We present a way out of Russell's paradox for sets in the form of a direct weakening of the usual inconsistent full comjprehension axiom scheme, which, with no additional axioms, interprets ZFC. In fact, the resulting axiomatic theory 1) is a subsystem of ZFC + “there exists arbitrarily large...

It is proved that the homology and cohomology theories of groups and associative algebras are non-abelian derived functors of the cokernel and kernel groups of higher dimensions of their defining standard chain and cochain complexes respectively. The same results are also obtained for the...

We study quasitriangular structures in the * which is the twisted smash product Hopf algebra. As an application, we consider a class of non-commutative and non-cocommutative Hopf algebras (, , , ) which are pointed non semisimple, and establish quasitriangular structures on (, , , ). Another...

A method of multivariate data compression is presented, based on a minimization of nodes number under an accuracy threshold. For making smooth restoration of the original data, a procedure of simplicial subdivision is used. Local functions are generated in nodes and finally they merge together...

An of a graph with edges and vertices is a bijection from the set of edges to the integers 1 such that all vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with the same vertex. A graph is called if it has an antimagic labeling. A conjecture of...

Smoothness results are estalished for hyper quasilinear systems of second order with data on two intersecting null hypersurfaces.Problème de Cauchy-Goursat pour des systèmes hyper quasi-linéaires hyperboliquesRésumé Des résultats de régularité sont établis pour des systèmes hyper...

Let be a positive Borel measure on ℝ and (, . . . , ; , . . . , ; ) be a generalized hypergeometric series. We define a := (, . . . , ; , . . . , ), as a series of convolution powers of the measure , and we investigate probability distributions which are expressible as generalized...

Let denote a field and let denote a vector space over with finite positive dimension. We consider an ordered pair of linear transformations : and : which satisfy both (i), (ii) below.(i) There exists a basis for with respect to which the matrix representing is irreducible tridiagonal and the...

“Sentential reflection” in the sense of [Fr03] is based on reflecting down from a category of classes. “Elemental sentential reflection” is based on reflecting down from a category of elemental classes. We present various forms of elemental sentential reflection, which are shown to...