Some clifford martingale spaces

We study the spaces Hp, Sp, Kp, ∑p and ,p of martingales with measure du=ψdυ,where ψ is a function with Clifford algebra values and satisfies bp+-condition. We proved they are equivalent and isomorphic to the corresponding spaces of martingales with real measure dυ, respectively(1≤p＜∞). In the end,we give a martingale f such that f=(fn) ∞∈1K∞ but f=(E(ψ| n)fn)n≥ ∈1K∞.     

Development of Triticum aestivum-Leymus racemosus ditelosomic substitution line 7Lr#1S（7A） with resistance to wheat scab and its meiotic behavior analysis

Leymus racemosus is highly resistant to wheat scab （Fusarum head bright）. The transfer of scab resistant gene from L. racemosus to Triticum aestivum is of great significance for broadening the base of wheat resistance. In the present study, the pollen of T. aestivum-L, racemosus monosomic addition line with scab resistance was treated by irradiation with 1200 R ^60Co-γ-rays prior to pollinating to emasculated wheat cv. Mianyang 85-45. Nine plants with a telocentric chromosome 7Lr#1S were observed in M1, and one ditelosomic substitution line 7Lr#1S was selected from selfcrossing progenies and confirmed by chromosome C-banding and GISH. Furthermore, a co-dominant EST-SSR marker CINAU 31 was employed to identify this substitution line. A pair of chromosome 7A of common wheat were found to be replaced by a pair of telocentric chromosome 7Lr#1S, and further investigation showed that chromosome configuration of the substitution line at MI of PMCs after GISH was 17.50Ⅱ^w ＋ 2.19Ⅱ^w ＋ 0.42Ⅱ^7Lr#1S ＋ 1.08 Ⅰ^7Lr#1S ＋ 0.69 Ⅰ^w. Two telocentric chromosomes paired as a bivalent in 59.7% of PMCs. Abnormal chromosome behaviors of telocentric chromosomes were observed in part of PMCs at anaphase I and telophase I, including the moving of two telocentric chromosomes to the same pole, lagging and earlier separation of their sister chromatid. All these abnormal behaviors can be grouped into three distinct types of tetrads according to different numbers of 7Lr#1S in their daughter cells and various micronucleus in some tetrads. However, due to the high transmission frequency of the female and male gametes with a 7Lr#1S, 84% of the selfcrossing progeny plants had ditelosomic substitution. The substitution line showed high resistance to wheat scab in a successive two-year test both in the greenhouse and field; hence, the line will be particularly valuable for alien gene mapping, small fragment translocation induction and telosomic cytological behavior analysis.     

Diagnostics of magnetic field strength for gyrosynchrotron radiation regions of the lower harmonics

A diagnostic formula of magnetic field strength of gyrosynchrotron radiation regions of the lower harmonics (5 ≤S≤10 ) is presented based on their emissivity η νBN , absorptivity κ νBN , and the turnover frequency of radio spectra ν P. Their diagnostic error is estimated. And an accurate relation between electron energy spectral index δ and brightness temperature spectral index β is also given.     

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.     

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 note on Jacobi-Eisenstein series

The so_called Jacobi_Eisenstein series is defined by E k, S (z, w)=∑y∈J ∞\J (1, j) Z 1|k, Sy(z, w) . The Fourier coefficients of E k, S is determined completely. The theorem extends the results of Eichler and Zagier to the case of general index matrices.     

An experimental study on the solubility of copper bichloride in water vapor

Using the solubility method, the solubility of CuCl2 in liquid-undersaturated HCl-bearing water vapor was investigated experimentally at temperatures of 330-370 ℃ and pressures of 4.2-10 MPa. The re-sults have shown that hydration could significantly enhance copper solubility and the concentrations of copper were positively correlated with PH2O. The solubility of copper in vapor phase increased with increasing PH2O at the constant temperature. CuCl2 was transported as hydrated species CuCl2(H2O)ngas in water vapor. The formation of complexes is proposed to be the result of the following reaction: CuCl2solid nH2Ogas = CuCl2 (H2O)ngas The hydration number n decreased slightly with increasing temperature. Statistical hydration numbers are 4.0, 3.6 and 3.3 at 330, 350 and 370 ℃ , respectively.     

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.     

A matrix version of the Wielandt inequality and its application to statistics

Suppose that A is an n × n positive definite Hemitain matrix. Let X and Y be n × p and n × q matrices (p+ q≤n), such that X* Y = 0. The following inequality is proved X*AY( Y* AY)-Y Y*AX≤( (λ1-λn)/(λ1+λn))2 X*AX, where λ1 and λn are respectively the largest and smallest eigenvalues of A, and M- stands for a generalized inverse of M. This inequality is an extension of the well-known Wielandt inequality in which both X and Y are vectors. The inequality is utilized to obtain some interesting inequalities about covari-ance matrix and various correlation coefficients including the canonical correlation, multiple and simple correlation.     

A novel advanced oxidation process――wet electro-catalytic oxidation for high concentrated organic wastewater treatment

A novel advanced oxidation process——wet electrocatalytic oxidation (WEO) was studied with p-nitrophenol as model pollutant and β-PbO2 electrode as the anode. Compared with the effect of the individual wet air oxidation (WAO) and electrochemical oxidation (EO), the effect of WEO showed syn- ergistic effect on COD removal under the conditions of temperature 160℃, C=1000 mg·L-1, PN2=0.50 MPa, PO2=0.9 MPa, current density = 3 mA·cm-2, Na2SO4 3 g·L-1. And the synergistic factor got the best value of 0.98 within 120 min after 180 min treatment. The synergistic factor was studied after 120 min treatment at 100℃, 120℃, 140℃ and 160℃, and the effect of 120℃ was the best with the value of 1.26. Possible mechanism for the synergistic effect was discussed based on the analysis of free-radical generation and intermediates detected by HPLC and GC/MS.     

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…     

Synthesis and antitumor activity of iodo-bridged binuclear platinum complex

Cisplatin antitumor activity was discovered in 1967, and cisplatin entered clinical phase I trial in 1971, and was approved for clinical use by the US Food and Drug Administration (FDA) in 1979. Cisplatin is the first metal complex available for the treat…     

Complete quantum circuit of Haar wavelet based MRA

Wavelet analysis has applications in many areas, such as signal analysis and image processing. We propose a method for generating the complete circuit of Haar wavelet based MRA by factoring butterfly matrices and conditional perfect shuffle permutation matrices. The factorization of butterfly matrices is the essential part of the design. As a result, it is the key point to obtain the circuits of I2t＋W ＋I2^n-2t-2· In this paper, we use a simple means to develop quantum circuits for this kind of matrices. Similarly, the conditional permutation matrix is implemented entirely, combined with the scheme of Fijany and Williams. The circuits and the ideas adopted in the design are simple and intelligible.     

The evolution model of the earth’s limited expanding

Based on the prerequisite that the earliest acid rock formed because of the initial global expanding tectonic processes, by combining it with other geological limitation conditions, and starting from the lithosphere elastic mechanics, the following is defined: the earth expansion started at about 4300 Ma ago, the average increasing rate of the earth radius is 0.40 mm/a, the initial expanding earth radius is 4651 km, and the initial global expansion of tectonic processes happened at 4183.7 Ma ago. From the natural and attenuation evolution condition of the earth and terrestrial planets, through the limit condition got from the combination of the mathematics logic and the geological significance, the limited expanding earth evolution model is established as follows: in whichR ₀= 4.651×10⁶ m,A =1.86×10⁶ m, β = -6.01×10⁻¹⁰/ a andt _s=3×10⁸ a. From this model the maximum radiusR _maxof the limited expanding earth evolution should be 6511 km. The earth’s radius increasing rate is about 0.1 mm/a at present.     

Synthesis of tungstophosphates of heteropoly compound and its catalytic property in oxidative desulfurization of diesel

Several kinds of Tungstophosphates of Heteropoly Compounds (TPHC) with different compositions and the same structure were synthesized using the method of solid-phase reaction to change the mol ratio of Na₄P₂O₇ · 10H₂O, WO₃ and Na₂WO₄ · 2H₂O. TPHC, as a catalyst, was used in oxidative desulfurization of diesel. The results show that TPHC has catalytic activity. With THPC existing, the highest desulfurization rate reaches 51.85%, 32.6% higher than that yield without TPHC. And the desulfurization rate increases with decreasing WO₃. FT-IR spectra of TPHC shows that the catalytic activity is related to the activity of end oxygen(O_d).The more active O_d is, the stronger the capability of obtaining or losing electron is. It means that TPHC has a good catalytic activity. FT-IR spectra of TPHC indicates that desulfurization rate is in linear correlation with ( is intensity of W-O_d vibration band, is intensity of P-O_a vibration band) and correlation coefficient reaches 0.965. Biography: BIN Xiaobei (1965–), female, Ph.D. candidate, Associate professor, research direction: environment science and environmental materials.     

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.     

Additive characters and orthogonal systems of polynomials in several indeterminates over residue class rings

Letm, n andk be positive integers, m> 1 andk≤ n. Let ‰ _m =‰m‰ denote the residue class ring modulom. Let ‰ _m denote the group of additive characters of ‰ _m denote the identity of ‰ _m . A necessary and sufficient condition for the systemf ₁,...,f _k ∈ ‰ _m [x ₁, ...,x _m ] to be orthogonal is given: for all additive characters ψ₁, ..., ψ _k ∈ ‰ _m with ψ_i,≠x₀ forsomei, . As corollaries, the result of Shiue-Sun-Zhang and the result of Sun are obtained.     

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 .…     

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.