For a given Cowen-Douglas operator T∈B_n(Ω), a special kind of cross-sections of the corresponding complex bundle E_T is presented. A new unitary invariant ［Φ］ is introduced, which is the conjugate classes of the complex C^∞ function valued n×n matrix Φ(T) i n the case of n≥2 and a real function in the case of n=1. For a given matrix Φ(T)=(φ_{ij/sub>)∈［Φ］, let F=∨ⁿi,j=1{φij}. dim F is independent of the choice of Φ(T). Define D［Φ］=dim F. By a di scussion on the behavior of D［Φ］, we show the uniqueness of a special kind of Cowen-Douglas operators. Moreover, we have proved that if a Cowen-Douglas operator T∈Bn(Ω) satisfies D［Φ］≥n²-2n+2, then T must be Hilbert irreducible.}

In this paper a new operator G_n(f;x) is constrcucted by means of the linear combination of Bernstein and Grünwald operators on the basis of taking the zeros of the first kind of Chebyshev polynomial of degreen as the interpolating nodes. G_n(f;x) converges to the f(x)∈C^j_［-1,1］, 0≤j≤9 on ［-1,1］ uniformly and has the best approximation order if the function f(x)∈C^j_［-1,1］, 0≤ j≤9. The saturation order is 1/n¹⁰.

The present paper presents the general form of the symmetric entropy loss function, (λ/δ)^q+(δ/λ)^q-2(q>0), which is called the q-symmetric entropy loss function, and deals with the Byaesian estimation, the minimum risk equivalent estimation and the minimax estimation for the scale parameter of the exponential istribution under the loss function, the conclusion is generalized. The admissbility and inadmissibility of estimator with the form of (cT+d)^-1 are discussed.

Let L be an alternating link in S³ and let L project on S² except near crossings of L where L lies on a bubble. If the projective diagram on S² has n crossings, then there are n bubbles. Thus are construced 2-spheres surfaces S²₊ and S²_- by the properties of the link. Let F be an incompressible and pairwise incompressible surface in S³-L, there is a collection of simple closed curves when the surface F is in a standard position. The surfaces are described by discussing the properties of F∩S²_±. The genus of the surface equals zero if the graph of F∩S²_± is special simple.

In this paper, the Dirichlet problem of a class of quasilinear elliptic systems with indefinite weights, which comes from mathematical models of Non Newton fluid flow, population evolution, pattern formation etc, is discussed by using Mountain Pass Lemma in critical point theory. The existence of a nontrivial weak solution is established with the help of the first eigenvalue of the corresponding eigenvalue problem, where the eigenvalue parameter is less than a known constant.

The numerical solution of the two dimensional dam break waves is described by a discrete-velocity model. Based on the analogy to gas d ynamic equation the discrete-velocity model can also be used to stimulate the shallow water wave equations. Two numerical calulations including a 2-dimensional circular dam break wave and a partial dam break wave were carried out. The numerical results show that the model is easy to implement, effective and stable.

Let T be in the commutant of Volterr a operator V, by construction and calculation, it is proved that if the function f(x)=1 is a cyclic vector of T, then A′(V)=A′(T).Thus all the invariant subspaces of V are hyperinvariant for T. Moreover, it is also proved that if only if ker T=｛0｝ran T=H, σ(T)=σ_e(T)=σ_lre(T).

We considered the finite volume element methods (FVM) based on circumcenter dual subdivision for the elliptic equations and parabolic equations. Let the primal triangular partition satisfy the restrictive condition, that is, the distances between the barycenter Q and the circumcenter C of any triangle element satisfy |QC|=O(h²), under this condition, firstly we have obtained the optimal L² error estimates of the finite volume element method based on circumcenter dual subdivision for the elliptic equation, furthermore we have also proved the optimal L² and H¹ error estimates of the semi-discrete and fully-discrete finite volume element method based on circumcenter dual subdivision for parabolic equation.

Using the tools of Hausdorff dimension and Hausdorff measure, we give quantitative version for the set of admissible kneading sequences to unimodal mappings. It is proved for the set that the Hausdorff dimension is 1 and the 1-dimension Hausdorff measure is zero in one-sided symbolic space with two symbols， which are more profound than those obtained by traditional qualitative analysis.

In this paper, we proposed a three-dimensional Fredkin-rule cellular automata. By using three-dimensional Von Neumann neighborhood and three-dimensional Fredkin-rule, we obtained a self-reproduction result to the simple initial pattern in the three-dimensional space.

Based on the fault analysis of real-time tasks, an improved version of EDF algorithm, named FR-EDF, is proposed, the necessary and sufficient condition of which is given. It is thus proved that the current research result on fault tolerant EDF is a nature consequence of the necessary and sufficient condition. The proposed algorithm is targeted at periodic tasks primarily and applicable to aperiodic tasks at the same time. It can also rectify a single fault which occurs beyond a fixed interval.

The progress of virtual enterprise construction is very complex and is supported by the decision support system. Aiming at the above special situation of virtual enterprise construction, restriction of CSCW on DSS is analyzed. Virtual enterprise construction decision is supported by many techniques and tools provided by CSCW. An integrating framework of CSCW and DSS is put forward in this paper. This technique is effective and feasible via evaluating the integrat ing framework.

On the basis of the analysis of traditional elastic graph matching, a face recognition algorithm based on local feature analysis and optimization matching is proposed. Firstly, some important face features are locat ed by means of neutral network. Secondly, the multiscale features of the feature points are extracted with the local mutiscale analysis feature of the Gabor wavelet. In this way, every face feature point is represented by a series of Gabor wavelet coefficients. Finally, in order to find the face needed, the test face is compared with the multiscale features of the corresponding feature points in the face database with the optimization matching. Here the optimization matching method is proved strictly. The test results about Yale and ORL face database show that not only the proposed method is far better than the traditional EigenFace method but also the effect of the illumination variation on the face recognition is obviously overcome and the method has quite good robust for face expression variation in some degree.

Ceramic coatings on aluminium alloy were prepared by means of microarc oxidation (MAO) technique, and the effects of anodic current density and the ratio of cathodic current (j_c) density to anodic current density (j_a) on the properties of the coatings were studied. The experimental results show that the content of α-Al₂O₃/γ-Al₂O₃ is closely relative to j_a but the effect of j_c/j_a on the phase con tent is unobvious. However, microhardness and microstructure as well as the density thickness of the coatings have something to do with j_a and j_c/j_a.

Microarc oxidation coatings on aluminium alloy were prepared in Na₂SiO₃ and (NaPO₃)₆ as well as NaAlO₂ aqueous solution, and the effects of electrolyte category and concentration on phase component and elementary composition were studied. The experimental results show that the content of α-Al₂O₃/ γ-Al₂O₃ is closely relative to electrolyte category and concentration. Elementary compositions of coated samples fabricated in diffe rent electrolyte solution are different, and the content of same element in surface and density layers of coatings prepared in same electrolyte are also different.

According to the crystal model of atomic physics and by using a new theory as well as an interaction potential between atoms, an analytical expression, which is represented by microscopic physical quantities, for Yo ungs modulus of metallic single crystal is given. The values of Youngs moduli of seven-kind metallic single crystals were calculated and consisted with the experimental values.

We fabricated a reverse amplification circuit as the modulation circuit of electro-optical modulator using an organic field\|effect transistors(OFET),whose active material is CuPc, and measured the modulation results of the light signal. The experimental results show that at the low-frequency, OFET can realize the amplification function. It can supply drive and modulation voltage to electro-optical crystal, hence realizing the modulation of the laser light. At the same time, we analyze the characteristic of OFET by the experimental results.

The star-shape inner-cladding Yb-ions-doped fiber laser was fabricated by using fiber grating, which was pumped by a 970 nm diode l aser source of which the pump power is 11.8 W, thus 7.5 W single-mode laser output was realized, central wavelength is 1 080 nm, slope efficiency 63.5%.

The paper contrasted CB junction reverse leak currents I_cbo and electronic noise spectrums S_vcb(f) of color TV high frequency video transistors(2688B, 2688S, 2688) produced by three kinds of techniques. Its discussed that interface state and surface movable charge cause surface leak current, which make devices produce electronic noise and affect other parameters such as reverse breakdown voltage and small current amplif ying coefficient. The experiment showed that surface leak current can be controlled, transistor electronic noise can be lowered and the reliability, stability and life can be enhanced by adopting surface passivation technique.

By means of small angle X-ray scattering, the fractal dimension D for carbonfiber nanometer micropore inner surface is studied. The results show that the size of the carbon-fibers obtained at different carbonification temperatures varies from 1.6 nm to 4.13 nm. And as the carbonification temperature goes up from 900 ℃ to 2 400 ℃, the value of D also goes up from 2.09 to 2.59. When the carbonification draft ratio is enlarged, the micropore fractal dimension will increase somewhat. By determining the mechanical intensity of the carbon-fibers which have different fractal dimension, it was found that those samples which have lower fractal dimension possess larger stretch intensity and condensation intensity.

By adsorbing phenolic compounds, Cr(Ⅵ) and I₂, the effect of the physicochemical characteristic of the porous carbon on its adsorption performance for different species was studied. It is shown that the adsorption of the porous carbon towards I₂ depends on the pore volume of the porous carbon; the adsorption of the porous carbon towards phenolic compounds depends on the density of carboxylic and lactonic groups on the surface of the porous carbon; the adsorption of the porous carbon towards Cr(Ⅵ) depends on the total content of basic, carboxylic and lactonic groups on the surface of the porous carbon.

Thermostable Tgo DNA polymerase is obtained from Thermococcus gorgonarius by the molecular cloning and express technology. Plasmid19, wild barley Na+/H⁺ reverse transporter gene, mous Cx37 gene and human CYT2C9 gene were successfully amplified with recombinase. The amplification capability and amplification fidelity of the enzyme were compared with those of Taq enzyme. The result indicates that the amplification capability of Tgo enzyme is the same as that of Taq enzyme. But the amplification fidelity of Tgo enzyme is over 30 times higher than that of Taqenzyme and 1.6 times higher than that of Pfu.

Human endostatin cDNA was cloned from total RNA of human embryo liver tissue by RT-PCR. Endostatin DNA sequence encoded His2 and His4 were double changed to Leu2 and Val4 using site directed mutation technique. The mutant endostatin cDNA was inserted into the pET28b containing promoter T7. The recombinant plasmid transformed the E.coli BL21(DE3). Recombinant human endostatin was highly expressed as inclusion body when theexpression strain BL21-Mute was induced with IPTG. The result of SDS-PAGE analysis reveals that recombinant mutant endostatin accounts for up to 30% of soluble protein in E.coli. The mutant endostatin was purified and refolded farther, its purity was up to 98%. Recombinant mutant endostatin was inactive in inhibiting endothelial cell proliferation.

A determination method for Mn²⁺ in natural surface coatings by single-column ion chromatography with a conductivity detector is described. The retention behavior and resolution of a series of cations including Fe²⁺, Mn²⁺, Zn²⁺, Ca²⁺, Mg²⁺ and Cd²⁺ were studied in different concentrations of eluent, flow rate and pH value, and the optimum analytical condition was established. The method was applied to the analysis of surface coatings with satisfactory results, which will contribute to the speciation analysis of manganese oxides in the natural surface coatings.

The urban soil samples in Changchun were studied for the potential chemical speciation of some heavy metals by chemical extraction in order to analyse the relationships between the chemical speciation and the total heavy met al as well as the physicochemical characteristics of urban soils. The results sh ow that Pb and Cu are mainly in residual and organic phases, Cd is largely associated with the residual and exchangeable fractions, while Zn is largely associated with the residual and Fe-Mn oxide phases. The highest percentage of Cd associated with available fractions is 31.98%. The total metal contents have direct influences on the exchangeable and available Cd and Zn contents, inverse influences on the Fe-Mn oxide Cu and Pb contents, and no influences on　the carbonate Zn and Pb contents. The exchangeable Cd contents are directly correlated with cation exchange capacity, and the available Cd contents are inversely correlated with cation exchange capacity. The carbonate fractions are directly correlated with pH, and Fe-Mn oxide fractions are directly correlated with oxidation-reduction potential. The organic Cu contents are directly correlated with organic contents.

The adsorption of lead(Ⅱ) and cadmium(Ⅱ) on the exopolysaccharide of natural biofilm was investigated. The exopolysaccharide was obtained from the extracellular polymers of superiority bacteria in Changchun South Lake. The results show that both Langmuir and Freundlich isotherm equations could describe the thermodynamics adsorption processes of Pb and Cd on the exopolysaccharide. One order kinetic model of Langmuir-Hinshelwood equation could describe the kinetic adsorption characteristics of heavy metals.The existence of Cd affects the adsorption of Pb, and Pb also affects the adsorption of Cd. Temperature and pH value could also affect the adsorption processes.