We construct a model containing a proper class of strongly compact cardinals in which no strongly compact cardinal κ is κ supercompact and in which every strongly compact cardinal has its strong compactness resurrectible.

The main objectives of this paper are to introduce the concept pairwise countably compact in bitopological space,and we some generalization spaces, and their properties, relate it other spaces.

A new approach to regression regularization called the Pairwise Elastic Net is proposed. Like the Elastic Net, it simultaneously performs automatic variable selection and continuous shrinkage. In addition, the Pairwise Elastic Net encourages the grouping of strongly correlated predictors based on a pairwise similarity measure. We give examples of how the approach can be used to achieve the obje...

Let H 0(X) (H(X)) denote the set of all (nonempty) closed subsets of X endowed with the Vietoris topology. A basic problem concerning H(X) is to characterize those X for which H(X) is countably compact. We conjecture that u-compactness of X for some u ∈ ω∗ (or equivalently: all powers of X are countably compact) may be such a characterization. We give some results that point into this direction...

We investigate the indestructibility properties of strongly compact cardinals in universes where strong compactness suffers from identity crisis. We construct an iterative poset that can be used to establish Kimchi-Magidor theorem from [22], i.e., that the first n strongly compact cardinals can be the first n measurable cardinals. As an application, we show that the first n strongly compact car...

We introduce the property ``$F$-linked'' of subsets posets for a given free filter $F$ on natural numbers, and define properties ``$\mu$-$F$-linked'' ``$\theta$-$F$-Knaster'' in way. show that $\theta$-$F$-Knaster preserve strong types unbounded families maximal almost disjoint families. Concerning iterations such posets, we develop general technique to construct $\theta$-$\mathrm{Fr}$-Knaster ...

Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...

We prove that there are infinitely many pairwise non-commensurable hyperbolic $n$-manifolds have the same ambient group and trace ring, for any $n \geq 3$. The manifolds can be chosen compact if 4$.

Proteins are responsible for most of the functions in life, and thus are the central focus of many areas of biomedicine. Protein structure is strongly related to protein function, but is difficult to elucidate experimentally, therefore computational structure prediction is a crucial task on the way to solve many biological questions. A contact map is a compact representation of the three-dimens...