We investigate the convergence rate of optimal entropic cost $$v_\varepsilon $$ to transport as noise parameter $$\varepsilon \downarrow 0$$ . show that for a large class functions c on $${\mathbb {R}}^d\times {\mathbb {R}}^d$$ (for which plans are not necessarily unique or induced by map) and compactly supported $$L^{\infty }$$ marginals, one has -v_0= \frac{d}{2} \varepsilon \log (1/\varepsil...

In this paper, we study the concentration and multiplicity of solutions to following fractional Schr\"{o}dinger-Poisson system \begin{equation*} \left\{ \begin{array}{ll} \varepsilon^{2s}(-\Delta)^su+V(x)u+\phi u=f(u)+u^{2_s^{\ast}-1} & \hbox{in $\mathbb{R}^3$,} \varepsilon^{2t}(-\Delta)^t\phi=u^2, u>0& \end{array} \right. \end{equation*} where $s>\frac{3}{4}$, $s,t\in(0,1)$, $\varepsilon>0$ is...

We propose a new deterministic Kaczmarz algorithm for solving consistent linear systems $A\mathbf{x}=\mathbf{b}$. Basically, the replaces orthogonal projections with reflections in original scheme of Stefan Kaczmarz. Building on this, we give geometric description solutions systems. Suppose $A$ is $m\times n$, show that generates series points distributed patterns an $(n-1)$-sphere centered sol...

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...

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 study the line bundle mean curvature flow defined by Jacob and Yau. The is a kind of parabolic flows to obtain deformed Hermitian Yang-Mills metrics on given K\"ahler manifold. goal paper give an $\varepsilon$-regularity theorem for flow. To establish theorem, provide scale invariant monotone quantity. As critical point quantity, define self-shrinker solution Liouville type se...