variables over some finite commutative rings.     

Limit-periodic arithmetical functions and the ring of finite integral adeles

In this paper, we show that the ring of finite integral adeles, together with its Borel field and its normalized Haar measure, is an appropriate probability space where limit-periodic arithmetical functions can be extended to random variables. The natural extensions of additive and multiplicative functions are studied. Besides, the convergence of Fourier expansions of limit-periodic functions is proved.     

One-dimensional local rings with reduced associated graded ring and their Hilbert functions

Let A be a one-dimensional reduced local ring with finite normalization. Let G(A) be the associated graded ring of A. In this paper we analyse the two conditions: Proj (G(A)) reduced and G(A) reduced together with their relations with the equality H(n)=H_R (n), where H(n) and H_R (n) are respectively the Hilbert function of the ring A and of the local ring R of G(A)_red=G(A)/nil (G(A)) at its homogenous maximal ideal. As a consequence of our results we get a class of ordinary singularities with H(n) locally decreasing for any embedding dimension H(1) greater then 4.