一类Liénard型方程周期解及概周期解的存在唯一性和渐近稳定性

应用 V-函数法讨论具有强迫项的 L iénard方程 x+f0 (x) x+f1 (x) x2 +g(x) =e(t)周期解与概周期解存在唯一性和渐近稳定性     

Strong Law of Large Numbers and Complete Convergence for Sequences of φ-Mixing Random Var, ables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.     

Asymptotic behavior of the solutions to the one-dimensional nonisentropic hydrodynamic model for semiconductors

In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson (or full hydrodynamic) model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed. Biography: LI Yeping(1972–), male, Associate professor, Ph.D., research direction: nonlinear partial differential equations.     

Characteristic singular integral equations with solutions having singularities of higher order on the real axis

Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter. Biography: ZHONG Shouguo (1941–), male, Professor, research direction: singular integral equations and their applications.     

A Note on the Property of ψ-Function

About the accurate value of ψ ( x ) = Γ′ ( x ) / Γ ( x), we know only ψ (1)and ψ (1/ 2).In this paper, by calculating the accurate values of some series expansion of a function and applying some skills of complex analysis, we prove that the expression of the ψ-function admits a finite expression in elementary function for rational number z. As an application, some examples are given.     

Y_CΩ_(2n)are easy terms

For any natural number n≥1, Y CΩ 2n is an easy term; that is, for any λ term M, λβ+Y\-CΩ 2n =M is consistent, where Y C is Curry fixed point combinator, Ω 2n ≡ω 2n ω 2n and ω 2n ≡λx.xx...x (there are 2n occurrences of x after λx ). This result is a partial solution to Jacopini's conjecture: Y CΩ n is an easy term for any natural number n≥2.     

具有Markov 跳参数随机微分时滞方程的吸引子

对有限维空间具有Markov参数的随机微分时滞方程的吸引子进行了讨论．根据半鞅收敛定理和Ito公式证明了一个引理．给出了吸引子的定义,并根据引理证明了方程的解无限许多次到达吸引子中,从而得到方程解的弱吸引子是存在的．通过一个例子对得到的结论进行了说明．     

A local asymptotic behavior for ruin probability in the renewal risk model

Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.     

A Linear Hyperbolic System with Stiff Source Terms

We consider the behavior of solutions to the system ut ＋vx =0, vt ＋ux =（au-v）/τ as the relaxation parameter τ approaches 0. If the sub characteristic condition｜a｜ is satisfied, then u approaches a solution to the equilibrium equation ut ＋ aux = 0 and v approaches au. If this condition is violated then solutions have not Fourier transformation when τ→0.     

Model of Markov Chains in Space-Time Random Environments

A general framework of stochastic model for a Markov chain in a space-time random environment is introduced, here the environment ξ^＊：={ξ1,x∈N,x∈ X}is a random field. We study the dependence relations between the environment and the original chain, especially the ＂feedback＂. Some equivalence theorems and law of large numbers are obtained.     

Research of Inclusion Complexation of 4,4＇-Thiodiphenol Effected by β-Cyclodextrin in Aqueous Solutions and the Effect on Photodegradation

The inclusion behavior of 4, 4＇ -Thiodiphenol （TDP）, a typical bisphenol and endocrine disruptor, reacts with β-cyclodextrin （β-CD） in aqueous solutions has been investigated by means of UV absorption spectrum and quantum-chemical calculation with Gaussian 98 software. The results show that the inclusion behavior of TDP is quite different in acidic solutions （pH 5.9） from that in alkaline solutions （pH 10.0）. This behavior difference is attributed to the different formula structures in aqueous solutions at acidic and alkaline pH values that are demonstrated by quantum- chemical modeling and calculation. TDP forms a 1 ： 1 fl-CD inclusion complex in aqueous solutions. The equiiibrium constant K was calculated to be 553.49 L/mol at pH 5.9 and 1 318.20 L/mol at pH 10.0 respectively for the inclusion complex reaction by using the modified Benesi-Heldbrand equation. After inclusion TDP＇s structure is changed especially at the inclusion part with the bond order becoming larger, which results in inhibitive photodegradation during direct photooxidation and H2O2 assisted photooxidation.     

Formation of the inclusion complex of Orange II with β-Cyclodextrin and its photostability

Inclusion complex of Orange II with β-Cyclodextrin (β-CD) and the anti-photolysis effect under UV-light were investigated. The molar ratio of inclusion complex of β-Cyclodextrin and Orange II is 1∶1. The formation constantK = 1.236×10³ L/mol was determined by the UV and Fluorescence spectra respectively, which was quite in accordance with the calculation with a modified Benesi-Hildbrand equation. The inclusion complex was characterized by the IR spectra and the molar ratio of inclusion complex is 1∶1 too. The formation constantK = 1.266×10³ L/mol was determined by¹H NMR analysis and was nearly the same by UV and fluorescence spectra. The photocatalytic decolorization rate of Orange II solutions containing β-CD and TiO₂ was smaller by 51.9% than that of the Orange II solutions only containing TiO₂, while in the case of direct photolysis of Orange II solutions, β-CD can lower the photolysis rate by 48.1% under UV-light. This result indicates β-CD can inhibit the photolysis and photocatalytic decolorization of Orange II under UV-light. The β-CD inclusion complex was found to be persistent to UV-light photolysis. Foundation item: Supported by the National Natural Science Foundation of China (20177017) Biography: Lu Ping (1958), male. Associate professor, research direction: environmental photochemistry.     

Solution of Cauchy’s problem for wave equations in higher space dimensions by means of D’Alembert’s formula

A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown. Foundation item: Supported by the Natural Science Foundation of Hubei Province (992P0307) and the National Natural Science Foundation of China (39970203) Biography: YAO Duan-zheng (1946-), female, Professor, Research direction: mathematical physics and nonlinear optics.     

Stability of a Neutral Stochastic Functional Differential Equations

0IntroductionStmoachnyas stiocp dhiifsftiecraetnetdia ld yenqauamtiicoanls s ycsatne mbse i uns epdh ytsoic adle s,cbriibo-elogical , medical andsocial sciences ,they have beenstudiedformore thanfifty years and developed very quicklly,in particu-lar ,Lyapunov’s second method has been developed to dealwith stochastic stability by many authcrs ,e.g.Ref .[1-3] in-troduced a class of neutral stochastic functional differentialequations .But sofar such equations have been discussed alit-tle unlike …     

一类广义Liénard型方程概周期解的存在唯一性和稳定性

考虑广义Li     

The iterative solution for a class of monotone operator equations

The iterative solution for a class of multivalued monotone operator equations just likeA(u)∈−B(u) is discussed, whereA is a positive definite linear single-valued operator,B is a bounded and monotone multivalued operator. The existence and convergence of approximate solutions are proved. The method of numerical realization is demonstrated in some examples. Foundation item: Supported by the National Natural Science foundation of China Biography: XIAO Jin-sheng (1975-), male, Ph.D. Candidate. Current research interest is in the approximate solution of differential equation.     

A novel method for thermodynamic study on binding of copper ion with Alzheimer’s amyliod β peptide

The interaction of Cu²⁺ with the first 16 residues of the Alzheimer's amyliod β peptide, Aβ (1-16), was studied by employing isothermal titration calorimetry at pH 7.2 and 37℃ in aqueous solution. The Gholamreza Rezaei Behbehani (GRB) solvation model was used to reproduce the enthalpies of Cu²⁺+ Aβ(1-16) interaction over the whole Cu²⁺ concentrations. The binding parameters recovered from the solvation model were attributed to the structural change of Aβ (1-16) due to the metal ion interaction. It was found that there is a set of two identical and non interacting binding sites for Cu²⁺ ions. The molar enthalpy of binding is ΔH=27.895 kJ/mol. The association binding constants are 1.895 μm^-1 and 1.891 μm^-1 for the first and second binding sites respectively.     

Preparation of (R)- and (S)-2-Allyl-1, 3, 2-dinaphtho (α, β) [d.f] dioxaborepin and their reactions with aldehydes

(R)- and(S)-2-Allyl-1,3,2-dinaphtho (α,β) [d.f] dioxaborepin ((R)-2 and(S)-2) have been first prepared by the reaction of(R)-(+)- or(S)-(−)-1, 1′-bi-2-naphthol and triallylborane in THF at room temperature, respectively.(S)-2 and(R)-2 are sensitive to moisture and oxygen in air and disproportionate easily to triallylborane and 1,1′-bi-2 naphthyl bis (1,1′-bi-2-naphtholborate) at ambient temperature. However, THF is a stabilizer for them. The reactions of(R)-2 or(S)-2 and some aliphetic or aromatic aldehydes in CH₂Cl₂ at −78°C for several hours afforded β-alkylenyl alcohols in up to 84.8%ee. Among them, optically active 1-(3, 5-dichlorophenyl)-3-butenol and 1-(2-methoxyphenyl)-3-butenol were first prepared Foundation item: Supported by the National Natural Science Foundation of China (29972033) Biography: Liu Dejun (1973), male, Ph. D, research direction: asymmetric synthesis     

Reverberatory activity in neuronal networks in vitro

It has been proposed that during cognitive processes, ＂online＂ memory traces in the brain are carried by reverberatory activity in neuronal circuits. However, the nature of such reverberation has remained elusive from experimental studies, largely due to the enormous complexity of intact circuits. Recent works have attempted to address this issue using cultured neuronal network and have revealed new dynamic properties of network reverberation as well as the underlying cellular mechanisms. These results demonstrate the effectiveness of in vitro networks as a useful tool for mechanistic dissection of neuronal circuit dynamics.     

A hybrid model for the mid-long term runoff forecasting by evolutionary computation techniques

The mid-long term hydrology forecasting is one of most challenging problems in hydrological studies. This paper proposes an efficient dynamical system prediction model using evolutionary computation techniques. The new model overcomes some disadvantages of conventional hydrology forecasting ones. The observed data is divided into two parts: the slow “smooth and steady” data, and the fast “coarse and fluctuation” data. Under thedivide and conquer strategy, the behavior of smooth data is modeled by ordinary differential equations based on evolutionary modeling, and that of the coarse data is modeled using gray correlative forecasting method. Our model is verified on the test data of the mid-long term hydrology forecast in the northeast region of China. The experimental results show that the model is superior to gray system prediction model (GSPM). Foundation item: Supported by the National Natural Science Foundation of China ( 60133010, 70071042, 60073043) Biography: Zou Xiu-fen(1966-),female,Associate professor, research direction:evolutionary computing, parallel computing.