The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated by using the considered functions. Furthermore, the weak, strong and converse duality theor...

An elliptic equation ∇· (F (∇u)) = f whose ellipticity strongly degenerates for small values of ∇u (say, F = 0 on B(0, 1)) is considered. The aim is to prove regularity for F (∇u). The paper proves a continuity result in dimension two and presents some applications.

Let f(n) be a strongly additive complex valued arithmetic function. Under mild conditions on f , we prove the following weighted strong law of large numbers: if X, X1, X2, . . . is any sequence of integrable i.i.d. random variables, then lim N→∞ ∑ N n=1 f(n)Xn ∑ N n=1 f(n) a.s. = EX.

We characterize those functions f : C → C definable in o-minimal expansions of the reals for which the structure (C,+, f) is strongly minimal: such functions must be complex constructible, possibly after conjugating by a real matrix. In particular we prove a special case of the Zilber Dichotomy: an algebraically closed field is definable in certain strongly minimal structures which are definabl...

According to the definition of quasiweak almost periodic point, we introduce QWG(f) in paper. We studied topological structure G-quasiweak point set. have following two results: (1) Let (Y,d′) be a compact G–metric space and f : X → equicontinuous. {fn}∞n=1 G-strongly uniform converge map xk ∈ QWG(fn). If limk ∞ = x, then x QWG(f); (2) G-metric is f, lim sup QWG(fn) ⊂ QWG(f). The conclusions re...

We introduce the notion of an everywhere strongly logifiable algebra: a finite non-trivial algebra A such that for every F 2 P(A)r {;, A} the logic determined by the matrix hA, F i is a strongly algebraizable logic with equivalent algebraic semantics the variety generated by A. Then we show that everywhere strongly logifiable algebras belong to the field of universal algebra as well as to the o...

In 1982 Thomassen asked whether there exists an integer f(k, t) such that every strongly f(k, t)-connected tournament T admits a partition of its vertex set into t vertex classes V1, . . . , Vt such that for all i the subtournament T [Vi] induced on T by Vi is strongly k-connected. Our main result implies an affirmative answer to this question. In particular we show that f(k, t) = O(kt) suffice...

We consider the convex-concave saddle point problem minx maxy f(x) + y>Ax− g(y) where f is smooth and convex and g is smooth and strongly convex. We prove that if the coupling matrix A has full column rank, the vanilla primaldual gradient method can achieve linear convergence even if f is not strongly convex. Our result generalizes previous work which either requires f and g to be quadratic fun...

In this paper, we introduce a new function called tri-ĝ continuous in tri-topological spaces. A map f : X → Y is if f-1(V) closed for each tri-closed set V Y. Also define, quasi tri-ĝ. perfectly tri-ĝ, contra totally and strongly maps are introduced some of their properties studied.