In this paper, we study the Cauchy problem for Benjamin-Ono-Burgers equation $${\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial u{u_x} = 0$$ , where $${\cal H}$$ denotes Hilbert transform operator. We obtain that it is uniformly locally well-posed small data in refined Sobolev space $${\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)$$ which a subspace of L2(ℝ). It worth noting ...

<p style='text-indent:20px;'>We study a uniform-in-time continuum limit of the lattice Winfree model(LWM) and its asymptotic dynamics which depends on system functions such as natural frequency function coupling strength function. The model(CWM) is an integro-differential equation for temporal evolution phase field. LWM describes synchronous behavior weakly coupled oscillators lying in co...

the combination of graphene and nickel oxide nanoparticles yields nanostructured electrochemical sensor formed a novel kind of structurally uniform and electrocatalytic activity material. in cyclic voltammetry studies, in the presence of epinephrine, nickel oxide / graphene  composite modified electrode shows a significantly higher current response for epinephrine oxidation. based on differenti...

We prove that the scaling limit of loop-erased random walk in a simply connected domain D $ C is equal to the radial SLE2 path. In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the uniform spanning tree in a Jordan domain exists and is conformally invariant. Assuming that ∂D is a C1 simple closed curve, the same method is applied to show that th...

Plan 1. Linnik and creation of the Leningrad school 2. Linnik’s students 3. 1951 4. Unimodal distributions 5. Classical limit theorems a) moment conditions for given convergence rate b) fast convergence rates in CLT c) Chebyshev-Cramér asymptotic expansions 6. Weak dependence a) uniform mixing condition b) central limit theorem under uniform mixing condition c) continued fractions d) central li...