Positive ground state solutions for Schrödinger–Poisson system with critical nonlocal term in ℝ3

This paper is dedicated to studying the following Schrödinger–Poisson system $$\left\{\begin{array}{ll}-\mathrm{\Delta }u+V(x)u-K(x)\varphi |u{|}^{3}u=a(x)f(u),& x\in {ℝ}^3,\\ -\mathrm{\Delta }\varphi =K(x)|u{|}^5,& x\in {ℝ}^3.\end{array}\right.$$ Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions.     

Stability of steady nonisothermal flow in a vertical layer with permeable boundaries in the microconvection model

The problem of the stability of steady convective viscous incompressible fluid flow in a vertical layer with boundaries at different temperatures is considered in the presence of transverse blowing through the layer. The complete spectral problem is solved for a silicon melt. The neutral curve is constructed and the critical Grashof number is found. The numerical calculations show that the presence of transverse blowing significantly affects the flow stability. As compared with the Oberbeck-Boussinesq model, in the microconvection model the instability develops at lower wavenumbers.     

带惩罚项与随机输入的BP神经网络在线梯度学习算法的收敛性

本文对三层BP神经网络中带有惩罚项的在线梯度学习算法的收敛性问题进行了研究,在网络训练每一轮开始执行之前,对训练样本随机进行重排,以使网络学习更容易跳出局部极小,文中给出了误差函数的单调性定理以及该算法的弱收敛和强收敛性定理。     

Oscillation theorems for differential equations with a nonlinear damping term

In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity, and, as a consequence, our results apply to wider classes of nonlinear differential equations. Two illustrative examples are considered.     

OSCILLATION RESULTS FOR A SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.     

Neutral Community Theory: How Stochasticity and Dispersal-Limitation Can Explain Species Coexistence

Neutral community theory explains biodiversity, i.e. the coexistence of several species, as the result of a stochastic balance between immigration and extinction on a local level, and between speciation and extinction on a regional level. The most popular model, presented by Hubbell in 2001, has seen many analytical developments in recent years, which can be used in model analysis, model testing and model comparison. We review these developments here, and present alternative derivations and shine previously unnoticed lights on them.     

Existence Results for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

In this paper we prove existence results for semilinear neutral functional differential inclusions with finite or infinite delay in Banach spaces. Our theory makes use of analytic semigroups and fractional powers of closed operators, integrated semigroups and cosine families.      

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

Fourier transform spectroscopy of CH3OH: rotation-torsion-vibration structure for the CH3-rocking and OH-bending modes

High-resolution Fourier transform spectra of CH₃OH have been investigated in the infrared region from 930 to 1450 cm⁻¹ in order to map the torsion-rotation energy manifolds associated with the ν₇ in-plane CH₃ rock, the ν₁₁ out-of-plane CH₃ rock, and the ν₆ OH bend. Upper-state term values have been determined from the assigned spectral subbands, and have been fitted to power-series expansions to obtain substate origins and effective B-values for the three modes. The substate origins have been grouped into related families according to systematic trends observed in the torsion-vibration energy map, but there are substantial differences from the traditional torsional patterns. There appears to be significant torsion-mediated spectral mixing, and a variety of “forbidden” torsional combination subbands with |Δυ_t|>1 have been observed, where υ_t denotes the torsional quantum number (equivalent to υ₁₂). For example, coupling of the (υ₆,υ_t)=(1,0) OH bend to nearby torsionally excited (υ₇,υ_t)=(1,1) CH₃-rock and (υ₈,υ_t)=(1,1) CO-stretch states introduces (υ₆,υ_t)=(1,0)←(0,1) subbands into the spectrum and makes the ν₇+ν₁₂−ν₁₂ torsional hot band stronger than the ν₇ fundamental. The results suggest a picture of strong coupling among the OH-bending, CH₃-rocking, and CO-stretching modes that significantly modifies the traditional energy structure and raises interesting and provocative questions about the torsion-vibration identity of a number of the observed states.     

高阶非线性时滞差分方程解的渐近性

研究如下的具强迫项的高阶非线性时滞差分方程△^my(n) u(n)l↑∑i=1 gi(y(n-τ))=v(n)其中，m≥1，u,v：N→R，gi：R→R且τ∈{0，1，2，3，…)，i=1，2，…，l，得到了使该方程的解具有某种渐近性态的充分条件。