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In this paper it is shown that, if a spacetime contains a Cauchy surface then the causally convex hulls of compact sets are compact. The converse is not true in general, however if the spacetime is causal then the compactness of causally convex hulls of compact sets of the spacetime ascertain the existence of a Cauchy surface. Also, the convex hull operator is denoted and some results regarding it has been explored.

INTRODUCTION: Having proper knowledge, attitude, and practices (KAP) towards chronic kidney disease (CKD) among type-2 diabetes mellitus (T2DM) patients is very important to reduce the disease burden. However, the information about KAP towards CKD among Bangladeshi T2DM patients is unknown, based on the available literatures till the date. OBJECTIVES: We aimed to assess the KAP towards CKD among T2DM patients attended a selected hospital in Dhaka city. METHODS AND MATERIALS: In this cross-sectional study, we conveniently selected Aalok hospital and also its 224 T2DM patients who attended the outdoor. We excluded the already developed CKD patients and aged over 70 years. We adopted a questionnaire from a validated instrument consisted of a 10 itemed knowledge, 8 itemed attitude, and 7 itemed practice domains towards CKD (total 25 items). Data were collected by face-to-face interviews. Both descriptive and comparative (Independent Sample t-tests and One-way ANOVA tests) statistics were used for data analysis where appropriates. RESULTS: Women respondents were higher (69.6%). The mean age of the respondents was 49.8±11.3 years. Most of them had average level of knowledge (69.6%) and attitude (60.7%). Majority also reported a good hypothetical practices in general if they would find out to have CKD. Knowledge was significantly associated (p

Let $R$ be an associative ring, $I$ a nonzero ideal of $R$ and $\sigma, \tau$ two epimorphisms of $R$. An additive mapping $F: R\rightarrow R$ is called a generalized $(\sigma,\tau)$-derivation of $R$ if there exists a $(\sigma,\tau)$-derivation $d: R\rightarrow R$ such that $F(xy)=F(x)\sigma(y)+\tau(x)d(y)$ holds for all $x,y\in R$. The objective of the present paper is to study the following situations in prime and semiprime rings: (i) $[F(x), x]_{\sigma,\tau} = 0$, (ii) $F([x, y]) = 0$, (iii) $F(x \circ y) = 0$, (iv) $F([x, y]) = [x, y]_{\sigma,\tau}$, (v) $F(x \circ y) = (x \circ y)_{\sigma,\tau}$, (vi) $F(xy)-\sigma(xy) \in Z(R)$, (vii) $F(x)F(y) -\sigma(xy) \in Z(R)$ for all $x,y\in I$, when $F$ is a generalized $(\sigma,\tau)$-derivation of $R$.