A sufficient condition fork′(z)(k(z)∈H q,q≥1) to be ofH 1

We proved ifk(z)∈H ^q (q≥1),g(z) is analytic on |z|=1, , thenk′(z)∈H ¹, especially, ifq=1, thenk(z) is an analytic function on the closed unit disk |z|≤1. Peng Zhigang: born in June 1970, Ph. D     

On the boundary value problem for harmonic maps of the Poincaré disc

The boundary value problem for harmonic maps of the Poincare disc is discussed. The emphasis is on the non-smoothness of the given boundary values in the problem. Let T . be a subspace of the universal Teichmüller space, defined as a set of normalized quasisymmetric homeomorphisms h of the unit circle S onto itself where h admits a quasiconformal extension to the unit disc D with a complex dilatation μ satisfying where ρ(z)|dz|2 is the Poincare metric of D. Let B . be a Banach space consisting of holomorphic quadratic differentials φ in D with norms It is shown that for any given quasisymmetric homeomorphism h : S1→S1∈ T . , there is a unique quasiconformal harmonic map of D with respect to the Poincare metric whose boundary corresponding is h and the Hopf differential of such a harmonic map belongs to B .     

A topological approach to the correlation of standard formation enthalpy with path index of benzenes derivatives

A mathematical model formulated as ΔfHθm(g)=a+sum from i=1 to 5bipi(i≠2) was constructed for the relationshipbetween standard formation enthalpy ΔfHθm(g) and path index Pi of substituted benzenes derivatives. An empiric equation for the calculation of ΔfHθm(g) was worked out. The calculated values of standard formation enthalpy based on this model are excellently consistent with those from experimental for 55 organic compounds. The model is shown to be simple and of practical usefulness, particularly when required experimental data are unavailable.     

Some limit theorems for weighted sums of random variable fields

1Preliminaries DuringthelastyearsthereappearedquiteafewpapersaboutlimittheoremsforBanachspacevaluedrandomvariables(r.v.’s)withmultidimensionalindex.Itistheaim ofthispapertogivecomparativeweakconditionswhichimply limittheoremsforweightedsumsofBanachspacevaluedr.v.fields.Thecurrentworkextendsthecorrespondingresultsof Refs.[15].Westartwithsomenotationsanddefinitions.LetNdbe thesetofalld dimensionallatticeofpointswithpositiveinte gersascomponents,whered≥1isafixedinteger.LetNdbe equippedwithco…     

Generalized Galerkin approximations for pseudoinverses and operator equations of the first kind

0 IntroductionLeqtuiliHnebaer afo rHimlbaenrtd sap baoceun.dLeedtlianaenardfufnbceti oan baolu onndeHd ,serse--spectively. Our goal is to seekv∈Hsuchthata(u,v) =f(u) , u∈ H (1)As a rule, we call the expression (1) a variational equationandva solutiontothis equation.By virtue of the Riesz repre-sentationtheorem,there exists a uniquely determined boundedlinear operatorA:H→Hsuchthata(u,v) =〈u,Av〉, u,v∈ H,where〈·,·〉is the inner product onH.If the sesquilinearformais also with posit…     

Almost sure convergence and complete convergence for the weighted sums of martingale differences

Let {(D _n, FFF_n),n/->1} be a sequence of martingale differences and {a _ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption. Foundation item: Supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation of China Biography: DENG Ai-jiao (1974-), female, Ph.D. candidate. Research interest is in stochastic processes and random fractal.     

The boundedness of singular integral operator along an open curve

It is well known that, the singular integral operatorS defined as: ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH ^μ(L) intoH ^μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH ^* intoH ^*. In this paper, we define a Banach space , and prove that is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators. Supported by the National Science Foundation of China Wang Xiaolin: born in Aug. 1950, Professor     

Application of thermogravimetry to study the kinetics and stability of porphyrin copper-sodium of ephedra

Thermogravimetry was used to study the non-isothermal decomposition kinetics and the stability of porphyrin copper-sodium from ephedra. The kinetic equation for the second step can be expressed as . The kinetic compensation effect is found to be: InA=0. 2468E _a −8. 0513.Ea is 206. 61 kJ/mol. The results show that porphyrin copper-sodium has a high activation energy and good stability. Biography: Zhang Lian-ru(1964), female, lecturer Research direction, applied biochemistry.     

Some polar sets for the generalized Brownian sheet

Let (t)(t ∈ R ₊ ^N ) be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for (t). It is proved that for any a ∈ R ^d , P{ (t) = a, for some t ∈ R _> ^N } = and the probability that (t) has k-multiple points is 1 or 0 according as whether 2kN > d(k − 1)β or 2kN < d(k−1)α. These results contain and extend the results of the Brownian sheet, where R _> ^N = (0,+∞) ^N ,R ₊ ^N =[10,+∞) ^N ,0< α≤1 and β≥1. Biography: LI Huiqiong (1966–), female, Associate professor, research direction: stochastic process and random fractal.     

Strong stability of linear forms in φ -mixing random variables

In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {x _n , n ⩾ 1} and two sequences of positive numbers {a _n , n ⩾ 1} and {b _n , n ⩾ 1} there exist d _n ∈ R, n = 1,2,L, such that a.s. under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables. Foundation item: Supported by the National Natural Science Foundation of China(10671149)     

Population-size-dependent branching processes in Markovian random environments

A branching model {Z n} n≥0is considered where the offspring distribution of the population's evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.     

The symmetric solutions of affiliated value model

0　IntroductionIntheprocessofR&Ditem ,thereisusuallycompetition .ManyfirmswanttoinvestR&Dtoobtainapatent.Lury[1 ] gaveanequilibriuminvestmentundertheconditionofone timeinvestmentandcontinuousinvestmentwhenthepayoffwasafixedprize.Ref.[2 ]analyzedtheeffectofinformationsharinginR&D .TherearemanyliteraturesaboutanalysisofR&DlevelswhenfirmscompeteinoutputmarketafterR&Dsucceeds[3 ,4] .Additionally ,todecideinvestmentlevel,therearemanyliteraturesaboutR&Ditem’spricing .MondherBellalah[5] ,K .…     

Characterization of type<Emphasis Type="Italic">p</Emphasis> Banach spaces by the weak law of large numbers

For weighted sums of the form where {a _nj , 1 ⩽j⩽k _n ↑∞,n⩾1} is a real constant array and {X _aj , 1≤j≤k _{n, n}≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL ^r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums. Foundation item: Supported by the National Natural Science Foundation of China (No. 10071058) Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.     

Synthesis of biodiesel from rapeseed oil using K2O/ γ -Al2O3 as nano-solid-base catalyst

Nano-solid-base catalyst K₂O/γ-Al₂O₃ was prepared and adopted for the synthesis of biodiesel by transesterification of rapeseed oil with methanol. The particle diameter of the catalyst was about 50 nm, which was measured by transmission electron microscopy (TEM). The variables affecting the yield of biodiesel during transesterification, such as mass ratio of KNO₃ to γ-Al₂O₃, calcination temperature, calcination time, and catalyst content, molar ratio of methanol to oil, reaction temperature and reaction time were investigated. The catalyst obtained by calcining a mixture of KNO₃ and γ-Al₂O₃ at 600 °C for 3 h, was found to be the optimum one, which gave the highest catalytic activity in reaction. With 3% (m _catalyst/m _oil) catalyst, when the transesterification carried out at a molar ratio of methanol to oil 12:1, a reaction temperature of 70 °C, and a reaction time of 3 h, yield of 94% was achieved. Foundation item: Supported by the National High-Technology Research and Development Program of China (863 Program) (2007AA100703)     

与高阶导数分担多项式的整函数

证明了如果$~f~$是非常数整函数满足超级$~\sigma_{2}(f)<\frac{1}{2}~$,~$~k~$是一正整数,~如果$~f~$和$~f^{(k)}~$分担多项式$~p(z)~$~CM,~其中$~p(z)=a_{m}z^{m}+a_{m-1}z^{m-1}+\cdots+a_{0}~$~($~a_{m}\neq 0,~a_{m-1},~\ldots,~a_{0}~$均为常数)~,~那么$~f^{(k)}(z)-p(z)=c(f(z)-p(z))~$,~其中$~c~$是非零常数.     

Almost sure convergence of weighted sums of NA sequences

For double arrays of constants {a _ni, 1≤i≤k _n, n≥1} and NA r.v. 's {X _n, n≥1}, conditions for almost sure convergence of are given. Both casesk _n ↑ ∞ andk _n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case. Supported by the National Natural Science Foundation of China Cheng Riyan: born in 1968, MS student     

Almost sure convergence of weighted sums of NA sequences

For double arrays of constants {a _ni, 1≤i≤k _n, n≥1} and NA r.v. 's {X _n, n≥1}, conditions for almost sure convergence of are given. Both casesk _n ↑ ∞ andk _n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case. Supported by the National Natural Science Foundation of China Cheng Riyan: born in 1968, MS student     

The Hàjek-Rènyi inequlity for Banach space valued random variable sequences and its application

In this paper we prove the following Hàjek-Rènyi inequality: Let 0≤p≤1, then for any Banach spaceB, anyL ^p integrableB valued random variable sequence {D _n , n≥1}, any real number sequence {b _n , n≥1} with 0<b _n, ↑ ∞, any integern≥1, there exist a constantC=C _p>0 (only depending onp) such that

Asymptotic normality of multi-dimension quasi maximum likelihood estimate in generalized linear models with adaptive design

0Introduction Considerthemodel:y=h(x′β)+e wherey=y(1)y(q),h(t)=h(1)(t)h(q)(t),e=e(1)e(q),h(i),i=1,2,…,qisaknownboundedinjection:Rq→R1,h′isapositive matrixwith h(i)(t)tjasits(i,j)elementj=1,2,…,q,t=(t1,t2,…,tq),thepartialderivativesof2thorderofhexistandcontinuous.eistherandomerror.βisthep×1unknowparameterandxiisthefixedknownp×qmatrix,i=1,…,n,η=x′βiscalledpredictor,andthismodeliscalledgeneralizedlinearmodel.Supposetheindependentobservationsy1,…,ynaregetfromq dimensionrespons…     

Kinetics of C2(a3Πu) radical reactions with NO, N2O, O2, H2 and NH3

Pulsed laser photolysis/laser-induced fluorescence (LP-LIF) is utilized to measure rate constants for C₂(a³Π_u) reactions with NO, N₂O, O₂, H₂ and NH₃. Multiphoton dissociation of C₂Cl₄ at 266 nm is employed for the generation of C₂(a³Π_u) radicals. The C₂(a³Π_u) concentration is monitored by the fluorescence of the (0, 0) band of the (d³Π_g&#8596;a³Π_u) transition at 516.5 nm. C₂(a³Π_u) removal rate constants for the reactions are determined as k_NO = (5.46 ± 0.10) × 10^-11 cm³ molecule^-1 s^-1 , k_N2O = (1.63 ± 0.20) × 10^-13 cm³ molecule^-1 s^-1 , k_N2O = (1.58 ± 0.16) × 10^-11 cm³ molecule^-1 s^-1, k_O2 = (5.92 ± 1.00) × 10^-14 cm³ molecule^-1 s^-1, k_H2< 1.0× 10^-14 cm³ molecule^-1 s^-1. Based on the data analysis and theoretical calculation, we suggest that the C₂(a³Π_u) reactions with H₂ and NH₃ proceed via the hydrogen abstraction mechanism, barriers exist at the entrance channel of the reactions of C₂(a³Π_u) with H₂ and NH₃.