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.     

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.     

Efficiency of Slit Dam Prevention against Non-Viscous Debris Flow

This paper describes an experimental work in order to assess the efficiency of slit dam on non-viscous debris flow. Some results have been acquired as follows： （1） there are three kinds of blocking type; Total-blocking, opening and part-blocking. The blocking conditions of slit dam are closely link to b/dmax （the ratio of slit width to maximum diameter of solid matter）, as b/dmax is less than 0. 739, the slit dam is total- blocking; and b/dmax is more than 1. 478, the slit dam will be opening; whereas b/dma ranges from 0. 739 to 1. 478, the slit dam is part-blocking. （2） Variation of the mean density passing through slit dam is the most obvious as b/dmax ranges from 0. 739 to 1. 232. （2） According to experimental results, slit dams have been shown to be effective in reducing debris flow density while slit density ∑ b/B （B is slit dam width） ranges from 0.2 to 0. 5.     

一类非线性系统概周期解的存在唯一性

用渐近概周期函数法研究一类非线性微分方程:x′=A(t,x)x+g(t,x)的概周期解的存在唯一性,得到保证该方程存在唯一概周期的充分性条件.     

On the Family of Thue Equation ｜x^3 ＋ mx^2y-（ m ＋ 3）xy^2 ＋ y^3｜= k

The family of cubic Thue equation which depend on two parameters ｜ x^3 ＋ mx^2 y-（m＋3） xy^2＋y^3｜=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is quite better than the present result. Moreover, we study two inequalities ｜ x^3 ＋ mx^2y-（m ＋ 3） xy^2＋y^3 ｜ =k≤2m＋3 and ｜x^3 ＋mx^2y- （m＋3）xy^2 ＋ y^3｜ = k≤ （2m＋3）^2 separately. Our result of upper bound make it easy to solve those inequalities by simple method of continuous fraction expansion.     

Studies on a series complexes of copper (II), zinc (II), cobalt (III) with Schiff base derived fromd-glucosamine and salicylaldehyde

Copper (II) zinc (II) cobalt (III) complexes with the Schiff base derived from salicylaldehyde andd-glucosamine were synthesized. These compounds abbreviated as SG, CuSG, ZnSG, CoSG were characterized by elemental analyses, IR, UV-Vis,¹H NMR and MS spectrum. ESR spectrum, magnetic susceptibility measured by Evans method for CuSG had also been done. It is suggested that the complexes in solution have pseudotetrahedral structure. It was found that SG would occur a photochemical reaction if a beach of 355 nm ultravisible light shone on its aqueous solution. The reaction was in further research. Supported by the National Natural Science Foundation of China Ye Yong: born in 1970, Ph. D graduate student     

Local time of additive Levy process

We studied the problem of existence of jointly continuous local time for an additive process.Here, “local time” is understood in the sence of occupation density, and by an additive Lévy process we mean a process X＝{X(t), t∈Rd+)} which has the decomposition X＝ X1 X2 … XN. We prove that if the product of it slower index and N is greater than d, then a jointly continuous local time can be obtained via Berman's method.     

A study of bacterial linear growth using a microcalorimetric method

By using an LKB-2277 bioactivity monitor, we have determined the thermogenesis curves of four kinds of anaerobes linear growth. From the thermogenesis curves, we established the growth thermokinetic equation: dP/dt=k _m·P ⁿ , the order of growth metabolismn=0, and calculated the mean specific rate constant of multiplication {ie95-1}. It is a new kind of bacterial growth, it was compared with exponential growth. Liu Yi: born Nov. 1970. Ph. D. Curent research interest is in biothermochemistry research Supported by the National Natural Science Foundation of China     

The numerical method of inversion for the interior Radon transform

The interior Radon transform arises from a limited data problem in computerized tomography. The corresponding operator R is investigated as a mapping between wightedL ₂-spaces. Our result is the explicit construction of a singular value decomposition for R. This immediately leads to an inversion formula by series expansion and range characterizations. Foundation item: Supported by the Foundation of the Ministry of Education of China and the Science Foundation of Wuhan University Biography: WANG Jin-ping (1963-), male, Ph.D candidate, Research interests are in numerical solution of singular integral equation and integral transformation.     

样条子空间逼近周期可微函数的最佳逼近度

样条函数类与周期函数类的逼近问题是函数逼近论的重要内容。为了在较大范围内研究最佳逼近问题,在Lp空间内研究最佳逼近方法的基础上,利用最佳逼近的对偶原理、Holder不等式等工具,借助抽象逼近的方法和技巧,研究了样条子空间在Orlicz空间内的最佳逼近问题,给出了最佳逼近度的估计式。研究结果对误差估计、精度分析可提供必要的理论分析依据和参考数据。     

Characterization of Anabaena cylindrica Solution System Using Synchronous-Scan Fluorescence Spectroscopy

The characterization of the algaeAnabaena cylindrica solution with Fe (III) was investigated using fluorescence emission and synchronous-scan spectroscopy. The ranges of concentrations of algae and Fe (III) in aqueous solutions were 5.0×10⁸ 2.5×10⁸ cell/L and 1060 μmol/L. respectively. The effective characterization method used was synchronous-scan fluorescence spectroscopy (SFS). The wavelength difference (Δλ) of 90 nm, was maintained between excitation wavelength (λen) and emission wavelength (λen). The peak was observed at about (λex) (λem) 326 nm for synchronous scan fluorescence spectroscopy. The fluorescence quenching in system of algae Fe(III)-HA was studied using synchronous-scan spectroscopy for the first time, Fe(III) was clearly the effective quencher. The relationship betweenI I (quenching efficiency) andc (concentration of Fe (III) added) was, a linear correlation for the algae solution with Fe(III). Also, Aldrich humie acid (HA) was found to be an effective quencher. Foundation item: Supported by the National Natural Science Foundation of China (20177017) and the Scientific Research Foundation of Wuhan Environmental Protection Bureau Biography: LIU Xian li(1965), male. Ph.D. Associate professor, research direction: environmental chemistry.     

The fourier transformations of positive distributions on lorentz groupSO (3, 1)

With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed intoμ=μ ₁+μ ₂, whereμ ₁ is a bounded measure on 0<=s<=2 andμ ₂ is slowly increasing measure on (sχC|Re(s)=1)} Foundation item: Supported by the National Natural Science Foundation of China (19871065) and Hua Cheng Mathematics Science Foundation. Biography: Zhu Li (1976-), male, Graduate student, research interest: partial differential equation     

On the thinness of non-tangential sets

Let Ω⊄R ^d and ξ∈∂Ω. LetE be any non-tangential subset of Ω. we prove that ifE is internal thin at ξ, then it is minimal thin at any minimal Martin boundary point of Ω. Supported by the National Natural Science Foundation of China Zhang Yiping: born in Dec. 1962. Professor     

A convenient preparation of enantiopure 1,1′-bi-2-naphtholsvia an inclusion complexation in the solid state

Inclusion reaction of racemic 1,1′-bi-2-naphthol and (S)-proline was examined under the solid state and the solid-liquid conditions. The results indicated that a solid mixture of racemic 1,1′-bi-2-naphthol and (S)-proline in a 1∶1 molar ratio was kept at 50–80 °C for 3–4 h, followed by treatment with benzene to give an insoluble solid and a benzene solution, from which (S)-(−)- and (R)-(+)-1,1′-bi-2-naphthols of a modest level of optical purity were obtained. After “kinetic” crystallization, both essentially enantiopure isomers were provided in 15%–35% overall yields, respectively. Foundation item: Supported by the National Natural Science Foundation of China (29972033) and the Key Science Research Foundation of Hubei Province (891P1305) Biography: Shan Zi-xing (1945-), male, Professor, research direction: asymmetric synthesis.     

Binding of Euplotes octocarinatus centrin with target peptide melittin

Interactions between model target peptide melittin (ME) and Euplotes octocarinatus centrin (EoCen) were investigated by fluorescence spectra, circular dichroism (CD) spectra and native polyacrylamide gel electrophoresis (PAGE). In 0.1 mol/L N-2-hydroxyethylpiperazine-N-2-ethanesulfonic acid (Hepes) and 150 mmol/L NaCl at pH 7.4, EoCen and isolated short C-terminal domain of EoCen (SC-EoCen) form 1:1 peptide:protein complexes. However, no detectable signal changes can be observed while isolated N-terminal domain of EoCen (N-EoCen) or isolated long C-terminal domain of EoCen (LC-EoCen) was added into solution of ME. The interaction between EoCen and ME is specified exclusively for the short C-terminal domain of EoCen. On the basis of fluorescence titration curves, the conditional binding constants of ME with EoCen and SC-EoCen were calculated to be logKME-EoCen = 6.81±0.33 and log- KME-SC-EoCen = 6.51±0.45, respectively.     

A Novel Polymethyl Methacrylate （PMMA）TiO2 Nanocomposite and Its Thermal and Photic Stability

A new kind of polymethyl methacrylate （PMMA）-TiO2 nanocomposite was synthesized through polymerization. The thermal and photic stability of this PMMA TiO2 nanocomposites were investigated. The as prepared samples were characterized by scanning electron microscopy （SEM）, UV-Vis spectroscopy, differential thermal analysis （DTA） and the photo-induced weight loss, The results show that the photostability of the PMMA-TiO2 nanocomposite is higher than that of the pure PMMA under UV-light irradiation, The weight loss of the pure PMMA reaches 30 % after 300 h UVirradiation, while the composite only 0.3% under the identical experimental condition. The glass transition temperature （TR） of pure PMMA is only 80℃, while the Tg of the composite reaches 258℃. Compared with pure PMMA, the thermal stability of the composite is greatly enhanced.     

Study on the charge transference and local magnetic moment of yttrium-cobalt compound

The electronic charge transference and local magnetic moment of the YCo₅ intermetallic compound were calculated using SCF-MO-DVXα method and multiple cluster model. The result shows that about one 4d-electron is transferred from anY atom to Co₁(2c), and the calculated local spin magnetic moments of Co_I(2c) and Co_II(3g) atoms in YCo₅ compound are 1.33 and 1.48μ _B , respectively, which are in very good agreement with experiments. Supported by the National Natural Science Foundation of China Qiao Haoxue: born in Apr. 1970, Master     

The characteristic of electrochemical oxidation of aniline on SnO2/Ti electrode

The characteristic of electrochemical oxidation of aniline on SnO₂/Ti electrode is studied. The results indicate that SnO₂/Ti electrode dopedF plays a wonderful role in the oxidation of aniline comparing with Pt electrode. The kinetics factors that influence the oxidation rate of aniline on the SnO₂/Ti electrode are determined by the dissolving of the film on the electrode. The dissolving of the film consisted of intermediate products on the electrode is the slow step. The effects of aniline concentration, pH in aniline solution and the current density (i) on the rate of aniline oxidation, the complexity of intermediate products and the basic category of the intermediate products consisted of the film are introduced. Foundation item: Supported by the National Natural Science Foundation of PRC(10971023) Biography: Wany Yu-ling (1975-), female, Master, research direction: photochemical catalysis and electochemical catalysis.     

Studies on the behaviors of PbSO4/Pb and PbO2/PbSO4 electrodes prepared from lead carbonate by powder microelectrode technique

The behaviors of PbSO₄/Pb and PbO₂/PbSO₄ electrode prepared from PbCO₃ have been examined using powder microelectrode(PME) technique and cyclic voltammetry(CV). Firstly, PMEs packed with PbCO₃ transformed into PbSO₄ PME in 1.0 mol/L H₂SO₄ solution at 30 °C, and then the PbSO₄ in the PMEs were formed to Pb or PbO₂ using an unsymmetrical signal (Q _a/Q _c for PbSO₄/Pb electrode andQ _c/Q _a for PbO₂/PbSO₄ electrode being 0.1–0.3) in 2.5 mol/L H₂SO₄ solution. The results show that the CV characteristic of either PbSO₄/Pb or PbO₂/PhSO₄ PME prepared from PbCO₂ are as good as that of both electrodes made from lead oxide powder produced by ball mill. Foundation item: Supported by the National Natural Science of China(29677013) and Chenguang Foundation of Wuhan Municipal Science and Technology Commission(20005004022) Biography: Dai Zhong-xu(1968-), male, Lecturer, Ph. D. candidate, research direction: electrochemistry.     

A Note on the Multifractal Decomposition of Directed Graph Self Similar Sets

We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e.,dim Ku^a DimKu^a =f(a), where fis the multifractal spectral function of the directed graph self similar measure. Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping.