We investigated the first initial boundary value problem of  -u_t+log S_k(λ(D²u))=ψ(x,t,u), which is a class of parabolic k-Hessian equations. In the general smooth region Ω, under the admissible subsolution, a prior estimation of the admissible solution was given. The existence of the admissible solution was obtained by using the method of continuity. The solution is unique if ψ_u≥0.

The authors studied the impulsive differential equation singular boundary value problem with integral boundary condition. First, the LerySchauder degree homotopy invariance was used to prove the existence of solutions principle for regular problems, then the existence of positive solutions was proved by means of this existence of solutions principle and the idea of approximation.

We constructed and analyzed an example of a secondorder threepoint boundary value problem. First, we used the analysis of upper and lower solution method to prove that the  solutions of this kind of problems of both resonance and nonresonance  cases, respectively are countably infinite, and finally, gave a numerical solution of such problem using  shooting method and Newton iterative method, and the corresponding image analyses.

Aiming at a class of noncooperative elliptic system, we obtained a nontrivial solution of this elliptic system using a generalized linking theorem and monotonicity technique.

The It formula and standard truncation procedure were used to study the existence and uniqueness of a stochastic differential delay equation with jumps when the coefficients satisfy local Lipschitz conditions and Khasminskii condition. This result is a Khasminskiitype theorem.

We applied the critical point theory for strongly indefinite functional to study timeperiodic solutions of nonlinear wave equations. A new existence result for the nontrivial timeperiodic solutions of asymptotically linear wave equations is obtained when the nonlinearity is not assumed to satisfy any resonance or nonresonance conditions at infinity.

We presented tanh\|function method and (G′/G) function expansion method to solve the solutions of nonlinear wave equation, confirm
ing the consistency of the traveling wave solutions by them. Such an analysis can make us find their common parts. As for the general nonlinear wave equation, we used tanh\|function method and (G′/G) function expansion method to solve their traveling wave solutions respectively.

Based on the properties of matrix, the conditions of absolute value equations with 2ⁿsolutions were obtained, meanwhile corresponding examples were given.

Compared with similar dimensions, two approximate box dimensions were defined, normalizing the estimator of box dimension, we defined
 the normal dimension with accuracy, and proved its convergence to the box dimension. Hence, the method of preestimating and correcting provides the correction dimension with accuracy. For the two dimensions, the computational examples illustrate the rationality and fesibility.

We studied the following stochastic integrodifferential equation Using the properties of almost periodic functions and exponential dichotomy, It isometry formula as well as Banach fixed point theorem, we established the theorem for the existence and uniqueness of squaremean almost periodic solutions of the equations.

Using “generalized approximations of the identity” and the double conditions of measure μ on spaces of homogeneous type, we esti
mated the boundedness of the multilinear commutators T_b generated by singular integral operators with nonsmooth kernels T and b(b∈Lip_β), and obtained a result from L^p(X) to L^q(X).

Two approximate optimality conditions of the weighted Euclidean onecenter (WEOC) problem were defined. Based on the idea of sequential minimal optimization (SMO) method, an SMOtype algorithm for the WEOC problem was proposed. By means of this algorithm, a (1+ε)approximate solution of the WEOC problem was computed, which satisfys the second approximate optimality condition. At each iteration, it updates only two components of the dual variable. The numerical results show the proposed SMOtype algorithm is simple to implement, can effectively solve largescale problem with a high degree of accuracy.

We studied the problems about geometric inequalities for ndimensional simplex in the nonEuclid hyperbolic space and spherical space by the theory and method of distance geometry, and established the ndimensional NeubergPedoe inequalities for the volumes and edgelengths of two nsimplexes in the hyperbolic space and the spherical space.

The author studied the polar factorization and generalized inverse and perturbation bound of quasirow (column) symmetric matrix, which leads to some new results, and presented the formula of the polar factorization and generalized inverse of quasirow (column) symmetric matrix, which makes calculation easier. In addition, some perturbation bounds of the polar factorization of quasirow (column) symmetric matrix were also presented.

We studied the blowup property of solutions to a class of nonNewtonian fluid equations [JP2]with damping term. Using energy method and constructing and analyzing different types of differential[JP] inequality according to the different ranges of nonlinear index q, we proved that the solution of the problem will blow up in finite time.

We gave an existence and uniqueness for the solution of a nonlinear fractional differential equation boundary value problem D^α₀₊u(t)=f(t,u(t)),0<t<1,u(0)=u(1)=u′(0)=u′(1)=0,where 3<α≤4 is a real number, and D^α₀₊ is the standard RiemannLiouville differentiation. Our result relies on a fixed point theorem for generalized contraction in partially ordered complete metric spaces.

This paper deals with the uniqueness of positive solutions of the Neumann problem for an elliptic system. With the help of transformation technique and maximal principle, we proved two inequalities of solutions under a definite condition, and then obtained the uniqueness of positive solution by taking the limit for them, which also shows that under more weak conditions, the problem has no any positive nonconstant solution.

By introducing the concept of two\|sided group Smash coproducts, the authors presented the necessary and sufficient conditions for two
sided group Smash coproducts to be Hopf group coalgebras. Using the integral theories of Hopf group coalgebras, we discussed the semisimplicity of twosided group Smash coproducts.

On the basis of  double ring of real associative algebra, the properties of Clifford algebra Cl_p,q which generated by Minko
wski space R^p,q were discussed, which indicates that  all the non divisible Cl_p,qhas a double ring as its subalgebra and all the Cl_p,q with center subalgebra non divisible is a double ring.

We used the lattice Boltzmann method to study the thermal wave equation and constructed a lattice Boltzmann model for the thermal wave
equation. By means of this model, the one and twodimensional thermal wave equations were simulated. Comparison between the result obtained by the lattice Boltzmann model and the result obtained by the classical method shows that this method can be used to simulate thermal wave problems.

We first introduced the dual schemes for a composed convex optimization problem. Then, using the properties of the epigraph of the conjugated functions, we introduced some new constraint qualifications. Finally, using these constraint qualifications, we obtained some necessary and sufficient conditions which characterize the stable strong and strong dualities for the composed convex optimization problem.

On the basis of comparing the characteristics of different strategies in homogenous networks in terms of efficiency, cost and robustness, the authors constructed a hybrid interdependent network and analyzed the efficiency of different immunization strategies in such network. The results show that although current immunization strategies can effective restrain virus propagation in homogeneous networks, the efficiency of strategies should be improved in interdependent networks.

TOUGHREACT is a simulator for nonisothermal multiphase reactive geochemical transport in saturated geologic media. In recent years, there has been an increasingly need in application of fieldscale simulation, which leads to intensive computational efforts. In order to scale up the simulation model and improve the performance of the simulator, the authors analyzed the mathematical model of coupled simulation and executed time proportion; designed a parallel computing scheme of numerical simulation on coupled reaction; reorganized the structure of coupled simulation program. Experiments on distribute memory computing nodes show 2—3 times speedup in simulation time.

We proposed a face recognition method based on local binary pattern and resampling bidirectional 2DLDA, called LBPRB2DLDA, to solve the small sample size problem and recognition problem caused by variations in lighting, facial expression, etc. Experiments of AR face database show that the proposed approach possesses high recognition accuracy and robustness.

A new kind of stability criteria was proposed for addressing the problem of stability analysis of continuoustime nonlinear systems with timevarying uncertainties based on the TakagiSugeno fuzzy model. In the process of stability analysis, a parameterdependent Lyapunov function and two methods for introducing additional variables were used. Since more freedom can be introduced in virtue of the above measures, the obtained stability criteria are less conservative than some existing results. More improtantly, the proposed results are given in terms of linear matrix inequality, which is easily solved via standard numerical software. Finally, a numerical example illustrates the effectiveness of the proposed approach.

A quantum shuffled frog leaping algorithm was proposed which combines with the quantum theory. In this algorithm, the individuals are expressed with Bloch spherical coordinates of qubits, the individual update is realized with the rotation of qubits in Bloch sphere, and the local search capabilities within the subgroup is improved with adaptive chaotic rotation angle operator. Then, to avoid premature convergence, the mutation of individuals is achieved with Hadamard gates. Above operations extend the search of the solution space effectively. Results of experiments show that compared with the SFLA, PSO and GA, the algorithm has a higher optimization capability and efficiency, and is more suitable for highdimensional optimization of complex functions.

In order to address the problem of the selection of distant targets on large displays, many techniques have been proposed. However, these techniques tend to be complex and relatively difficult to operate. We presented a simple and easy technique. A formal experiment was conducted to compare the performance of shiftable with that of direct picking and one of the latest techniques, gesture select. Analysis of variance was used to evaluate this technique. Our results show that shiftable significantly outperforms gesture select and direct picking in selection time and it outperforms gesture select in error rate.

The method to use  secret information to verify the legitimacy of the nodes was presented and Diffie-Hellman algorithm was used to generate the shared key for guaranteeing the security of the key so as to overcome the weakness of localized encryption and authentication protocol. The analysis of the original scheme and the improved scheme from the security and node overhead shows that the computational cost is slightly  increased in the improved scheme, but the security of the network is improved.

On the basis of intersection matrix representation, we established a model representing the topological relation  between concave region and simple broad boundary region. Three constraints were proposed that are reasonable, from which 67 topological relations that are realizable in 2D space were derived.

The authors presented theoretical solution and numerical analysis of the acoustic field of Stoneney and flexural waves in a fluid\|filled borehole surrounded by the transversely isotropic two-phase formation with the Biot\|squirt mechanisms. The effects of the characteristic squirt\|flow length on the dispersion and attenuation of fundamental guided waves were emphatically studied. The results show that the velocity dispersions are almost independent of characteristic quirt\|flow length; attenuation coefficients of Stoneley wave and flexural wave based on BISQ model are obviously bigger than that based on Biot model only. The attenuation coefficient of stoneley wave tends to increase with the  increase of horizontal characteristic squirt\|flow length R₁, and decrease with the  increase of vertical characteristic squirt\|flow length R₃. The attenuation coefficient of flexural wave tends to increase with the increase of R₁ below a certain frequency and  to decrease with the increase of R₁ above a certain frequency, while the variation tendency of attenuation coefficient due to R₃  is just opposite to above variation trend.

The variation of the energy for the  ground states of single electron concentric quantum ring with its radius and  potential barrier was obtained, which was analyzed via dynamics and uncertainty relation. Electronic probability distribution of the ground states was demonstrated via the density functions. The result indicates that when the ground\|state energy is less than the potential barrier, electronic probability in the potential barrier is not zero.

Nitrogen\|rich g-C₃N₄ nanobelts were  synthesized via the pyrolysis of melamine (C₃N₆H₆). The as\|synthesized microbelts are structurally uniform, and each belt is uniform in width and thickness along its length direction. The typical width is in a range of 3 μm to 6  μm. The typical length of the belts is in a range of several hundreds of micrometers, some of which  even have a length of millimeters. The structure and morphology were researched by XRD, SEM, CEA and XPS measurement. The result indicates the sample is graphite-C₃N₄. 

Particle swarm optimization algorithm, which uses the product of the transimpedance gain and common mode rejection ratio to  divide the output resistance as the fitness function,  was used to adaptively optimize the values of the resistance of two\|level direct coupled negative feedback differential\|common emitter circuit under the requirements of  large transimpedance gain, high common\|mode rejection ratio, low output resistance. The results indicate that the values of resistance always tend to set value limit to derive the maximal fitness function when the transimpedance gain and output resistance are respectively restricted, and the results were obtained under  the requirements of the algorithm. Moreover,   the optimal parameters can be found by changing fitness function under considering the different needs of the amplifier in engineering. With EWB software simulation, the relative error between transimpedance gain and theory for the calculation of feedback amplifier is 0.515％.

A series of highly ordered mesoporous silica nanoparticles (MSNs) with tunable particle sizes were synthesized by a direct cocondensation method. The hydrothermal posttreatment was adopted to improve the structure order of the materials characterized by small angle Xray diffraction (SAXRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM) and N2 adsorptiondesorption measurements. Then the highly ordered MSNs with tunable particle sizes from 80 nm to 320 nm were successfully prepared by changing the amount of TEOS and NH₃·H₂O. The results show that all the samples with wellordered mesoporous structures are typical MCM41 type mesoporous silica materials.

Three dimensional structures of phosphotriesterase-like lactonases (PLLs) from Thermaerobacter marianensis\% were modeled by means of homology and molecular dynamics methods. On the basis of the modeling, the components and the structures of active sites TmPLLs were analyzed and compared. The docking was also performed. Arg44 was key residue for the combination of two substrates (γ-nonanoic lactone and ethyl paraoxon) with the enzyme.

According to the DNA sequence of the F1L gene which was stored in GenBank, the authors designed one pair of primers to amplify F1L gene of JLSY04 by PCR. The amplified positive production was sequenced and the sequence of it was compared with the sequences of several reference strains domesticisolated. The results show that JLSY04 stain and OV/Torino strain show the lowest homology of 960% with respect to F1L gene, and the highest homology of Jilin strain was up to 994%. There was little difference of F1L gene between JLSY04 strain and each of other reference strains isolated from different species and different areas in China. The analysis result of homology suggests that the F1L gene can be used as the target genes of the genetically engineered vaccine.

Four main hosenkosides, hosenkoside A,B,C and K were used as the indexes of extraction of total hosenkosides from the seeds of Impatiens balsamina L. Solvent concentration, the ratio of material to liquid and reflux time were tested via orthogonal experiments. The confirmed optimum extracting conditions of total hosenkosides were that the seeds of Impatiens balsamina L.were extracted in hot reflux by 70% ethanol V(liquid)∶m(material)=6 for 4 times (60,45,30,30 min, respectively). The results showed that the extraction rate was 98.19%.

We adopted pot culture method to study the transport law of the cadmium in the ground and underground parts of  cabbage system after the  addition of the homemade newspaper fertilizer. In each group, the analysis of cabbage biomass shows that if the cadmium was added, the use of fertilizer would promote the roots of the cabbage to absorbe cadmium. When the concentration of cadmium was 40 mg/kg, the absorption of cadmium was increased to  215.5% compared to that of blank. With the increasing of the concentration of the fertilizer, there was no obvious  inhibitory action on the growth of the cabbage’s roots. When the cadmium was polluted, there was also little influence on the ground part of the cabbage. The supplement of the fertilizer still promoted the growth of the ground part of the cabbage. As the fertilizer concentration was 3 g/kg, the promoting effect was the highest. The root tolerance index (RTI) and transport factor (TF) of cabbage were analyzed. The results show that the root of the cabbage had great effect on the cadmium pollution. After its root came into contact with cadmium, most of the cadmium was kept in root, rather than moving.

The mixed simulated acid rain solutions at different pH levels were spayed on pakchoi in different spray ways within the greenhouse. The results show that strong acid rain inhibits the formation of the nutrients in the cabbage, while week acid rain increases the formation of the nutrients in the pakchoi. Among the three spay ways, more spray amounts and longer spray intervals in the single spray ways have the bigger influence on the quality of pakchoi nutrition.

Europium (one of the rare earth element) was doped into Bi₂O₃ to extend the light response scope of bismuth oxide photocatalyst and
 the effects of europiumtobismuth ratio, concentration of ionic liquid, calcination temperature, calcination time and dosage of the catalyst on the photocatalytic activity of europium doped bismuth oxide were investigated. Methyl orange was used as the target pollutant. The optimum preparation conditions are europiumtobismuth ratio (n(Eu)∶n(Bi)) is 025, concentration of ionic liquid is 0.002 5 mol/L, calcination temperature is 400 ℃ and calcination time is 5 h. The optimum dosage of the catalyst is 5.0 g/L. Furthermore, the prepared sample under optimum conditions has well photocatalytic activity under visible light where the degradation rate of methyl orange is up to 92.57%. But the degradation rate of methy orange was only 29.26% when it was degraded by nondoped photocatalyst. The prepared samples were characterized by Xray diffraction (XRD) and ultravioletvisible diffuse reflectance spectroscopy (UVVis DRS) techniques. The results suggest that the prepared photocatalyst belongs to the tetragonal system. Based on UVVis spectra, the band gap of europium doped bismuth oxide is 2.37 eV which is 0.49 eV narrower than that of the nondoped photocatalyst. Absorption edge shows a red shift of 120 nm. Thus, europium doping extends the light response scope of bismuth oxide photocatalyst and provides a good photocatalytic activity.