Journal of Linear and Topological Algebra
Volume:12 Issue: 4, Autumn 2023

We introduce the Hausdorff measure of noncompactness in the sequence space $bv_{\infty}$ and investigate the existence of solution of infinite systems of differential equations with respect to Hausdorff measure of noncompactness. Finally, we present an example to defend of theorem of existential.

Recently, soft set theory has been extensively studied both theoretically and practically with different approaches. On the other hand, fixed-circle problem has been investigated as a geometric generalization of fixed-point theory and this problem can be applied to some applicable areas. With these two perspectives, in this paper, we obtain some soft fixed-circle results using different auxiliary functions on a soft metric space. To do this, we are inspired various contractive conditions. The obtained results can be considered as an existence or uniqueness theorem. The proved theorems are supported by some illustrative examples. Finally, we give a list of geometric consequences of these results.‎

$X$-bar control charts are widely used to monitor and control business and manufacturing processes. Design of control charts refers to the selection of parameters, including sample size, control-limit width, and sampling frequency. Many researchers have worked on this issue and have also proposed various solutions. However, despite the numerous advantages, the proposed methods also have their own set of problems. The biggest challenge is the complexity of solving these issues. Due to the fact that optimal design of control charts can be formulated as a multi objective optimization problem, in this paper to solve this problem, we used initial solution Spider's web data envelopment analysis method. In previous methods used multiple algorithms to resolve the issue. But in the proposed method once using Data Envelopment Analysis method and without any other algorithm can solve multi objective problem and this method can yield desirable efficient. Lastly, we compare our method with others and demonstrate its application in a real industrial context.

In this paper, we first define two new characteristic subgroups of a group $G$. Then we identify the relationships of these subgroups with $G'$, $S(G)$, $Ivar(G)$, and some different homomorphisms. Particularly, with one of these two subgroups, we determine the structure of $Ivar(G)$ and a subgroup of it that fixes $Z(G)$ element-wise.

In this paper, for a given set of real interval numbers $\sigma$ that satisfies in special conditions, we find an interval nonnegative matrix $C^I$ such that for each point set $\delta$ of given interval spectrum $\sigma$, there exists a point matrix $C$ of $C^I$ such that $\delta$ is its spectrum. For this purpose, we use unit lower triangular matrices and especially try to use binary unit lower triangular matrices. We also study some conditions for existence solution to the problem.