Asymptotic convergence to steady-state solutions for solutions of the initial boundary problem to a simplified hydrodynamic model for semiconductor

We studied the asymptotic behavior of solutions to the initial boundary value problem on the spatial interval [0,1] for a one-dimensional simplified gydrodynamic model for semiconductors wheng(t)→b ^*, and proved the unique global existence of smooth solutions to the initial boundary problem. We also show that the solutions converge to the corresponding steady-state solutions time-asymptotically by introducing the suitable shift functions. Biography: Ying Gu-liang(1958-), male, Lecturer, research interest: differential equation.     

Riemann Boundary Value Problem with Square Roots on an Open Arc

The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.     

非线性四阶抛物型方程Cauchy问题整体经典解

本文对具有耗散条件的一类非线性四阶抛物型方程Cauchy问题的小初值情形及其经典解的整体存在唯一性与衰减渐近性进行了研究．     

一类非严格双曲型可化约组Cauchy问题的整体经典解

讨论了线性退化情形下的非严格双曲型可化约组Ｃａｕｃｈｙ问题经典解的整体存在性，给出了保证其经典解整体存在的充分及必要条件．     

Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order

0　IntroductionIn Ref. [1 3], Lu Jian ke first discussed singular integralequations with solutions having singularities of order oneK≡a(t0)(t0) b(t0)πi∫L(t)t- t0dt ∫Lk(t0,t)(t)dt= f(t0), t0 ∈L (1)wh     

等熵磁气体动力学方程组的柯西问题

 研究等熵磁气体动力学方程组的柯西问题.在初值是连续且分片光滑函数的假设下,首先证明了当初始时刻不出现真空时,解中也不会出现真空.其次,证明了该柯西问题存在唯一的连续且分片光滑的整体解.     

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.     

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.     

Large time behavior of solutions for general Navier-Stokes systems in multi-dimension

Through the estimates for Green's function of linearized system, we obtainL′ estimates of the asymptotic behavior of solutions of the Cauchy problem for the Navier-Stokes systems of compressible flow in several space dimensions. Supported by the National Natural Science Foundation of China Wang Weike: born in March 1954, Professor     

An Improved Genetic Algorithm for Problem of Genome Rearrangement

In view of the fact that the problem of sorting unsigned permutation by reversal is NP-hard, while the problem of sorting signed permutation by reversal can be solved easily, in this paper, we first transform an unsigned permutation of length n,π （π1 ,… ,πn）, into a set S（π） containing 2^n signed permutations, so that the reversal distance of π is equal to the reversal distance of the optimal signed permutation in S（π）. Then analyze the structural features of S（π） by creating a directed graph and induce a new computing model of this question. Finally, an improved genetic algorithm for solving the new model is proposed. Experimental results show that the proposed model and algorithm is very efficient in practice.     

Attraction and stability for neutral stochastic functional differential equations

The main aim of this paper is to establish several new criteria on the attractor for the solutions of neutral stochastic functional differential equations. A kind of ψ-function is introduced to our discussion, and some results on the attractor for the product of the ψ-function and the solutions are obtained. As a byproduct, a number of new criteria on asymptotic stability are also shown. Biography: CEN Liqun(1975–), female, Ph.D. candidate, research direction: theory and applications of stochastic differential equations.     

绝热气动力学方程组的整体光滑解

本文研究Lagrange坐标下绝热气动力学方程组的Cauchy问题,得到了其整体光滑解存在性的若干结果。     

一类奇异扩散方程解的若干估计

］讨论了一类具源项的奇异扩散方程的Cauchy问题,证明了该问题的整体光滑正解的存在唯一性, 并且给出了解的若干重要估计     

Nonlinear Liouville Theorem in the Quaternionic Heisenberg Group

This paper deals with the problem of the type △nf f^p=0 in quaternionie Heisenberg group, where △n is the quaternionic Heisenberg Laplacian. It is proved that, un der suitable conditions on p and f. the only solution of △nf f^P=0 is f=0.     

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.     

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.     

具有特殊压力含有源项一维可压Euler方程组的弱解存在性

 研究一类双曲系统——具有特殊压力含有源项的一维可压Euler方程组的Cauchy问题,应用补偿紧性理论和最大值原理,得到其有界弱解的整体存在性结果。所研究系统的齐次形式是1858年Earnshaw在研究等熵流体时第一次被推导出来,同时也被称为一位可压流的Euler方程组。其中的关键是用最大值原理得到相应的抛物方程组解的L^∞估计,同时举出满足定理1条件(C1)–(C3)的一些具体源项。     

Weak solutions of the isothermal bipolar hydrodynamic model for semiconductors with large data

This paper is devoted to weak solutions of Cauchy problem to the isothermal bipolar hydrodynamic model with large data. The model takes the bipolar Euler-Poisson form, with electric field and relaxation terms added to the momentum equations. Using Glimm scheme to the hyperbolic part and the standard theory to the ordinary differential equations, we first construct the approximation solutions, then from the facts that the total charge is quasi-conservation, we can obtain a uniform estimate of the total variation of the electric field, which allows to prove the L∞ estimate of densities and velocities, and the convergence of the scheme. Then we can prove the global existence of weal solution to Cauchy problem with large data.     

Polynomial Analysis of DH Secrete Key and Bit Security

In this paper, we lower the upper bound of the number of solutions of oracle transformation polynomial F(x) over GF(q). So one can also recover all the secrete keys with fewer calls. We use our generalized ““““““““even-and-odd test““““““““ method to recover the least significant p-adic ‘bits‘ of representations of the Lucas Cryptosystem secret keys x. Finally, we analyze the Efficient Compact Subgroup Trace Representation (XTR) Diffie-Hellmen secrete keys and point out that if the order of XTR subgroup has a special form then all the bits of the secrete key of XTR can be recovered form any bit of the exponent x.     

Some Results about the Sample Path Properties of Markov Processes with Independent Self-Similar Components

This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.