On the basis of constructing the functions of class S_α it is proved that the viscosity solutions of parabolic equations belong to the functions of class S_α under certain conditions. Thus the discu ssion of studying viscosity solutions is converted to that of studying the functions of class S_α. The Aleksandrov-Bakel'man-Pucci-Krylov-Tso maximum principle is generalized to a more general one and it is proved that the functions of class S_α obey the generalized Aleksandrov-Bakel'man-Pucci-Krylov-T so maximum principle, by means of which some regularity results to the viscosity solutions of fully nonlinear parabolic equations are obtained.

With the aid of further improving some procedures of the tanh-function generalized by solving nonlinear partial equations, we obtain many new soliton-like solutions to the (2+1)-dimesional Broer-Kaup equation with variable coefficient.

The present paper deals with the partly linear model, Y=β^T₀X+g₀(T)+σ₀(X)ε presents the least square estimator and demonstrates the strong consist ence of the least square estimator of β and g.

This paper presents a kind of unconnected graph St(m)∪K_p,q for natural numbers m，p，q∈N⁺(N⁺ represents the set of positive integers). And it is proved that graph St(m)∪K_p,q is a k-graceful graph when k>1 and min{p，q}≥2, while the graph is a (k，d) arithmetic graph when k>(q-1)d+1(d>1 and d∈N⁺) .

Some fundamental properties of topological inverse semigroups are discussed and it has been proved that the direct product/sum of a family of inverse semigroups is still an inverse semigroup and the semidirect product of two inverse semigroups is still an inverse semigroup under some certain conditions. In addition, it has been shown that in a given compact inverse semigroup, the closure of an inverse subsemigroup is a topological inverse subsemigroup, and the closure of a Clifford subsemigroup is a Clifford topological inverse subsemigroup. Thus the corresponding results related to topological semigroups or topological groups have been generalized.

The property of the viscosity solutions of the Cauchy problem of a degenerate parabolic equation not in divergence form is studied. The viscosity solution means a weak solution in the distribution sense obtained by the vanishing viscosity method. Using some techiques of studying weak solutions and establishing some estimates on the viscosity solution, we prove the continuity of the viscosity solution with respect to aparameter contained in the equations.

The concept of generalized positive subdefinite matrix is given, and its properties and determinant theories are discussed, and many new results are obtained. As application, some famous theorems and inequalities named after Schur, HUA Loo-geng, Minkowski,Hadamard, Openheim and Ostrowski-T aussy are generalized, and the index scope of Minkowski inequality is enlarged.

On the basis of the Marr's algorithm, a new fast algorithm for image reconstruction based on bivariate polynomial approximation on a circular domain is presented. The computational complexity of the algorithm is O(Nlg N). The execution time of the new algorithm is far shorter than that of the old one. Furthermore, compared with the traditional method__filter back projection algorithm, the quality of the reconstruction image from the algorithm based on polynomial approximation is better. The computer simulation experiment has shown the efficiency of the algorithm.

This paper studied multivariate rational interpolation of Cauchy type with the help of the algebraic theory about multivariate polynomial interpolation. It's expression and existence condition was given. The concl usion obtainal is similar to univariate Cauchy rational interpolation.

The present paper deals with the existence of non-trivial nonnegative solutions of a nonlocal boundary value problem for the p-Laplacian equation with nonlinear sources. The proof is based on the fixed point theorem in a cone.

In this paper, we discussed the compact pseudo-umbilical submanifolds in a Riemannian manifold of quasi constant curvature. We gave an integral inequality of Simons' type.

The present paper gives out a kind of graph K₂∧K_m,n for natural numbers m,n∈N⁺ (N⁺ represent s the set of positive integers). By establish the labeling function it is proved that the graph K₂∧K_m,n is a graceful graph.

The Lyapunov function is used to derive a set of easily verifiable sufficient conditions for the global asymptotic stability of the Lo tka-Volterra system with variable time delays. Some new results are obtained, some related known results are improved and generalized.

The present paper covers the newsboy model with budget cost constraint. The mathematical model with common cost constraint, the mathema tical model with budget cost constraint for being in short supply and the mathematical model with budget cost constraint for commodity treatment have been built up, the corresponding optimum solutions have been workded out and the sensitivities of the three mathematical models have been analyzed.

We studied the existence and stability of limit cycles for a class of Volterra equations by constructing the Dulac function and Poincaré region, and applying the uniqueness theorem and the Friedrich methods for bifurcations and obtained several results on the existence and stability of limit cycles.

The topological entropy of a crazy dynamic system with Σ_N×S¹ as the basic space is investigated, and its range is pointed out: lg N~2lg N. Moreover, a more exact result is given when the rotation maps occur in the fiber maps.

We separately stated BV solutions for the Cauchy problems of the first order quasilinear equation and the first order quasilinear equation with source term with measure as initial value. Firstly, we displayed the general theory of above two Cauchy problems, such as existence, uniqueness and asymptotic behavior of solutions, etc. Then we displayed someresults based on it, i.e., existence, uniqueness and other properties of BV solutions for the cauchy problems of above two equations with σ-finite Borel measure as initial condition。

The centralized control layer was introduced into the Web Cache architecture. The centralized control was used to watch the status of all the caches, through a overall and effective control of their memory and w orkload to make the storage structure reasonable and the workload balance. We realized the arithmetic of workload balance, the arithmetic of prefetch based on the Pull mechanism, the arithmetic of wash out based on the combination of the TTL and the life modulus. The arit hmetic of workload balance helps to resolve the bottleneck of caches, and the ot her two increase the hitrate and system efficiency. By introduce the arithmetic, the control lay can control the Cache layer effectively, it can increase the hi trate of the architecture and decrease the response time of the architecture.

The present paper presents a code and decode system based on the digital code of wavelet transform theory in order to implement multiresolution data flow encode and enha nce the interpolation of a system. This system is based on wavelet transform technique with digital signal processi ng method. An embedded zerotree encoder is designed on the basis of wavelet transform theory applied to the encode of video images a nd a video collection-play system is established that implements the data collection-play and is suitable to the play meeting the needs of proposed frequency and band width.

By using a generalization distribution table (GDT) as a hypothesis search space, this paper presents an algorithm to discover default rules from the information system with inconsistencies and incompleteness, by which the default rule can be mined and the noisy in the data can be filtered, and unseen instances can be predicted.

The present paper deals with the technique how to solve the problem of cycle links in internet crawling by directed graph. First, the problem is proposed. Then, the formal definition of cycle links in internet crawling is described. Finally, the algorithm to solve the problem by directed graph is given. The key problem to a crawler is how to find directed loops effectively in web pages crawled by the crawler. The algorithm described in this paper can make the crawler avoid dropping in the pitfall created by cycle links.

In the theoretical framework of the relativistic mean field, nuclear matter including delta isobars is studied. An analysis shows that with the increase of the relative delta isobar density the binding energy at saturation point goes down and moves toward the direction of the increase in density, then the equation of state becomes soft. We proposed that the neutron star matter including delta isobars may be possible phase structure for neutron stars.

In this article, the quantum properties of light field of the two identical two-level entangled atoms interacting with the binomialoptical field were studied by means of time evolution operator and numerical calcu lations. The results show that the time evolution of the squeezing and coherence properties of the light field depends on the entanglement degree of the initial two identical two-level entangled atoms and the parameters of the binomial optical field. The optical field fluctuation can be completely squeezed via choosing appropriate parameters.

The dynamic procedure of frequency upconversion excitation of 4f5d level of Pr^３＋ in Pr^３＋ ∶ZBLAN fiber was calculably simulated based on the population rate equations and the related transition theories. The distributions of the pump powers along the fiber and the effective fiber lengths under the different pump powers were studied. Pumping efficiency as a function of the pump powers was given. Possible population inversion between 4f5d level and 4f² levels was found from calculated results.

With the help of Ginzburg-Landau-Devonshire (GLD) theory, the influence of imperfect surface layers on the properties of first-order ferroelectric thin films intercalated between two metal electrodes is theoretically studied. The results show that the imperfect surface layer of ferroelectric thin films lowers the phase transition temperature. When the imperfect surface layers are asymmetric, the hysteresis hoop of the ferroelectric thin film loses its center symmetry.

The attitude dynamic equations of a spacecraft with deploying flexible plates are derived by means of the momentum theorem. The dynamic equations by differentiation with respect the mass of the flexible plates are derived with the aid of Newtons second law. When the flexible plates deploying at a uniform velocity the dynamic equations of the system are alternated. By using Runge-Kutta method the numerical results are obtained. The responses of amplitudes of the vibration of the flexible plates to time are given. The responses of attitude angular velocity of the spacecraft to time are given.

A simplified and compact electron paramagnetic resonance (EPR) spectrometer is constructed by putting a self-detecting microwave marginal oscillator, as a wave source, a sample and a detector in one cavity-structure on the basis of small magnetic modulation, computer control and data superimp osing. The final sensitivity is 3×10⁸ spins/T.

The present paper covers the method to reconstruct the waveform and phase of ultrashort optical pulse by means of fringe-resolved second harmonic generation correlation (FRSHG), the feasibility and the numerical simulation of which are proved and performed, respectively.

The present paper deals with the extracts from six raw coals and they were indexed according to the NIST database by PBM method, then their molecular configurations were confirmed via GC/FTIR. Many biomakers have been found in the extracts, which suggests that the configuration of coal molecules are very complicated; the compress degree of the coal increases along with the coalization.

A series of Cr-containing MCM-41 molecular sieves has been synthesized and characterized by XRD, IR and Extend X-ray Absorption Fine Structure(EXAFS) techniques. It has been shown that a certain amount of chromium ions has been incorporated into the framework of MCM-41 and the rest part of the contained Cr ions still existed as other types of Cr-containing compounds, which can be washed off by a NH₄Ac solution. The octadecan-1-ol c onversion and octadecanoic acid selectivity are not decreased after Cr-MCM-41 and Cr-MCM-41-t catalysts have been repeatedly used for the selective oxidation of octadecan-1-ol to octadecanoicacid.

Bi₂O₃ nanoparticles were prepared by the microemuls ion chemical method. The structureand properties of the as-prepared Bi₂O₃ nanoparticle s were studied by means of XRD， BET， XPS and UV-vis absorption spectrum. The photocatalytic oxidation reactions of benzene， toluene and xylene were used as model reaction to measure the phot ocatalytic activity of Bi₂O₃ nanoparticles, respectively. The results show that the pr epared crystals had a tetragonal structure. The size of Bi₂O_{3 nanoparticles was 25.6～35.1　nm. The structure of Bi2O3 nanoparticles changes as the calcining temperature increases, and the electron conbining energy of the Bi2O3 surface increas es accordingly, at the same time, the photocatalytic activity for pollutants degradation is increased. The order of the degradation rates of aromatic hydrocar- bons is xylene>toluene>benzene．}

On the basis of the theory of plant trace geochemistry prospect mine an analytic method of rare elements in plant is established, providing a rapid credible new means for plant was ashed by the method of high temperature furnace bake over a weak flame. The hydrof luoric acid-hydrochloric acid-nitric acid-vitriol (HF-HCl-HNO₃-H ₂SO₄) system was used for the determination of 15 rare earthelements in the ash of plant by inductively coupled plasma mass spectroscopy (ICP-MS). The method of inductively coupled plasma mass spectroscopy can reduce the error introduced by chemistry separate and enrichment complex operating process, the operation is simple and the examine is quickly. The result of method is in agreement with the standard of nationality standard substance GBW07603. The experiment method measurement accuracy is 3.00%～14.10% in relative error, t heprecision(relatively standard deviation, number=8) is in the range of 3.22%~20.00%.

To get soluble form of single-chain Fv of antibody (scFv) and generate selenium-containing scFv with glutathione peroxidase (GPX) activity, scFv expression vector pTMF-2F3 was replaced by a new vector pRose-2F3. Non-essential amino acids of 18 were removed from pTMF-2F3 and a signal peptide was introduced in t he pRose at the N end of 2F3. The 2F3 antibody was expressed as a soluble prote in in the periplasm cavity of E. coli BL21 (lys S). The purified product was con firmed by Western Blotting. Se-2F3-ScFv is generated by the chemical mutatio n of 2F3-ScFv. The GPX activity of Se-2F3-ScFv is 2　530 U/μmol. For studying its protection of epidermal cell from UVB damage, the effects of UVB and Se-2F3- ScFv on lipid peroxidation, the cell viability and cell membrane integrity were investigat ed. It was found that Se-2F3-ScFv possessed strong ability to prevent epidermal cells from UVB damage and was an effective membrane peroxidation inhibitor.

An AG to GC switch at nucleotide positions 3064-3065 encoding the wild type NG2　proteoglycan was made by sequential PCR reactions using overlapping primers, res ulting in the change of serine to alanine at amino acid position 999 in the NG2 core protein. Expression constructs pcDNA3.1+/NG2 and pcDNA3.1+/NG2/S999A were made. Transfection of wild-type and mutant forms of NG2 and expression vector pcNA3.1+in U251 cell were performed with LipofectAmine. The NG2 transfectants were isolated, identified by Western Blot. The NG2/S999A transfected U251 cells lack the chondroitin sulfate glycosaminoglycan (CS-GAG) chain. Cell migration assays were performed with these three U251 transfectants. The result suggests that NG2 plays a role in promoting the cell migration. Furthermore, it indicates that the CS-GAG of NG2 could modulate this process.

The high performance liquid chromatographic method was employed for determining the acetic acid （AC） in furfural waste water on a symmetry 5 μm C_１８ （4.6 mm×150　 mm） column with 0.002 0 mol /L H_２ＳＯ₄ as the mobile phase at a flow rate of 1.0　m Ｌ/min. The detection was made on a UV detector at 210 nm with external standard calibration． The liner operating range of the method is 0.040 0[KG-*4]～0.400 0　g/L(r=0.999　8) with a r elative standard division (RSD) of 0.536%（n=6）. The average standard addition recovery of the wastewater samples is 105.5%[KG-*4]～115.7%.

The biosorption of Cd^２＋ and Pb^２＋ onto the dominant dead bacteria in the Yitong River and the effects of temperature, initial pH, initial metal ions and bacteria biomass on the biosorption were investigated. The results show that bacteria biomass had more influence on Pb^２＋ biosorption than on Cd^２＋ biosorption. The bacteria show the highest Pb^２＋ uptake capacities at an initial pH value of 4.5, and show the highest Cd^２＋ uptake capacities at an initial pH value of 6.0. The bacteria exhibited the highest Pb^２＋ and Cd^２＋ uptake capacities at 30 ℃. The concomitant Pb^２＋ had no considerable effect on the biosorption of Cd^２＋, and the concomitant Cd^２＋ had a considerable effect on the biosorption of Pb^２＋.

Water solutions containing Cd^２＋ were treated thoroughly with nano-wate r-purifying material developed in the laboratory. The results show that this ki nd of nano-material can efficiently remove Cd ^２＋ ions with a low concentration in solutions with the highest removing rate of nearly 100%. This novel nano-material has many advantages such as convenient operation method, low cost, good effect, and high efficiency for treating Cd^２＋ ions with a low concentration.

methyl orange solution was treated by means of the UV-Fenton method. The results show that the concentrations of H₂O₂ and Fe^２＋ and pH value exhibit a great effect on the degradation of methyl orange. The decolorization ratio of methyl orange is determined by the concentration of H₂O₂, the rate of degradation is determined by t he concentration of Fe^２＋ and increases with the decrease of pH value. Also, the change of TOC of the methyl orange solution with the reaction time is discussed and the rate of degradation is faster than that of TOC removal.