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(...

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...

The $SU(2)$ unitary matrix $U$ employed in chiral descriptions of hadronic low-energy processes has both exponential and analytic representations, related by $U=\mathrm{exp}[i\mathbit{\ensuremath{\tau}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{\mathbit{\ensuremath{\pi}}}\ensuremath{\theta}]=\mathrm{cos}\ensuremath{\theta}I+i\mathbit{\ensuremath{\tau}}\ifmmode\cdot\else\textperiodce...

The frequency stability of lasers is limited by thermal noise in state-of-the-art references. Further improvement requires operation at cryogenic temperature. In this context, we investigate a fiber-based ring resonator. Our system exhibits first-order temperature-insensitive point around $3.55$ K, much lower than that crystalline silicon. observed low sensitivity with respect to vibrations ($<...

In this work, we studied the curvature tensors of (k,$\mu$) satisfying conditions $\widetilde{Z}(\xi ,\alpha _{3})\cdot P=0$, S=0$, $R(\xi S=0$ and $P\cdot C=0$. Besides this, classify $(k,\mu)$-paracontact manifolds. Also researched conformally flat $\phi $-conformally a $(k,\mu )-$paracontact metric

Abstract In this paper, we mainly consider the real interpolation spaces for variable Lebesgue defined by decreasing rearrangement function and corresponding martingale Hardy spaces. Let $$0&lt;q\le \infty $$ 0 &lt; q ≤ ∞ </mml:mat...