Nonsingularity of the combinations of two orthogonal projectors

The invertibility of combinations of two orthogonal projectors is researched by using the CS-decomposition of matrices and properties of orthogonal projectors. The Moore-Penrose inverse of the combinations is presented under some special conditions.     

幂等矩阵与另一矩阵的组合的k-幂等性

研究了一个幂等矩阵P和另一个与P可交换的矩阵Q的组合aP＋bQ＋cPQ的k一幂等性。给出了当aP＋bQ＋护Q是k-幂等时，Q的分类。利用这个分类给出了两个可交换的幂等阵P、Q的组合护＋bQ＋ceQ是幂等阵和3-幂等阵的充要条件。这个结果推广了Benitez J，Thome N在2006年的结论。     

矩阵的拟相似

本文引入矩阵的若干等价关系,并对其中之一——拟相似作了进一步研究。作为处理拟相似对角化的工具,我们定义了秩幂等阵并证明了矩阵的秩幂等+幂零分解定理。     

二维1:-5 Lotka-Volterra复四次系统的可线性化条件

本文考虑了如下的一类平面四次复Lotka-Volterra系统的可线性化问题ẋ=x（1-a₃₀x³-a₂₁x²y-a₁₂xy²-a₀₃y³）,ẏ=-y（5-b₃₀x³-b₂₁x²y-b₁₂xy²-b₀₃y³）.该系统为四次齐次多项式扰动下的具有$1:-5$线性项的复Lotka-Volterra系统,给出了该系统可线性化的充分必要条件.     

Integral Points on a Class of Elliptic Curve

0 IntroductionZasegairerc[h1]fodre sbcirgibientde gsreavle rpaolin tmse tohnocdsert waihnicehlli ppetircm citur ovnese btyogiving the upper bound of solution. Unfortunately,this upperbound was verylarge andsometi mes beyondthe range of com-puter searching.For a particular elliptic curvey2=x3-30x+133(1)he mentioned he can find all integral points and the largestpoint is (x,y) =(5 143 326 ,±11 664 498 677) by using Mas-ser and W櫣stholz bounds on elliptic logarithms .Although recent results on…     

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.     

两个二次矩阵线性组合的二次性

目的当P1,P2是2个满足方程(x-α)(x-β)=0的矩阵(称为二次矩阵),讨论了线性组合c1P1+c2P2仍是二次矩阵时系数(c1,c2)的完全分类。方法通过二次矩阵的性质和矩阵方程恒等式的性质。结果与结论将幂等矩阵、幂幺矩阵、幂零矩阵的线性组合的保持性问题推广到了二次矩阵的情形,概括了特殊矩阵线性组合性质的相关结果。     

关于除环上矩阵秩的几个等式

推广和改进了文[2]的一些结果,建立了除环K上关于幂等矩阵秩的几个等式:(i)设A,B∈Pn(K),则r(A+B-AB)=r-r(B)=r(B)+r[AB B0]-r(B)=r(B)+r[(I-B)A(I-B)];(ii)设c}K≠2,A,B∈Pn(K),则(1)r(A+B)=r[AB B0]-r(B);(2)r(A+B)=r(B)+r[(I-B)A(I-B)];(iii)设chK=2,A,B∈Pn(K),则 r(A+B)=r(A+AB)+r(B+AB).并得到几个推论.     

Synthesis,Structure and Antitumor Activities of [Ni（dien）2][Ni（CN）4] Complex

Ni(II)-dien complex was prepared and characterized by X-ray diffraction. The crystal belongs to triclinic system, space group P-1, with crystallographic parametersa=0.888 13(18) nm,b=0.890 10(18) nm,c=1. 591 8(3) nm, α=77.71(3)°, β=89.12(3)°, γ=61.24(3)°,Z=2. The two dien molecules coordinate to the central Ni atom, the six nitrogen atoms form a distorted octahedron. Preliminary pharmacological tests showed this complex had antitumor activity against HepG₂ and HL-60 cell linesin vitro. Foundation item, Supported by the National Natural Science Foundation of China (29972034) Biography: Li Tao (1976-), male, Ph. D candidate, research direction: ophthalmology and chemicalbiology.     

mLLDPE/LDPE共混物相结构的研究

采用SAXS方法研究了不同配比的茂金属催化聚乙烯（mLLDPE）/低密度聚乙烯（LDPE）共混物的界面层厚度σ_b、Porod指数α、分散相尺寸a_c值、积分不变量Q值等相结构参数。研究结果表明,共混物中两相具有部分相容性,分散相以片状存在;当共混质量比为80/20和20/80时,显示良好的混合均匀性。     

Correlation between the standard formation enthalpy and the path index of pyridine-derivatives

A formulated as △fH _m ^◯ (PPDs,g)=a+Σb_iP_i + c_if_i is put forward for estimating standard formation enthalpies of pyridine-derivatives (PDDs), in which,P _i is path index andc _i f _i is an amended term of interaction between substituent and N atom on pyridine ring. The Calculations based on the model were carried out for some pyridine-derivatives. The values of standard formation enthalpy calculated are consistent with those in literature. Foundation item: Supported by the National Natural Science Foundation of China (29971024) Biography: LI Liang-chao (1958-), male, Associate professor, Research direction: calculating chemistry.     

Synthesis and Characterization of Polyamide-Containing 2, 6- （Substituded） pyridine Derivatives

0 IntroductionPayrriodminaetiics hoenteer oofc ythcleics m .os tC oambupnoduanndts a cnodn tbaeisntin kgno twhnepyridine ring are widely distributedin nature,principally asenzymes and alkaloids . Pyridine enzymes have been foundintissues of all plants and ani mals examined thus far ,andare derivedfromeither nicotinic acid or Vitamin B6[1].Pyr-idine derivatives are also the building block of many phar-maceuticals with a wide range of functionalities that includeantitubercular compounds ,antivi…     

The nonwandering set of some Hénon map

For the Hénon mapT _{a, b}(x, y) = (1 −ax ² +y, bx), Benedicks and Carleson proved that for (a,b) near (2, 0) andb > 0, there exists a setE with positive Lebesgue measure, whose corresponding mapT _{a, b} possesses a strange attractor. Viana conjectured that if (a, b) ∈E, then the nonwandering set of the mapT _a, b Ω(T_{a, b}) = ∧_{a, b},Uq _a, b, where ∧_{a, b}, is the strange attractor, q_a,b is a hyperbolic fixed point in the third quadrant. It is proved that this conjecture holds true for a positive measure set E₁ ⊂E.     

Preparation by a rheological phase reaction method and thermal decomposition reaction mechanism of nickelous salicylate tetrahydrate

0　IntroductionInrecentyears,studiesonBinghamfluid ,suchasElec trorheologicalfluid ,areactivelypursued[1 6] .Rheologicaltechniqueshavebeenplayinganimportantroleinsyntheticchem istry .Therheologicalphasereactionmethodisthe processofpreparingcompoundsormaterialsfromasolid liquidrheologicalmixture.Thatis,thesolidreactantsarefullymixedinapropermolarratio ,andmadeupbyaproperamountofwaterorothersolventstoaBinghambodyinwhichthesolidparticlesandliquidsubstanceareuniformlydistributed ,sothattheprodu…     

Remote sensing of algal blooms using a turbidity-free function for near-infrared and red signals

HARMFUL ALGAL BLOOM ACTS UPON IMPORTANT ENVIRON-MENTAL PROBLEMS IN COASTAL WATERS.A UNIFIED AND IM-PLEMENTING METHOD FOR SURVEY AND MONITORING ALGALBLOOMS HAS BEEN DEVELOPED SINCE LAST DECADE.HOWEVER THERE IS A DATA GAP OF ABOUT TENS YEARS IN THE PERIOD W…     

Dashnic-Zusmanovich矩阵线性互补问题误差界的估计

研究P-矩阵的新子类Dashnic-Zusmanovich矩阵线性互补问题的误差界.利用Dashnic-Zusmanovich矩阵M和■=I-D+DM的性质、不等式的性质,以及M矩阵的逆矩阵无穷范数上界的估计式,得到了矩阵M的线性互补误差界的估计式.     

QSPR between Physical-Chemical Properties and Molecule Parameters of Alkanes

A set of molecule parameters, namely, N, N′, p, q, n, were used to express the structures of alkanes. A correlative model was established between certain physical-chemical properties and molecular parameters of alkanes by regression method. Eight physical-chemical properties, such as evaporation heat （△vHm^20）, density（D^20 ）, capacity （C^20）, surface tension （δ^20）, boiling point （Tb）, critical temperature（Tc）, critical pressure（Pc） and critical volume（Vc）, of fifty-six C3-C16 alkanes were calculated directly from the model in this paper. The calculated values are in good accordance with the literature ones reported for alkanes, and the correlation coefficients （R） equal or exceed 0.99 . The research results indicate that the principle of the method is simple and clear, the method is practical, the correlativity is excellent, and the predicted data are credible.     

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.     

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.     

正定Hermite矩阵流形上代数Lyapunov方程的信息几何算法

对于正定Hermite矩阵流形上的代数Lyapunov方程 A H X + XA + P =0, 基于流形的黎曼几何结构, 作者以矩阵- A H X + XA 和 P 之间的测地距离为目标函数, 提出了代数Lyapunov方程数值解的信息几何算法. 最后,给出了正定Hermite矩阵流形上的代数Lyapunov方程的数值模拟结果.