We experimentally demonstrate time-domain storage and retrieval of amplitude- phase-encoded optical data, using Raman coherent population trapping, despite the loss information about absolute phases that occurs as a result dissipative nature process. In this process homogeneous decay coherence does not prevent interference between time-separated fields, thus relaxing requirement for long-lived coherences.

Abstract In this paper, we obtain equivalent conditions of complete moment convergence the maximum for partial weighted sums independent identically distributed random variables under sublinear expectations space. The results obtained in paper are extensions classical linear expectation

By an inequality of partial sum and uniform convergence the central limit theorem under sublinear expectations, we establish precise asymptotics in law iterated logarithm for independent identically distributed random variables expectations.

<abstract><p>In this article, we study complete convergence and moment for negatively dependent random variables under sub-linear expectations. The results obtained in expectation spaces extend the corresponding ones probability space.</p></abstract>

Abstract In this paper, we study the complete convergence and moment of linear processes generated by negatively dependent random variables under sub-linear expectations. The obtained results complement ones Meng, Wang, Wu (Commun. Stat., Theory Methods 52(9):2931–2945, 2023) in case

We investigate the complete <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>p</mi> </math> th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using inequality and truncation methods, we prove equivalent conditions id="M3"> space, which complement corresponding results obtained in Guo Shan (2020).

This paper is concerned with constructing nodal radial solutions for generalized quasilinear Schrödinger equations in $\mathbb{R}^N$ critical growth which arise from plasma physics, fluid mechanics, as well the self-channeling of a high-power ultashort laser matter. We find exponents and obtain existence sign-changing solution k nodes any given integer $k ≥ 0$.

In this paper, we study the existence and concentration of positive solutions for following fractional Schr\”odinger logarithmic equation: \begin{equation*} \left\{ \begin{aligned} &amp; \varepsilon^{2s} (-\Delta)^{s} u+V(x)u =u\log u^2,\ x\in \mathbb{R}^N,\\ &amp;u\in H^s(\mathbb{R}^N), \end{aligned} \right. \end{equation*} where $\varepsilon &gt; 0$ is a small parameter, $N&gt;2s,$ $s \in ( 0 ,1), (-\Delta)^{s}$ Laplacian, potential $V$ continuous function having global minimum. Using...

A connected graph is called fragile if it contains an independent vertex cut. In 2002 Chen and Yu proved that every of order $n$ size at most $2n-4$ fragile, in 2013 Le Pfender characterized the non-fragile graphs $2n-3.$ It natural to consider minimum cuts. We prove two results. (1) Every with $n\ge 7$ $\lfloor 3n/2\rfloor$ has cut; (2) $2n$ a foresty Both results are best possible.

By using Lebesgue bounded convergence theorem, we prove precise asymptotics in the law of iterated logarithm for independent and identically distributed random variables under sublinear expectation.

In this paper, we consider the fractional p&q-Laplacian equation: (−Δ)psu+(−Δ)qsu+V(x)(|u|p−2u+|u|q−2u)=K(x)f(u)inRN, where s∈(0,1),1<p<q<Ns, and (−Δ)ts with t∈{p,q} is t-Laplacian operator, f a C1 real function V, K are continuous, positive functions. By using constrained variational methods, quantitative Deformation Lemma Brouwer degree theory, prove existence of least energy sign-changing solution.

&lt;abstract&gt;&lt;p&gt;This paper is dedicated to studying the following Kirchhoff-Schrödinger-Poisson system:&lt;/p&gt; &lt;p&gt;&lt;disp-formula&gt; &lt;label/&gt; &lt;tex-math id="FE1"&gt; \begin{document}$ \begin{equation*} \left\{\begin{array}{ll} - \left(a+b \int_{ \mathbb{R}^3} |\nabla u|^2 dx \right) \Delta u+V(|x|) u+\lambda\phi u = K(|x|)f(u), &amp;amp; x \in \mathbb{R}^{3}, \\ -\Delta \phi u^2, \end{array}\right. \end{equation*} $\end{document}...

Let X , n ≥ 1 be a sequence of independent, identically distributed random variables under sublinear expectations with and . Write S 0 = 0, M max 0≤ k ≤ | |, 1. For d &gt; o ((log log ) − ), we obtain the exact rates in law iterated logarithm kind weighted infinite series as ε ↓ 0.

Abstract In this paper, we study the existence of ground state solutions for following fractional Kirchhoff–Schrödinger–Poisson systems with general nonlinearities: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mrow> <m:mo>{</m:mo> <m:mtable columnalign="left"> <m:mtr <m:mtd <m:mo>(</m:mo> <m:mi>a</m:mi> <m:mo>+</m:mo> <m:mi>b</m:mi> <m:msubsup> <m:mo>[</m:mo> <m:mi>u</m:mi> <m:mo>]</m:mo> </m:mrow> <m:mi>s</m:mi> <m:mn>2</m:mn> </m:msubsup> <m:mo>)</m:mo>...

The complete convergence for weighted sums of sequences independent, identically distributed random variables under sublinear expectations space was studied. By moment inequality and truncation methods, we establish the equivalent conditions space. results extend corresponding obtained by Guo (2012) to those