If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ-strategically closed forcing and λ is weakly compact, then we show that A = {δ < κ | δ is a non-weakly compact Mahlo cardinal which reflects stationary sets} must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to cons...

A weakly o-minimal structure M = (M,≤,+, . . .) expanding an ordered group (M,≤, +) is called non-valuational iff for every cut 〈C,D〉 of (M,≤) definable in M, we have that inf{y − x : x ∈ C, y ∈ D} = 0. The study of non-valuational weakly o-minimal expansions of real closed fields carried out in [MMS] suggests that this class is very close to the class of o-minimal expansions of real closed fie...

Order statistics arising from exponentiated gamma (EG) distribution are considered. Closed from expressions for the single and double moments of order statistics are derived. Measures of skewness and kurtosis of the probability density function of the rth order statistic for different choices of r, n&nbsp;and /theta&nbsp;are presented. Recurrence relations between single and double moments of r...

In this paper, we will define a new class of sets, called fuzzy neutrosophic weakly- generalized closed then proved some theorems related to definition. After that, studied relations between weakly-generalized sets and α regular pre semi sets.

Submodular functions are a broad class of set functions, which naturally arise in diverse areas such as economics, operations research and game theory. Many algorithms have been suggested for the maximization of these functions, achieving both strong theoretical guarantees and good practical performance. Unfortunately, once the function deviates from submodularity (even slightly), the known alg...

we consider the space of weakly almost periodic functions on a transformation semigroup (s, x , ?) and show that if x is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of s on x, then every continuous function on x, vanishing at infinity is weakly almost periodic. we also use a number of diverse examples to show that th...

We prove that the class of Banach function lattices in which all relatively weakly compact sets are equi-integrable (i.e. spaces satisfying Dunford–Pettis criterion) coincides with 1-disjointly homogeneous lattices. New examples such provided. Furthermore, it is shown criterion equivalent to de la Valleé Poussin rearrangement invariant on interval. Finally, results applied characterize pointwis...

An operator T : E → X between a Banach lattice E and a Banach space X is called b-weakly compact if T (B) is relatively weakly compact for each b-bounded set B in E. We characterize b-weakly compact operators among o-weakly compact operators. We show summing operators are b-weakly compact and discuss relation between Dunford–Pettis and b-weakly compact operators. We give necessary conditions fo...