Using weaker versions of the cardinal function $$\psi_c(X)$$ , we derive a series new bounds for cardinality Hausdorff spaces and regular that do not involve nor its variants at all. For example, show if X is then $$|X|\leq 2^{c(X)^{\pi\chi(X)}}$$ 2^{c(X)\pi\chi(X)^{ot(X)}}$$ where $$ot(X)$$ introduced by Tkachenko, has property $$ot(X)\leq\min\{t(X),c(X)\}$$ . It follows from latter space with...

In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, ...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

Six 1-month-old piglets were intravenously injected with deoxynivalenol (DON) at the concentration of 1 mg/kg body weight, with three pigs each necropsied at 6 and 24 h post-injection (PI) for investigation of hepatotoxicity and immunotoxicity with special attention to apoptotic changes and cytokine mRNA expression. Histopathological examination of the DON-injected pigs revealed systemic apopto...

A property of graphs is any class of graphs closed under isomorphism. Let P1,P2, . . . ,Pn be properties of graphs. A graph G is (P1,P2, . . . ,Pn)-partitionable if the vertex set V (G) can be partitioned into n sets, {V1, V2, . . . , Vn}, such that for each i = 1, 2, . . . , n, the graph G[Vi] ∈ Pi. We write P1◦P2◦ · · · ◦Pn for the property of all graphs which have a (P1,P2, . . . ,Pn)-partit...

A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs P1,P2, . . . ,Pn a vertex (P1,P2, . . . ,Pn)-partition of a graph G is a partition {V1, V2, . . . , Vn} of V (G) such that for each i = 1, 2, . . . , n the induced subgraph G[Vi] has property Pi. The class of all graphs having a vertex (P1,P2, . . . ,Pn)partition is denoted by P1◦P2◦ · · · ◦Pn....

In this study, we aimed to identify processes that enabled the involvement of a person with complex speech and motor disorders parent young these as co-researchers in U.K. research project. Semi-structured individual focus group interviews explored participants’ experiences perceptions public (PI). Sixteen participants were recruited, representation from (a) interdisciplinary project team; (b) ...