for all w, x, y and showed by example that (1.1) can fail to hold. Prior to this, Kleinfeld [l ] generalized the Skornyakov theorem in another direction by assuming only the absence of one sort of nilpotent element. We now specify Kleinfeld's result in detail. Let F be the free nonassociative ring generated by Xi and x2 and suppose that R is any right alternative ring. Kleinfeld calls t, u, v i...

The lecture is devoted to general characteristic and prevalence of criminal offenses against property, their types are considered. main attention paid illegal mercenary acts related the seizure (or) circulation other people's property in favor perpetrator or persons: analysis provided at generic level; signs (physical, economic, social, legal) as subject encroachment on considered; meanings ter...

The purpose of this paper is to illustrate the relationship between the topological property of the Euler characteristic and a combinatorial object, the Möbius function, in the context of finite T0-spaces. To do this I first explain the fundamental connection between such spaces and finite partially ordered sets by proving some facts fundamental to the study of finite spaces. Then I define the ...

1.1 Complex random variables 1.2 Definition and basic properties of characteristic functions 1.3 Examples 1.4 Inversion formulas 2. Applications 2.1 Characteristic function for sum of independent random variables 2.2 Characteristic functions and moments of random variables 2.3 Continuity theorem 2.4 Weak law of large numbers 2.5 Central Limit theorem 2.6 Law of small numbers 1. Definition of ch...

For a first-order formula φ(x; y) we introduce and study the characteristic sequence 〈Pn : n < ω〉 of hypergraphs defined by Pn(y1, . . . , yn) := (∃x) ∧ i≤n φ(x; yi). We show that combinatorial and classification theoretic properties of the characteristic sequence reflect classification theoretic properties of φ and vice versa. The main results are a characterization of NIP and of simplicity in...

We compute the gluon distribution in deep inelastic scattering at small x by solving numerically the angular ordering evolution equation. The leading order contribution , obtained by neglecting angular ordering, satisfies the BFKL equation. Our aim is the analysis of the subleading corrections. Although not complete — the exact next-to-leading contribution is not yet available — these correctio...

The classification of preservers began about 100 years ago. In 1897, Frobenius characterized the linear operators on Mn which preserve certain matrix functions: those linear operators on Mn preserves the determinant and those preserves the characteristic polynomial (spectrum). He proved that if M M n n → : T is a linear transformation satisfying) det()) (T det(A A = , M A n ∈ , then either UAV ...