In set theory without the axiom of choice (AC), we observe new relations following statements with weak principles. $\circ$ If in a partially ordered set, all chains are finite and antichains countable, then is countable. have size $\aleph_{\alpha}$, has $\aleph_{\alpha}$ for any regular $\aleph_{\alpha}$. Every maximal element two disjoint cofinal sub sets -- CS. well-founded subset CWF. Dilwo...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

We present a notion of convergence for sequences of finite graphs {Gn} that can be seen as a generalization of the Benjamini-Schramm convergence notion for bounded degree graphs, regarding the distribution of r-neighbourhoods of the vertices, and the left-convergence notion for dense graphs, regarding, given any finite graph F , the limit of the probabilities that a random map from V (F ) to V ...

Background. Imagery ability is one of the most potent factors influencing imagery effectiveness. Therefore, prior to imagery training, it is important to assess the participant’s imagery ability, typically using a self-report questionnaire. Objectives. This study examined the factorial validity and internal consistency of the Malaysian adapted SIAQ using confirmatory factor analysis and Cronba...

Given a finite and connected two-dimensional CW complex K with fundamental group $$\Pi $$ second integer cohomology $$H^2(K;\mathbb {Z})$$ of odd order, we prove that: (1) for each local coefficient system $$\alpha :\Pi \rightarrow \textrm{Aut}(\mathbb over K, the corresponding twisted $$H^2(K;_{\alpha }\!\mathbb is say order $$\mathfrak {c}^{*}(\alpha )$$ , there exists natural function—which ...

This paper introduces accumulation into list homomorphisms for systematic development of both efficient and correct parallel programs. New parallelizable recursive pattern called H-homomorphism is given, and transformations from sequential patterns in the H-form and Hform into (H-)homomorphism are shown. We illustrate the power of our formalization by developing a novel and general parallel pro...

‎let $m$ be a non-zero finitely generated module over a commutative noetherian local ring $(r,mathfrak{m})$ with $dim_r(m)=t$‎. ‎let $i$ be an ideal of $r$ with $grade(i,m)=c$‎. ‎in this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎the main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎tor^{r}_c(k,h^c_i(m))to kotim...

Twelve children, ranging in age from 8.9 to 12.4 years, with histories of severe otitis media with effusion (OME) before age 3, were compared to age-matched cohorts in their ability to discriminate the frequency of tone pulses of 20-, 50-, and 200-msec duration. An adaptive procedure was used in combination with a two-alternative forced-choice paradigm to measure difference limens (DLs) for dig...