in this paper‎, ‎we consider a general integral operator $g_n(z).$ the main object of the present paper is to study some properties of this integral operator on the classes $mathcal{s}^{*}(alpha),$ $mathcal{k}(alpha),$ $mathcal{m}(beta),$ $mathcal{n}(beta)$ and $mathcal{kd}(mu,beta).$‎

A hypergraph $\mathcal H$ is super-pancyclic if for each $A \subseteq V(\mathcal H)$ with $|A| \geqslant 3$, contains a Berge cycle base vertex set $A$. We present two natural necessary conditions to be super-pancyclic, and show that in several classes of hypergraphs these are also sufficient. In particular, they sufficient every $ \delta(\mathcal H)\geqslant \max\{|V(\mathcal H)|, \frac{|E(\ma...

We deal with the question of Masayoshi Hata: is every Peano continuum a topological fractal? A compact space $X$ fractal if there exists $\mathcal{F}$ finite family self-maps on such that $X=\bigcup_{f\in\mathcal{F}}f(X)$ and for open cover $\mathcal{U}$ $n\in\mathbb{N}$ all maps $f_1,\dots,f_n\in\mathcal{F}$ set $f_1\circ\dots\circ f_n(X)$ contained in some $U\in\mathcal{U}$. In paper we prese...

The purpose of this paper is to study certain notions metric positivity called “minimal extension property” for the lowest nonzero piece in Hodge filtration a module. Let X be complex manifold and let $$\mathcal {M}$$ polarized pure module on with strict support X. $$F_p\mathcal smallest filtration. Assume that smooth outside closed analytic subset Z $$j:X\setminus \hookrightarrow X$$ open embe...

Let M be a monoid and \(G:\mathbf {Mon} \rightarrow \mathbf {Grp}\) the group completion functor from monoids to groups. Given collection \(\mathcal {X}\) of submonoids for each \(N\in \mathcal {Y}_N\) subgroups G(N), we construct model structure on category M-spaces M-equivariant maps, called \((\mathcal {X},\mathcal {Y})\)-model structure, in which weak equivalences fibrations are induced sta...

Partition identities are often statements asserting that the set \(\mathcal P_X\) of partitions n subject to condition X is equinumerous P_Y\) Y. A Beck-type identity a companion \(|\mathcal P_X|=|\mathcal P_Y|\) difference b(n) between number parts in all and equals \(c|\mathcal P_{X'}|\) also P_{Y'}|\), where c some constant related original identity, \(X'\), respectively \(Y'\), on very slig...

let $mathcal{a}$ and $mathcal{b}$ be two $c^{*}$-algebras such that $mathcal{b}$ is prime. in this paper, we investigate the additivity of maps $phi$ from $mathcal{a}$ onto $mathcal{b}$ that are bijective, unital and satisfy $phi(ap+eta pa^{*})=phi(a)phi(p)+eta phi(p)phi(a)^{*},$ for all $ainmathcal{a}$ and $pin{p_{1},i_{mathcal{a}}-p_{1}}$ where $p_{1}$ is a nontrivial projection in $mathcal{a...

Let $(X, \tau)$ and $(Y, \sigma)$ be topological spaces in which no separation axioms are assumed, unless explicitly stated if $\mathcal{I}$ is an ideal on $X$.Given a multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$, $\alpha,\beta$ operators \tau)$, $\theta,\delta$ proper $X$. We introduce study upper lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions.A said to...

Let $\mathcal {L}(X;Y)$ be the space of bounded linear operators from a Banach $X$ to $Y$. Given an operator-valued function $u:\mathbb {R}_{\geq 0}\rightarrow \mathcal {L}(X;Y)$, suppose that every orbit $t\mapsto u(t)x$ has re

For a frame $L$, consider the $f$-ring $ mathcal{F}_{mathcal P}L=Frm(mathcal{P}(mathbb R), L)$. In this paper, first we show that each minimal ideal of $ mathcal{F}_{mathcal P}L$ is a principal ideal generated by $f_a$, where $a$ is an atom of $L$. Then we show that if $L$ is an $mathcal{F}_{mathcal P}$-completely regular frame, then the socle of $ mathcal{F}_{mathcal P}L$ consists of those $f$...