in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

We study algorithms for solving a problem of constructing text (a long string) from dictionary sequence small strings). The has an application in bioinformatics and connection with the assembly method reconstructing DNA fragments. Our is construction string t length n using strings $$s^1,\dots , s^m$$ possible overlapping. Firstly, we provide classical (randomized) algorithm running time $$O\le...

Utilizing the linking algebra of a Hilbert $C^*$-module $\big(\mathscr{V}, {\|\!\cdot\!\|}_{_{\mathscr{V}}}\big)$, we introduce $\Omega(x)$ as definition numerical radius for an element $x\in\mathscr{V}$ and then show that $\Omega(\cdot)$ is norm on $\mathscr{V}$ such $\frac{1}{2}{\|x\|}_{_{\mathscr{V}}} \leq \Omega(x) {\|x\|}_{_{\mathscr{V}}}$. In addition, obtain equivalent condition $\Omega(...

notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

This paper deals with classical solution of system $ \begin{array}{*{20}{l}}{\begin{eqnarray} { } \left\{ \begin{array}{ll} u_t = \epsilon_1\Delta u-\chi_{1}\nabla\cdot(u\nabla v)-\chi_{2}\nabla\cdot(u\nabla z)+\mu_1 u(1-u-a_1w), &\\ 0 \Delta v-v+w^{\sigma_1}, w_t \epsilon_2\Delta w-\chi_3\nabla\cdot(w\nabla z)-\chi_4\nabla\cdot(w\nabla v)+\mu_2 w(1-w-a_2u), z-z+u^{\sigma_2} & \end{arra...