奇数阶中立型微分方程微正解或微负解判据

本文给出了奇数阶中立型微分方程在不同的变系数情形下微正解或微负解存在的判据。

中立型微分方程的强迫振动性

本文给出了中立型微分方程的强迫振动准则，且根据方程的不同特点得到了不同的振动性条件。

The Solvability of the Degenerate Differential Systems with Delay

In this paper we study the degenerate differential system with delay:E(t)=Ax(t)+Bx(t-1)+f(t),give the canonical form of this systems and study this form of degeneration system with delay,have some results for the solvability of such systems and the uniqueness of their solutions.

Influence of carbon coating prepared by microwave pyrolysis on properties of LiNi_(1/3) Mn_(1/3) Co_(1/3) O_2

A novel synthesis method of carbon-coated LiNil/3Mnl/3COl/302 cathode material for lithium-ion battery was reported. The carbon coating was produced from a precursor, glucose, by microwave-pyrolysis method. The prepared powders were characterized by scanning electron microscopy （SEM）, X-ray diffraction （XRD）, X-ray fluorescence （XRF） and charge/discharge tests. XRD results indicate that the carbon coating does not change the phase structure of LiNil/3Mnl/3C01/302 material. SEM results show that the surface of spherical carbon-coated material becomes rough. Electrochemical performance results show that the carbon coating can improve the cycling performance of LiNii/3Mnl/3C01/302. The specific discharge capacity retention of the carbon-coated LiNi1/3Mnt/3Col/30z reached 85.0%-96.0% at the 50th cycle at 0.2C rate, and the specific discharge capacity retention is improved at a high rate.

On Miranda's Normal Criterion

In this paper, we study the normality of a family of analytic functions and prove the following theorem. Let F be a family of analytic functions in a domain D , k be a positive integer and a(z) , a 1(z) , a 2(z) , ... , a k(z) be analytic in D such that a(z)0 . If f(z)≠0 and the zeros of f (k) (z)+a 1(z)f (k-1) (z)+...+a k(z)f(z)-a(z) are of multiplicity at least 2 for each f∈F , then F is normal in D . This result improves Miranda s norm...

Oscillation of Unstable Second Order Neutral Differential Equations with Positive and Negative Coefficients

This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.

On the Existence of Positive Solutions for Impulsive Neutral Differential Equations

Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.

Positive Solutions of p-Laplacian Functional Difference Equations

In this paper, the author studies the boundary value problems for a p-Laplacian functional difference equation. By using a fixed point theorem in cones, sufficient conditions are established for the existence of the positive solutions.

On the Existence of Positive Solutions of Neutral Differential Equations

Consider the first order neutral delay differential equation with positive and negative coefficients:[x(t)-c(t)x(t-γ)]+p(t)x(t-τ)-Q(t)x(t-δ)=0,t≥t 0,(1)where c,p,Q∈C((t 0,∞),R +),R +=(0,∞),γ】0,t】δ≥0. We obtain the sufficient condition for the existence of positive solutions of Eq.(1). As a corollary, we improve the correspondent result in by removing the condition∫ ∞ c 0 (t) d t=∞,where (t)=p(t)-Q(t-τ+δ)≥0.

Existence of positive solutions in a delay logistic difference equation

The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreasing sequence of integers, τ(n)<n and lim n →∞ τ(n) =∞. A sufficient condition for the existence of positive solutions of the equation was given.

Solitary Wave and Periodic Wave Solutions for the Relativistic Toda Lattices

In this work, an adaptation of the tanh/tan-method that is discussed usually in the nonlinear partial differential equations is presented to solve nonlinear polynomial differential-difference equations. As a concrete example,several solitary wave and periodic wave solutions for the chain which is related to the relativistic Toda lattice are derived.Some systems of the differential-difference equations that can be solved using our approach are listed and a discussion is given in conclusion.

The Uniqueness and Nonexistent Results for Some Nonlinear Partial Equations on Riemannian Manifolds

The paper studies a class of nonlinear elliptic partial differential equations on a compact Riemannian manifold （M,g） with some curvature restriction. The authors try to prove some uniqueness and nonexistent results for the positive solutions of the equations concerned.

Isolation and in-situ bioremediation of halophile oil degradation bacteria

Crude oil exploration has resulted in alarming pollution. It is thereforenecessary to isolate native bacterial strains for contaminated crude oil bioremediation.In this study, three bacteria strains were isolated from the Dagang Oil Field, Tianjing,China, which belonged to the genera Pseudomonas sp. and Bacillus sp., as determinedby 16S rRNA genera sequence similarity analysis. The optimum degradation conditionsof the three bacteria were studied by single factor experiment, and they were 30 °C, 7.2pH, and 3% salinity, 35 °C, 7.5 pH, and 3% salinity, and 37 °C, 7.5 pH, and 5% salinity,respectively. The results showed that the oil degradation rate was the best when theproportion of the different strains was 2:1:2. Moreover, the most effective treatmentconditions were found by orthogonal test to be 10% inoculum, 0.2% oil content, 7.0 pH,3:1 N:P, 3.5% salinity, and 35 °C, the oil degradation rate reached 71.03% under thiscondition.

B→ρ(ω,φ)η(′)Decays and NLO Contributions in pQCD Approach

By employing the perturbative QCD （pQCD） factorization approach, we calculate some important next- to-leading-order （NLO） contributions to the two-body charmless hadronic decays B^＋ →ρ^＋η（＇） and B^0 → ρ^0（ω, φ）η（＇）, induced by the vertex QCD corrections, the quark-loops as well as the chromo-magnetic penguins. From the numerical results and phenomenological analysis we find that （a） for B^± → ρ^±η（＇） （B^0 → ρ^0（ω, φ）η（＇）decays, the partial NLO contributions to branching ratios are small （large） in magnitude; and （b） the pQCD predictions for ACP^dir（B^± → ρ^±η（＇）） are consistent with the data, while the predicted .ACP（B^0 → ρ^0（ω）η（＇）） are generally large in magnitude and could be tested by the forthcoming LHCb experiments.

Boundary Value Problems of Quasi-linear Ordinary Differential Equations on the Semi-infinite Interval

Existence of positive solution is established for boundary value problems of nonsingular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the nonlinear alternative of Leray-Schauder method.

A Predictor-Corrector Scheme for the Microscopic Depletion Solver of the COCAGNE Core Code

EDF R＆D is developing a new calculation scheme based on the transport-Simplified Pn （SPn） approach. The lattice code used is the deterministic code APOLLO2, developed at CEA. The core code is the code COCAGNE, developed at EDF R＆D. The latter can take advantage of a microscopic depletion solver expected to improve the treatment of spectral history effects. However, the direct use of the microscopic depletion solver is computationally very intensive because very small evolution steps （typically 100 MWd/t） are needed to reach a good accuracy, which is not always compatible with industrial applications. In order to reduce the calculation time associated with the use of the microscopic depletion solver, a predictor-corrector scheme has been implemented within COCAGNE. It enables the use of larger evolution steps, up to 1000 MWd/t. Tests show that the predictor-corrector procedure gives fairly accurate results while significantly reducing the calculation time.

The Smoothness of Weak Solutions to the System of Second Order Differential Equations with Non-negative Characteristics

In this paper,we will discuss smoothness of weak solutions for the system of second order differential equations eith non-negative characteristies.First of all,we establish boundary,and interior estimates and then we prove that solutions of regularization problem satisfy Lipschitz condition.

Globally Asymptotic Stability of Equilibrium of a Dynamical Model with Infinite Delay

By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in the reference [ 10] got by the second author herself.

Existence of Positive Solutions to Second Order Neumann Boundary Value Problems

The existence of positive solutions to second-order Neumann BVPs -u' + Mu = f(t, u), u'(0) = u'(1) = 0 and u' + Mu = f(t, u), u'(0) =u'(1) is proved by a simple application of a Fixed Point Theorem in cones due to Krasnoselskii[1,6].

Existence of Solutions to a Class of Higher-Order Singular Boundary Value Problem for One-Dimensional p-Laplacian

This paper deals with the existence of positive solutions for the problem {（Фp（x^（n-1）（t）））′＋f（t,x,…,x^（n-1）=0,0〈t〈1, x^（i）（0）=0,0≤i≤n-3, x^（n-2）（0）-B0（x^（n-1）（0））=0,x^（n-2）（1）＋B1（x^（x-1）（1））=0, where Фp（s） = ｜s｜^p-2s, p 〉 1. f may be singular at x^（i） = 0, i = 0,...,n- 2. The proof is based on the Leray-Schauder degree and Vitali＇s convergence theorem.