Search results for "Number"
showing 10 items of 3939 documents
FORMAL CONCEPTION OF ROUGH SETS
1996
In the paper we present a formal description of rough sets within the framework of the generalized set theory, which is interpreted in the set approximation theory. The rough sets are interpreted as approximations, which are defined by means of the Pawlak's rough sets.
Upper and lower generalized factoraggregations based on fuzzy equivalence relation
2014
We develop the concept of a general factoraggre-gation operator introduced by the authors on the basis of an equivalence relation and applied in two recent papers for analysis of bilevel linear programming solving parameters. In the paper this concept is generalized by using a fuzzy equivalence relation instead of the crisp one. By using a left-continuous t-norm and its residuum we define and investigate two modifications of such generalized construction: upper and lower generalized factoraggregations. These generalized factoraggregations can be used for construction of extensional fuzzy sets.
Partial $\ast$-algebras of distributions
2005
The problem of multiplying elements of the conjugate dual of certain kind of commutative generalized Hilbert algebras, which are dense in the set of C ∞ -vectors of a self-adjoint operator, is considered in the framework of the so-called duality method. The multiplication is defined by identifying each distribution with a multiplication operator acting on the natural rigged Hilbert space. Certain spaces, that are an
On a problem of L.A. Shemetkov on superradical formations of finite groups
2014
Abstract Subgroup-closed saturated formations F which are closed under taking products of F -subnormal F -subgroups are studied in the paper. Our results can be regarded as further developments in the hunt for a solution of a problem proposed by L.A. Shemetkov in 1999 in the Kourovka Notebook.
On formations of finite groups with the generalized Wielandt property for residuals II
2018
A formation [Formula: see text] of finite groups has the generalized Wielandt property for residuals, or [Formula: see text] is a GWP-formation, if the [Formula: see text]-residual of a group generated by two [Formula: see text]-subnormal subgroups is the subgroup generated by their [Formula: see text]-residuals. The main result of this paper describes a large family of GWP-formations to further the transparence of this kind of formations, and it can be regarded as a natural step toward the solution of the classification problem.
Degrees of Characters and Values on Prime Order Elements
2008
Two irreducible characters of a finite group with the same value on prime elements have the same degree.
On the group of the automorphisms of some algebraic systems
1968
Within a framework of general algebra we firstly formulate a proposition on the group of the automorphisms of some irreducible algebrae (id est algebrae without proper non trivial subalgebrae). This proposition includes as particular cases the uniqueness of the automorphisms of the rational field and the Burnside theorem on the commutant of an irreducible set of operators of a finite dimensional vector space over an algebraically closed field. Afterwards we apply the general proposition to modules with irreducible sets of semilinear operators and we obtain a theorem which generalises from several points of view the Burnside theorem. Finally we derive as an application a proposition which sp…
Miscellaneous Periods: An Outlook
2017
In this chapter, we collect several other important examples of periods in the literature for the convenience of the reader.
Some problems in number theory that arise from group theory
2021
In this expository paper, we present several open problems in number theory that have arisen while doing research in group theory. These problems are on arithmetical functions or partitions. Solving some of these problems would allow to solve some open problem in group theory.
A constructive semantics for non-deducibility
2008
This paper provides a constructive topological semantics for non-deducibility of a first order intuitionistic formula. Formal topology theory, in particular the recently introduced notion of a binary positivity predicate, and co-induction are two needful tools. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)