The purpose of this paper is to introduce the notion of soft ideal in soft set theory. The concept of soft local function is also introduced. These concepts are discussed with a view to find new soft topologies from the original one. The basic structure, especially a basis for such generated soft topologies also studied here. Finally, the notion of compatibility of soft ideals with soft topolog...

Chiral Photonic Micromotors Liquid crystalline polymers present an attractive option for the development of soft micro- and nanorobots. In article number 2207095, Kristiaan Neyts co-workers report on chiral photonic microparticles that show light-induced uni- bidirectional spinning speed control. The results offer a new approach to create light-powered rotary micromotors at micrometer scale.

let $r$ be a commutative ring with identity‎. ‎a proper ideal $p$ of $r$ is a $(n-1,n)$-$phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin r$‎, ‎$a_1cdots a_nin pbackslash p^m$ ($a_1cdots a_nin pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin p$‎, ‎for some $iin{1,ldots,n}$; ($m,ngeq 2$)‎. ‎in this paper several results concerning $(n-1,n)$-$phi_m$-prime and $(n-1,n)$-...

Let $mathcal{A}$ be a Banach algebra and $X$ be a Banach $mathcal{A}-$bimodule. We study the notion of approximate $n-$ideal amenability for module extension Banach algebras $mathcal{A}oplus X$. First, we describe the structure of ideals of this kind of algebras and we present the necessary and sufficient conditions for a module extension Banach algebra to be approximately n-ideally amenable.

background: marine pollution is a global environmental problem that its monitoring by ideal biomonitors is of great importance. marine organisms, especially mussels, have the ability to accumulate metals from the environment they can be considered as a biomonitoring agent. methods: in this study, concentrations of heavy metals were measured in saccostrea cucullata collected from seven sites on ...

This article investigates the soft-interior (se) and the soft-cover (sc) of operator ideals. These operations, and especially the first one, have been widely used before, but making their role explicit and analyzing their interplay with the arithmetic mean operations is essential for the study in [10] of the multiplicity of traces. Many classical ideals are “soft”, i.e., coincide with their sof...

Background: Marine pollution is a global environmental problem that its monitoring by ideal biomonitors is of great importance. Marine organisms, especially mussels, have the ability to accumulate metals from the environment they can be considered as a biomonitoring agent. Methods: In this study, concentrations of heavy metals were measured in Saccostrea cucullata collected from seven sites on...

Cofiniteness of the generalized local cohomology modules $H^{i}_{mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ with respect to an ideal $mathfrak{a}$ is studied for some $i^{,}s$ witha specified property. Furthermore, Artinianness of $H^{j}_{mathfrak{b}_{0}}(H_{mathfrak{a}}^{i}(M,N))$ is investigated by using the above result, in certain graded situations, where $mathfrak{b}_{0}$ is an idea...