‎In this paper‎, ‎we introduce the notion of strongly $k-$spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)‎. ‎We characterize the strongly $k-$spaces and investigate the relationships between preclosedness‎, ‎locally strongly compactness‎, ‎pre-first countableness and being strongly $k-$space.

Introduction: Dynamic knee valgus and poor technique during landing are not only key risk factors for lower extremity injuries especially knee injury, it also can reduce performance. Sportsmetrics soccer training is one of the successful knee injury prevention and enhancement performance protocols in female soccer players. But, the effect of Sportsmetrics soccer training has not been investigat...

A space X is said to be strongly base-paracompact if there is a basis B for X with |B| = w(X) such that every open cover of X has a star-finite open refinement by members of B. Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions F with cardinality equal to the weight such that every open cover has a l...

In the theory of optimization an essential role is played by the differentiability of convex functions. In this paper we shall try to extend the results concerning differentiability to a larger class of functions called strongly α(·)-paraconvex. Let (X, ‖.‖) be a real Banach space. Let f(x) be a real valued strongly α(·)-paraconvex function defined on an open convex subset Ω ⊂ X , i.e. f ( tx+(...

We say a polynomial P over ZZM strongly M -represents a Boolean function F if F (x) ≡ P (x) (mod M) for all x ∈ {0, 1} . Similarly, P one-sidedly M -represents F if F (x) = 0 ⇐⇒ P (x) ≡ 0 (mod M) for all x ∈ {0, 1} . Lower bounds are obtained on the degree and the number of monomials of polynomials over ZZM , which strongly or one-sidedly M -represent the Boolean function deciding if a given nb...

In this paper, we prove the following results: Let K be a closed convex subset of a real Banach space E. Let T := {T (t) | t ∈ R+} be strongly continuous semigroup of asymptotically nonexpansive mappings from K into K such that F (T ) := ∩t∈R+F (T (t)) 6= ∅, where F (T (t)) = {x ∈ K |T (t)x = x} and R+ denotes the set of nonnegative real numbers. Then for arbitrary x0 ∈ K, the implicit iteratio...

We study isometries of the Kobayashi and Carathéodory metrics on strongly pseudoconvex and strongly convex domains in C and prove: (i) Let Ω1 and Ω2 be strongly pseudoconvex domains in C and f : Ω1 → Ω2 an isometry. Suppose that f extends as a C map to Ω̄1. Then f |∂Ω1 : ∂Ω1 → ∂Ω2 is a CR or anti-CR diffeomorphism. Hence it follows that Ω1 and Ω2 must be biholomorphic or anti-biholomorphic. (ii)...

Given a separable strongly self-concordant function f : Rn → R, we show the associated spectral function F(X) = ( f ◦ λ )(X) is also strongly self-concordant function. In addition, there is a universal constant O such that, if f (x) is separable self-concordant barrier then O2F(X) is a self-concordant barrier. We estimate that for the universal constant we have O ≤ 22. This generalizes the rela...

In this paper we obtain asymptotic expansion for the geometric mean of values positive strongly multiplicative function $f$ satisfying $f(p)=\alpha(d)\,p^d+O(p^{d-\delta})$ any prime $p$ with $d$ real and $\alpha(d),\delta>0$.

Let (,) be a measurable space with -finite continuous measure, ()=. A linear operator T:L1()+L()L1()+L() is called the Dunford-Schwartz if ||T(f)||1||f||1 (respectively, ||T(f)||||f||) for all fL1() fL()). {Tt}t0is strongly in L1() semigroup of operators, then each At(f)=1t∫0tTs(f)ds∈L1(Ω){{{A_t(f)} ={\frac{1}{t}} {\int_0^t} {T_s(f)} ds \in L_1(\Omega)}} has unique extension to operator, which ...