in this paper, the numerical technique based on hybrid bernoulli and block-pulse functions has been developed to approximate the solution of system of linear volterra integral equations. system of volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. these functions are formed by the hybridi...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

This article presents an innovative way to engage schoolchildren in discussions on multilingualism and multilingual identity using research data they helped generate. Adopting exploratory, participatory approach research, our study uses digital visualisations interactive sessions aimed at engaging lower secondary students formation negotiation. The paper starts with a contextualisation of langu...

In order to better understand how junior high school pupils solve arithmetic issues involving flat sided spaces, this study will examine their mathematical communication abilities. At SMPN 3 Tirtajaya, research was done. There are five measures of students' ability communicate mathematically, including the first measure, which links visuals ideas, second makes conjectures, gathers evidence, and...