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.     

A Large Deviation Principle for the Risk Process with Varying Premium

Let u ∈ R ,for any ω 〉 0, the processes X^ε = {X^ε（t）; 0 ≤ t≤ 1} are governed by the following random evolution equations dX^ε（t）= b（X^ε（t）,v（t））dt-εdSt/ε, where S={St; 0≤t≤1} is a compound Poisson process, the process v={v（t）; 0≤t≤1} is independent of S and takes values in R^m. We derive the large deviation principle for{（X^ε,v（.））; ε〉0} when ε↓0 by approximation method and contraction principle, which will be meaningful for us to find out the path property for the risk process of this type.     

Multi-parameter infinite-dimensional (r,δ)-OU process

The definition of n-parameter infinite-dimensional (r,δ) -Ornstein-Uhlenbeck process {xt (·) } ((r, δ)-OUPn∞ for short) is given. The absolute continuity of distribution μt of Xt(·) and the limit of Xt(·) when |t| →∞ is discussed.     

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.     

Absolute continuity of interacting measure-valued branching processes and its occupation-time processes

Let X t be the interaction measured_valued branching α_ symmetric stable process over R d(1<α≤2) constructed by Meleard_Roelly . Frist, it is shown that X t is absolutely continuous with respect to the Lebesgue measure (on R ) with a continuous density function which satisfies some SPDE. Second, it is proved that if the underlying process is a Brownian motion on R d (d≤3), the corresponding occupation_time process Y t is also absolutely continuous with respect to the Lebesgue measure.     

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.     

New method on constructing analytic potential function of diatomic molecules

A new method on constructing analytical potential energy functions is presented, and then a relatively universal analytical potential energy function for precisely calculating the spectra of diatomic molecules and ions is derived. Furthermore, six kinds of common potential energy curves containing three main potential curves i.e. steady state, metastable state and repulsive state are obtained from this potential energy function. Finally, spectroscopic parameters of thirteen diatomic molecules and ions including BeD-X ² Σ ⁺, BeT-X ² Σ ⁺ and Na₂-X ¹ Σ _g ⁺ etc are calculated by using the potential function, as a consequence, all calculation results are in good agreement with experimental data. Biography: YU Changfeng (1962–), male, Associate professor, research direction: theoretical physics.     

On the limiting behavior of weighted partial sums for<Emphasis Type="Italic">B</Emphasis> valued martingale difference sequences

Let {X_n, n≥1} be a martingale difference sequence and {a _nk , 1⩽k⩽n,n⩾1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ _k=1 ⁿ a _nk X _k is investigated and some new results are obtained. Foundation item: Supported by the National Natural Sciene Foundation of China (No. 10071058 and No. 10071019) Biography: Gan Shi-xin (1939-), male, Prof lessor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.     

On random Taylor series

This paper deals with random Taylor series whose coefficients consist of independent random variables {X _n } with the property: αE ^1/2{|X _n |²}≤E{|X _n |}<∞,E{X _n }=0 (Ån) for some positive constant α. The convergence, growth, and value distribution of the series are investigated. Supported by the National Natural Science Foundation of China (No. 101960433) Ding Xiaoqing: born in Oct. 1958, Doctoral candidate     

B-Valued Dyadic Derivative

The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.     

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.     

Blowup rate of positive solution of a semilinear parabolic system

It is dealt with positive solutions to the systems: u-t-u- XX =v+p, v-t-v XX =u+q in Ω×(0, T) subject to either initial conditions or boundary_value conditions. The exact blowup rate estimates of solution are established under some monotonicity assumptions on the initial values.     

Preliminary Mo isotope data of Phanerozoic clastic sediments from the northern margin of the Yangtze block and its implication for paleoenvironmental conditions

Mo isotopes along with Nd isotopes and other geochemical characteristics of the Phanerozoic clastic sediments from the northern margin of the Yangtze block were analyzed by MC-ICP-MS and some other techniques, spanning the period from Cambrian to Jurassic. The δ 98Mo values and εNd(t ) in these sedimets were observed to exhibit a large range of variation (?0.65‰―+1.87‰, ?1.46―?10.90, respec-tively). Specifically, the sample from Late Permian Maokou Formation has relatively positive values in both δ 98Mo and...     

The exact measure functions of the images for a class of self-similar processes

Let {ie1-1} be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the imageX([0,t]) are obtained. Foundation item: Supported by the National Natural Science Foundation of China Biography: HUANG Li-hu(1972-), male, Ph. D graduate student, research interest is in stochastic processes.     

Fluorescence Determination of Artemisinin Using Hemoglobin as Catalyst and Pyronine B as Substrate

0 IntroductionMaalnadria siusb atr ompajicosr .he aAltrthe pmrisoibnlienmi (n qtihneghtraoopsiucs,QHS,Fig.1) is a sesquiterpene endoperoxide isola-ted fromArtemisia annuaL., an ancient Chineseherbal medicine usedfor treatment of fever and ma-laria.Studies of the structure and activity relation-ship have shownthat endoperoxide groupis essentialfor anti malarial activity of QHS and absence of thismoiety lead to completely loss in activity of thedrug. Many techniques have been developed to de…     

Finite Time Ruin Probability with Variable Interest Rate and Extended Regular Variation

Consider an insurance risk model, in which the surplus process satisfies a recursive equation Un=Un-1(1 rn)-Xn for n≥1, where U0=x≥0 is the initial surplus, {rn；n≥1} the interest rate sequence, {Xn；n≥l} the sequence of i. i. d. real-valued random variables with common distribution function F, which denotes the gross loss during the nth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result as x→∞.     

Quantitative Estimates of Outcrossing Rates in a Natural Population of Caldesia grandis （Alismataceae）

Outcrossing rate in a natural population of Caldesia grandis was estimated by the dominant random amplified polymorphism DNA (RAPD) marker using 10 open-pollinated progeny arrays of 24 individuals. The multilocus outcrossing rate estimated based on all 25 RAPD loci was 0.872 ±0.033 and the single-locus outcrossing rate was 0.795 ±0.032. Multilocus estimates did not differ significantly from the single-locus estimates. The fixation index, F, in the progeny estimated from RAPD data was -0.142 ±0.000. The estimates of multilocus outcrossing rates (t_m) and single-locus outcrossing rates (t_s) obtained from MLDT clearly indicate that outcrossing is predominant in the open-pollinated C. grandis population. An empirical analysis suggests that 15 should be the minimum number of dominant marker loci necessary to achieve robust estimates of t_m.     

Determination of crystal structure of omphacite

The chemical formula of omphacite was expressed with (MⅡ MⅠ ) (Si, AI)2O6. Cations that occupied the MⅡ site were large cations such as Ca or Na, and (Na/(Na+Ca)) ratio ranged from 0.2 to 0.8; the 6-coordinated MⅠ site accommodated cations such as Mg, Fe2+, Al, Fe3+ ,and(AI/(AI+Fe3+)) ratio was more than 0.5. Omphacite space groups reported were C2/ c, P2, P2/n, P2/c, cell parameters are α0 = 0.9600-0.9630 nm,b0 = 0.8750-0.8830 nm,c0 = 0.5230-0.5290 nm,β = 106°40′-107°10'. The sample was picked up from the eclogites in Zhucheng County, Shangdong Province. The intensity data were collected with the RIGAKU RASA Ⅱ -S four-circle single crystal diffractometer.The correct structure model was obtained by using the Patterson method and Fourier synthesis, SHELX-76 program, structure refinement with 905 independent diffraction points (| F0 |> 3σ |F0 |). After the structure parameter refinement, the R-factor reduced to 0.0515. The crystal structure analysis indicates that omphacite has a new space group-Pn space group.     

线性变换半群T_(X×X)的格林关系和正则元

设X是自然数集N或整数集Z,T_(X×X)是X×X上的线性变换半群.通过分析整除关系,获得了半群T_(X×X)的格林关系和正则元.     

Near-infrared to visible up-conversion emissions of Er^3＋ doped Al2O3 powders derived from the sol-gel method

The Er3 doped Al2O3 powders were prepared by the sol-gel method using the aluminium isopropoxide [Al(OC3H7)3]-derived Al2O3 sols with addition of the erbium nitrate [Er(NO3)3.5H2O]. The different phase structure, including three crystalline types of (Al,Er)2O3 phases, γ, θ, α, and two Er-Al-O phases, ErAlO3 and Al10Er6O24, was obtained with the 1 mol% Er3 doped Al2O3 powders at the different sintering temperatures of 600―1200℃. The green and red up-conversion emissions centered at about 523, 545 and 660 nm, corresponding respectively to the 2H11/2, 4S3/2→4I15/2 and 4F9/2→4I15/2 transitions of Er3 , were detected by a 978 nm semiconductor laser diodes excitation. The phase structure and OH content had evident influence on the up-conversion emissions intensity. The maximum intensities of both the green and red emissions were obtained respectively for the Er3 doped Al2O3 powders sintered at 1200 ℃, which was composed mainly of α-(Al,Er)2O3, less of ErAlO3 and Al10Er6O24 phases, and with the least OH content. The two-photon absorption up-conversion process was involved in the green and red up-conversion emissions of the Er3 doped Al2O3 powders.