The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions

In this paper, first, we consider the existence of a positive solution for the nonlinear fractional differential equation boundary value problem where 0≤λ < 1,^CD^α is the Caputo's differential operator of order α, and f:[0,1] × [0,∞)→[0,∞) is a continuous function. Using some cone theoretic techniques, we deduce a general existence theorem for this problem. Then, we consider two following more general problems for arbitrary α, 1≤n < α≤n + 1: Problem 1: where , 0≤λ < k + 1; Problem 2: where 0≤λ≤α and D^α is the Riemann–Liouville fractional derivative of order α. For these problems, we give existence results, which improve recent results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

On the symmetry analysis and conservation laws of the (1 + 1)‐dimensional Hénon–Lane–Emden system

We carry out a complete Lie symmetry analysis and Noether symmetry classification of the (1 + 1)‐dimensional H non–Lane–Emden system. It is shown that the principal Lie algebra, which is one dimensional, extends in several cases. It is also shown that four main cases transpire in the Noether classification with respect to the Lagrangian. In addition, conservation laws for the H non–Lane–Emden system are constructed. Furthermore, we briefly discuss the importance and the physical interpretation of these conserved vectors. Copyright © 2016 John Wiley & Sons, Ltd.     

Exploring the Interactions of Atomic Oxygen on Silver Clusters with Hydrogen

The interactions between Ag_nO^-(n=1-8) and H₂ (or D₂) were explored by combination of the mass spectroscopy experiments and density function theory (DFT) calculations. The experiments found that all oxygen atoms in Ag_nO^-(n=1-8) are inert in the interactions with H₂ or D₂ at the low temperature of 150 K, which is in contrast to their high reactivity with CO under the same condition. These observations are parallel with the preferential oxidation (PROX) of CO in excess hydrogen catalyzed by dispersed silver species in the condensed phase. Possible reaction paths between Ag_nO^-(n=1-8) and H₂ were explored using DFT calculations. The results indicated that adsorption of H₂ on any site of Ag_nO^-(n=1-8) is extremely weak, and oxidation of H₂ by any kind of oxygen in Ag_nO^-(n=1-8) has an apparent barrier strongly dependent on the adsorption style of the "O". These experiments and theoretical results about cluster reactions provided molecule-level insights into the activity of atomic oxygen on real silver catalysts.     

On the existence of free-surface azimuthal equatorial flows

This paper is concerned with the governing equations (together with the free boundary and the bottom boundary conditions) for an inviscid, incompressible fluid, written in spherical coordinates which are fixed at a point on the rotating Earth. For a special type of a steady flow moving only in the azimuthal direction, with no variation in this direction, we provide a functional-analytic study of the link between the pressure at the free surface of the ocean and the distortion of that surface.     

A Gibbs sampling method to determine biomarkers for asthma

PurposeTo identify potential biomarkers and to uncover the mechanisms underlying asthma based on Gibbs sampling.MethodsThe molecular functions (MFs) with genes greater than 5 were determined using AnnotationMFGO of BAGS package, and the obtained MFs were then transformed to Markov chain (MC). Gibbs sampling was conducted to obtain a new MC. Meanwhile, the average probabilities of MFs were computed via MC Monte Carlo (MCMC) algorithm, followed by identification of differentially expressed MFs based on the probabilities of MF more than 0.6. Moreover, the differentially expressed genes (DEGs) and their correlated genes were screened and merged, called as co-expressed genes. Pathways enrichment analysis was implemented for the co-expressed genes.ResultsBased on the gene set more than 5, overall 396 MFs were determined. After Gibbs sampling, 5 differentially expressed MF were acquired according to alfa.pi > 0.6. Moreover, the genes in these 5 differentially expressed MF were merged, and 110 DEGs were identified. Subsequently, 338 co-expressed genes were gained. Based on the P value < 0.01, the co-expressed genes were significantly enriched in 6 pathways. Among these, ubiquitin mediated proteolysis contained the maximum numbers of 35 co-expressed genes, and cell cycle were enriched by the second largest number of 11 co-expressed genes, respectively.ConclusionsThe identified pathways such as ubiquitin mediated proteolysis and cell cycle might play important roles in the development of asthma and may be useful for developing the credible therapeutic approaches for diagnosis and treatment of asthma in future.     

Accurate Theoretical Study of LiS Radical and Its Singly Charged Cation and Anion in their Ground Electronic State

Potential energies of LiS(²Π), LiS^-(¹Σ⁺) and LiS⁺(³Σ^-) are calculated by using the multireference configuration interaction method including Davidson correction and the augmented correlation-consistent basis sets aug-cc-PV(X+d)Z (X=T, Q). Such obtained potential energies are subsequently extrapolated to the complete basis set limit. Both the core-valence correction and the relativistic effect are also considered. The analytical potential energy functions are then obtained by fitting such accurate energies utilizing a least-squares fitting procedure. By using such analytical potential energy functions, we obtain the accurate spectroscopic parameters, complete set of vibrational levels and classical turning points. The present results are compared well with the experimental and other theoretical work.     

The p-th moment stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion

In this paper, we consider a class of impulsive stochastic differential equations driven by G-Brownian motion (IGSDEs in short). By means of the G-Lyapunov function method, some criteria on p-th moment stability and p-th moment asymptotical stability for the trivial solutions of IGSDEs are established. An example is presented to illustrate the efficiency of the obtained results.     

用指数型整函数的最佳限制逼近

我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果.     

Continuity in law with respect to the Hurst index of some additive functionals of sub-fractional Brownian motion

In this article, first, we prove some properties of the sub-fractional Brownian motion introduced by Bojdecki et al. [Statist. Probab. Lett. 69(2004):405–419]. Second, we prove the continuity in law, with respect to small perturbations of the Hurst index, in some anisotropic Besov spaces, of some continuous additive functionals of the sub-fractional Brownian motion. We prove that our result can be obtained easily, by using the decomposition in law of the sub-fractional Brownian motion given by Bardina and Bascompte [Collect. Math. 61(2010):191–204] and Ruiz de Chavez and Tudor [Math. Rep. 11(2009):67–74], without using the result of Wu and Xiao [Stoch. Proc. Appl. 119(2009):1823–1844] by connecting the sub-fractional Brownian motion to its stationary Gaussian process through Lamperti’s transform. This decomposition in law leads to a better understanding and simple proof of our result.     

Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general‐shaped domains

In present work, a kind of spectral meshless radial point interpolation (SMRPI) technique is applied to the time fractional nonlinear Schrödinger equation in regular and irregular domains. The applied approach is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. It is proved the scheme is unconditionally stable with respect to the time variable in and also convergent by the order of convergence , . In the current work, the thin plate spline are used as the basis functions and to eliminate the nonlinearity, a simple predictor‐corrector (P‐C) scheme is performed. It is shown that the SMRPI solution, as a complex function, is suitable one for the time fractional nonlinear Schrödinger equation. The results of numerical experiments are compared to analytical solutions to confirm the reliable treatment of these stable solutions. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1043–1069, 2017