The fractal structures of the sample path of a general subordinator and the random re-orderings of the Cantor set

In this paper we have found a general subordinator,X, whose range up to time 1,X([0, 1)), has similar structure as random re-orderings of the Cantor setK(ω).X([0, 1)) andK(ω) have the same exact Hausdorff measure function and the integal test of packing measure. Supported by the National Natural Science Foundation, the Excellent Young Faculty Foundation of the State Education Commission of China and the Foundation for the Scholars Coming Back from Abroad Hu Xiaoyu: born in Apr. 1964, Professor     

Inorganic-organic hybrids constructed of bis（undecatungstogerma- nate）lanthanates polyoxoanions and oxalate-bridged dinuclear copper complexes and their magnetic properties

A series of inorganic-organic hybrids K₂Na _m H_9−m [{Ln(GeW₁₁O₃₉)₂}{Cu₂(bpy)₂(μ-ox)}]·nH₂O (bpy = 2,2-bipyridine and ox = oxalate; Ln = La, Nd, Sm, Eu, Gd; n = 19, 17, 22, 20, 19; m = 4, 4, 4, 9, 2) were isolated after reacting in a potassium acetate buffer. X-ray structural analyses show that compounds 1–5 are isomorphic and consist of [Ln(GeW₁₁O₃₉)₂]¹³⁻ polyoxoanion building blocks and oxalate-bridged dinuclear copper metalorganic complex with a 1D chain structure. The 1D chain further connects into the 3D framework by π-π interactions with neighboring bpy groups. The magnetic susceptibility data indicate that antiferromagnetic coupling between the neighboring Cu²⁺ ions in the structure and the rare earth ions affects magnetic property of the structure.     

Chaos in the sense of Li-Yorke and the order of the inverse limit space

Let I= [0,1] and ω0 be the first limit ordinal number. Assume that f: I→I is continuous , piece-wise monotone and the set of periods of f is { 2': i∈ {0} ∪ N}. It is known that the order of (I, f) is ω0 or ω0 + 1. It is shown that the order of the inverse limit space (I, f) is ω0 (resp. ω0 + 1) if and only if f is not (resp. is) chaotic in the sense of Li-Yorke.     

Operational properties and matrix representations of quantum measures

Denoted by M(A), QM(A) and SQM(A) the sets of all measures, quantum measures and subadditive quantum measures on a σ-algebra A, respectively. We observe that these sets are all positive cones in the real vector space F(A) of all real-valued functions on A and prove that M(A) is a face of SQM(A). It is proved that the product of m grade-1 measures is a grade-m measure. By combining a matrix M _μ to a quantum measure μ on the power set A _n of an n-element set X, it is proved that μ ≪ ν (resp. μ ⊥ ν) if and only if M _μ ≪ M _ν (resp. M _μ M _ν =0). Also, it is shown that two nontrivial measures μ and ν are mutually absolutely continuous if and only if μ·ν∈QM(A _n ). Moreover, the matrices corresponding to quantum measures are characterized. Finally, convergence of a sequence of quantum measures on A _n is introduced and discussed; especially, the Vitali-Hahn-Saks theorem for quantum measures is proved.     

Isotope effect of the stereodynamics in the reactions F+HCl→HF+Cl and F+DCl→DF+Cl

Using a new ground-state ab initio potential energy surface reported by Deskevich et al., the product polarizations in the reactions F+HCl→HF+Cl and F+DCl→DF+Cl were studied by employing the quasi-classical trajectory method. At a collision energy of 10 kcal/mol, the four generalized polarization-dependent differential cross-sections (2π/σ)(dσ₀₀/dω _t ), (2π/σ)(dσ₂₀/dω _t ), (2π/σ)(dσ₂₂₊/dω _t ) and (2π/σ)(dσ₂₁₋/dω _t ) were calculated in the center-of-mass frame. The distribution of the angle between k and j′, P(θ _r ), the distribution of the dihedral angle denoting the k-k′-j′ correlation, P(φ _r ), and the angular distribution of the product rotational vectors in the form of polar plots P(θ _r , φ _r ) were also calculated. The evident influence of isotope substitution on the product polarization is revealed. This effect may result from the different mass factors of the two reactions.     

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     

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     

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.     

Raman and infrared spectroscopic investigation of some hydrous LnTPPTS complexes (Ln=La,Sm)

The Raman and IR spectra of LnTPPTS·10H₂O [Ln=La,Sm, TPPTS=P(m-C₆H₄SO₃) ₃ ³⁻ ] complexes are reported. Based on the observed Raman and IR characteristic frequencies, a vibrational assignments has been made for these complexes. Coordination induces a lengthening of the S−O bonds and a shortening of the C−S bond. The C−S stretching frequencies should therefore increase while the position of the should move to a lower wavenumber. Vibrational modes of metal-oxygen polyhedron V _(La-O) at 146, 168,253 cm⁻¹ are the structural charactrization for coordinate bond of LnTPPTS complexes. Chen Zhenhua: Born in 1938, Professor     

Third-order optical nonlinearities for lanthanum (III) complexes with 1, 10-phenanthroline components

The nonlinear refractive indexesn ₂ for the ethanol solutions of 1, 10-phenanthroline (2.0 × 10⁻³ mol · L⁻¹), [bis(l, 10-phenanthroline) lanthanum (III)] nitrate (1.0 × 10⁻³ mol · L⁻¹), and [nitrato-fluoracil-bis (1, 10_{-phenanthroline}) lanthanum (III) ] nitrate (1.0 × 10⁻³ mol · L⁻¹) are first measured, the third-order nonlinear optical susceptibilities χ(³) and 〈γ〉 are calculated, and the mechanisms of the third-order optical nonlinearities enhanced by lanthanum (III) are discussed preliminarily.     

Kinetic studies of the decomposition reaction of adducts of dinuclear Fe(Ⅱ)/O2

Kinetic studies of the decomposition reaction of dinuclear Fe(Ⅱ) adducts [Fe₂(N-Et-HPTB){O₂P(OPh)₂}](Cl- O₄)₂ (1) and [Fe₂(N-Et-HPTB) {O₂P(Ph)₂}] (ClO₄)₂ (2) with O₂ have been carried out at low temperature using UV-vis spectra. The decomposition reaction of Fe(Ⅱ)/O₂ adducts was first-order in the experimental conditions, and the activation parameters were obtained. ?H^¹ = 85.62 kJ·mol^-1, ?S¹ = 19.43 J·mol^-1·K^-1 for compound (1) and ?H^¹ = 97.97 kJ·mol^-1, ?S^¹ = 55.68 J·mol^-1·K^-1 for compound (2). These results are similar to those of dioxygen adducts of other metals complexes and natural enzymes such as methane mono- oxygenase (MMOH).     

Quasisymmetric boundary correspondence and Grötzsch problem

Two necessary and sufficient conditions for the validity of the conjectureK ₀(h) =K ₁(h) are given, which are independent of the complex dilatations of extremal quasiconformal mappings, where K₀(h) is the maximal conformal modulus dilatation of the boundary homeomorphismh, K ₁(h) is the maximal dilatation of extremal quasiconformal mappings that agree withh on the boundary. In addition, when the complex dilatation of an extremal quasiconformal mapping is known, the proof of the result simplifies Reich and Chen Jixiu-Chen Zhiguo’s result.     

糖蜜酒精废液脱钾树脂的解吸动力学

【目的】研究糖蜜酒精废液脱钾树脂BK-001中K~+的静态解吸过程。【方法】考察洗脱剂温度、浓度及树脂粒径对K~+解吸过程的影响,用动边界模型描述K~+的解吸过程。【结果】确定糖蜜酒精废液脱钾树脂BK-001中K~+的解吸过程为颗粒扩散控制,该反应的表观活化能为40.9kJ/mol,反应级数为1.19,表观频率因子为5.27×10~4 min~(-1),假二级动力学模型更适合描述K~+的解吸过程(R~20.995)。K+解析过程的总动力学方程式为1-3(1-F)~(2/3)+2(1-F)=5.27×104r20[H2SO4]~(1.19)e_((-4.09×10~4))/RT。【结论】脱钾树脂BK-001的解吸动力学方程为糖蜜酒精废液脱钾树脂的再生及钾盐资源的综合利用提供理论依据。     

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.     

Magnetic properties and applications of newly-developed-nanocrystalline Fe72Cu1mV2Si14B9 and Fe72CulNblMo1V2Si14B9 alloys

Conclusions  

Turbidite and bottom-current evolution revealed by anisotropy of magnetic susceptibility of redox sediments in the Ulleung Basin,Sea of Japan

Anisotropy of magnetic susceptibility(AMS) from above and below 7.31 m in a core from the southern Ulleung Basin shows clear differences on an equal area projection of the lower hemisphere.Rather concentrated steep inclination of K 3 and horizontal inclination of K 1 and K 2(K1 ≥K2 ≥K3) are located within the upper part,and the latter two axes lie perpendicular to each other near the bedding plane.In contrast,random distribution of the three axes and extremely high value of shape parameters(Q=(K1-K2)/[(K1+K2)/2-K3]) are evident in the lower part,indicating complete destruction of the original sedimentary structure.This result is consistent with data from X-radiographs,which show numerous conglomerates,distortions and cleavages in the lower part.According to age models by Liu et al.(2010) and Zou et al.(2010),the bottom age at 7.31 m is 48 cal ka BP,and the time domain is discussed below.The degree of AMS(P) is low,1-1.08,and linearly related to the foliation(F)(R2 =0.95,N=176).The relationship between F and linearity(L) implies oblate aligning patterns that are typically sedimentary in origin.At least five redox couplets were found with the aid of S ratios and other rock magnetic parameters,and in most cases,the original signals of climate survived early diagenesis.The paleomagnetically reoriented AMS show corresponding changes with millennial events in the last 48 cal ka.Clearly tilted K 3 directions and reduction of P and F occurred within DO1-BA warm events,when melt water pulse 1A nd the YD cold event took place.The turbulent conditions therein,synchronous with coarsening of sediments,provide evidence of strong bottom currents and possible directional changes,as evidenced by different K3 tilting directions.A NE current direction in the last 4.5 cal ka is consistent with in situ measurements of bottom currents.Responses of AMS,mainly to climatic modulation,show on the one hand,the limited influence of diagenesis on rock magnetic signals and,on the other hand,the dramatic change of hydrodynamic conditions and terrigenous inputs during rapid sea level rise during the last deglaciation.     

Relation between standard entropies of elements and electronic configurations

A close relationship has been found between the standard entropies of elements and their electronic configurations. Based on the positions of elements in the periodic table and the variation in the standard entropies of elements, the standard entropies of elements can be expressed as the sum of two functions:S ⁰=f(N) +f(E), whereS ⁰ is the standard entropy of an element,N the principal quantum number, andE the number of outermost electrons. And the specific formula isS ⁰ = 99.05N ^1/3 + [0.32(sp −4)⁴ -119.76] + [-56.56N ^1/3+ 0.70(sd ∼-7)² −42.12] + [−11.95 × 10⁻⁴(df-8)⁻⁴ -105.70], wheresp, sd, df are the numbers of the outermost electrons in thesp, sd, df regions of the periodic table, respectively. This formula helps reveal the essence of the standard entropies of elements and deepens our understanding of the thermodynamic characteristics of compounds.     

Effect of CO<Subscript>2</Subscript> concentrations on the activity of photosynthetic CO<Subscript>2</Subscript> fixation and extracelluar carbonic anhydrase in the marine diatom <Emphasis Type="Italic">Skeletonema costatum</Emphasis>

The growth and activity of photosynthetic CO2 uptake and extracellular carbonic anhydrase (CAext) of the marine diatom Skeletonema costatum were investigated while cultured at different levels of CO2 in order to see its physio-logical response to different CO2 concentrations under either a low (30 靘ol·m-2·s-1) or high (210 靘ol·m-2·s-1) irradiance. The changes in CO2 concentrations (4—31 靘ol/L) affected the growth and net photosynthesis to a greater extent under the low than under the high light re-gime. CAext was detected in the cells grown at 4 mol/L CO2 but not at 31 and 12 靘ol/L CO2, with its activity being about 2.5-fold higher at the high than at the low irradiance. Photo- synthetic CO2 affinity (1/ K1/2(CO2)) of the cells de-creased with increased CO2 concentrations in culture. The cells cultured under the high-light show significantly higher photosynthetic CO2 affinity than those grown at the low-light level. It is concluded that the regulations of CAext activity and photosynthetic CO2 affinity are dependent not only on CO2 concentration but also on light availability, and that the de-velopment of higher CAext activity and CO2 affinity under higher light level could sufficiently support the photosyn-thetic demand for CO2 even at low level of CO2.     

Studies on reduced extent method for inhibited thermokinetics of enzyme-catalyzed reaction

The thermokinetic reduced extent equations of reversible inhibitions for Michaiels-Menten enzymatic reaction were deduced, and then the criteria for distinguishing inhibition type was given and the methods for calculating kinetic parameters,K _M,K _i andv _m were suggested. This theory was applied to inverstigate the inhibited thermokinetics of laccase-catalyzed oxidation ofo-dihydroxybenzene bym-dihydroxybenzene. The experimental results show the inhibition belongs to reversible competitive type,K _M=6.224×10⁻³ mol·L⁻¹,K _i=2.363×10⁻² mol·L⁻¹. Xiong Ya: born Sep. 1961, Ph. D. graduate student. Curent research interest is in biothermochemistry research Supported by the National Natural Science Foundation of China     

Exponential inequality for a class of NOD random variables and its application

In this paper,an exponential inequality for weighted sums of identically distributed NOD (negatively orthant dependent) random variables is established,by which we obtain the almost sure convergence rate of which reaches the available one for independent random variables in terms of Berstein type inequality. As application,we obtain the relevant exponential inequality for Priestley-Chao estimator of nonparametric regression estimate under NOD samples,from which the strong consistency rate is also obtained.