for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

We relate two complexity notions of bipartite graphs: the minimal weight biclique covering number Cov(G) and the minimal rectifier network size Rect(G) of a bipartite graph G. We show that there exist graphs with Cov(G) ≥ Rect(G). As a corollary, we establish that there exist nondeterministic finite automata (NFAs) with εtransitions, having n transitions total such that the smallest equivalent ...

From the interpretation of Linear Logic multiplicative disjunction as the ε-product defined by Laurent Schwartz, we construct several models of Differential Linear Logic based on usual mathematical notions of smooth maps. This improves on previous results in [BET] based on convenient smoothness where only intuitionist models were built. We isolate a completeness condition, called k-quasi-comple...

We study a two-level transition probability for finite number of avoided crossings with small interaction. Landau–Zener formula, which gives the one crossing as $$e^{-\pi \frac{\varepsilon ^{2}}{h}}$$ , implies that parameter h and interaction $$\varepsilon $$ play an opposite role when both tend to 0. The exact WKB method produces generalization formula under optimal regime $$\scriptstyle {\fr...

Let (M, g) be a closed locally conformally flat Riemannian manifold of dimension $$n \ge 7$$ and positive Yamabe type. If $$h \in C^1(M)$$ $$\xi _0$$ is non-degenerate critical point the mass function we prove existence, for any $$ k 1$$ blowing-up solution $$u_\varepsilon $$\begin{aligned} \triangle _g u_\varepsilon +\big ( c_n S_g +\varepsilon h\big ) = ^{2^*-1} \end{aligned}$$ that blows up,...

In this paper,  we provide two different kinds of fixed pointtheorems in  fuzzy metric spaces. The first kind is for the fuzzy$varepsilon$-contractive type mappings and  the second kind is forthe fuzzy order $psi$-contractive type mappings. They improve thecorresponding  conclusions in the literature.

In this paper we report the impact of uniaxial strain $\varepsilon$ applied along crystalline $a$ axis on newly discovered kagome superconductor CsV$_3$Sb$_5$. At ambient conditions, CsV$_3$Sb$_5$ shows a charge-density wave (CDW) transition at $T_{\rm CDW}=94.5$ K and superconducts below $T_C = 3.34$ K. our study, when is varied from $-0.90\%$ to $0.90\%$, $T_C$ monotonically increases by $\si...

We consider a 2D smectics model \begin{equation*} E_{\epsilon }\left( u\right) =\frac{1}{2}\int_\Omega \frac{1}{\varepsilon u_{z}-\frac{1% }{2}u_{x}^{2}\right) ^{2}+\varepsilon \left( u_{xx}\right) ^{2}dx\,dz. \end{equation*} For $\varepsilon _{n}\rightarrow 0$ and sequence $\left\{ u_{n}\right\} $ with bounded energies $E_{\varepsilon _{n}}\left(u_{n}\right) ,$ we prove compactness of $\{\part...