The authors presented  a strainconstructed point interpolation method (SC-PIM) by combining techniques of FEM and nodebased point interpolation method (NS-PIM). By introducing a parameter,  we further discussed the convergence, upper bound and lower bound solution, and superconvergence under the assumption of strain field being a linear combination of compatible stains and smoothed strains from SC-PIM.

Linear summation method was applied to the truncations on parallel hexagon of double Fourier series associating with threedirectional coordinates. The parallel hexagon’s summation of double Fourier series of a function was putted forward. A specific convergence factor was constructed. A linear integral operator with the convergence factor was obtained. It has been proved that
 the operator converges uniformly to any given continuous double function with periodic domain Ω, where Ω is a parallel hexagon domain.

Using the atomic decomposition of weighted Hardy spaces to show the boundedness of commutators generated by the Lipcsihtz function and generalized CalderónZygmund operator on the weighted Hardy type spaces, we obtained the commutators are bouneded from H^p(ω) to L^q(ω^q/p) and from H^p_b(ω) to L^q(ω^q/p).

We gave some properties and characterizations of Wnilinjective modules, and under the condition that every simple singular left module is Wnilinjective, we discussed the relationship of some special rings (such as reduced rings, semiprime rings and quasi ZI-rings).

We first introduced the notions of partial DoiHopf group structures and partial DoiHopf group modules which generalize Doi-Hopf structures and DoiHopf modules. Then we gave some examples and basic properties. Mainly we combined the idea of group coalgebras with partial entwining structures to construct the forgetful functor from the category of partial DoiHopf group modules to that of modules and proved that it has a right adjoint functor.

By the relation of generalized quadratic matrices to idempotent matrices and the known results on rank and nullity for linear combinations of idempotent matrices, we studied the invariance of rank and nullity for linear combinations of generalized quadratic matrices, which unified and generalized the related results in literature on rank and nullity for linear combinations of scalarpotent matrices, scalarinvolutory matrices and quadratic matrices.

With the help of  the Chern connection in Finsler manifolds, we analyzed the convexity of distance function in a Finsler manifold, then discussed harmonic maps between two Finsler manifolds in the point of view of the topology, and obtained a nonexistence theorem about nontrivial harmonic maps from a Finsler manifold with the limited fundamental group to nonfocus Finsler manifold, and  studied some problems on homotopy class of mapping and got a simple existence theorem.

A fourunit redundant system with commoncause was discussed. First we transformed the system to an abstract Cauchy problem in a Banach space. Second, by analyzing the spectrum of the system operator and its dual operator, the authors proved that 0 was unique spectral point on the imaginary axis and the others spectra lie on the left side of the complex plane. As a result, the asymptotic stability of the fourunit redundant system with commoncause was obtained.

The authors investigated the topological classification of the orbit structures of Lienard systems with closed orbits using the method  of qualitative analysis. The classification rules and methods were given by the corresponding relationship between the set of Y⁺ and the set of Y^-, and 40 kinds of orbit structures of Lienard systems with closed orbits were yielded.

The main purpose of the present paper is to give some properties for subideals of Jordan Lie algebras. Every perfect subideal of Jordan Lie algebras is its ideal and solvable subideals are contained in its solvable radical. Moreover, every subalgebra of nilpotent Jordan Lie algebras is its subideal and some necessary conditions under which subideals become ideals for
Jordan Lie algebras have been obtained.

Using the duality of greatest common factor and least common multiple of polynomials, we obtained the identities for the sum of the ranks of finite matrix polynomials without any constraint.

With the help of continuous variation method and the explement principle, the singlevalue branch problem for general multiplevalued function was discussed. The fulcrum criterion theorem and singlevalue branch explicit were shown in the two cases of R and C, so are shown those for two special states.

Using the perturbation method, we constructed the Green’s function for second order linear differential equations associated to a multipoint boundary condition. Moreover, we presented a sufficient condition for the positiveness of the Green’s function.

Using the continuation theorem based on coincidence degree theory, we studied the existence of positive periodic solutions for a Lotka-Volteraa facultative mutualism system of three species with several delays. One bounded open set and a set of sufficient conditions for this system to have at least one positive periodic solution were obtained by using analytic technique. It was revealed that when the facultative mutualism coefficient and density dependence coefficient of three species are under certain conditions, the system will bring periodic oscillation of biological nature.

Some certain examples were mentioned in order to prove that  not all the setvalued submartingle could be decomposed even in one dimension real space. In other words, the setvalued submartingle means the sum of setvalued martingle and setvalued submartingle. A new definition about the Riesz decomposition of setvalued submartingle was presented. We  proved that the set valued submartingle possesses the new form of definition in one dimension real space. In order to illustrate that the new definition is not available in two\|dimension real space, some examples were given here. At last, we gave and proved that the sufficient and necessary conditions of this new Riesz decomposition.

We studied the problems of general nonlinear programming with equality constrains. First, the inequality constrain was expressed as an nonsmooth inequality constrain by means of the maxvalue function, then with aggregate technique this constrain was smoothed. With the help of combined homotopy interiorpoint method and the weak normal condition, the existence of solution of the generalized K-K-T equation was verified. The algorithm was proved to be globally convergent. The results of numerical experiments show that the algorithm is effective and convenient.

Let f denote a system induced by a nonprimitive and nonconstantlength substitution over the alphabet {0,1}. We investigated the topological entropy of f and the possibilities for f to occur chaoticbehaviors and proved that the topological entropy of f is zero, and gave a sufficient condition for f to contain no distributively chaotic pairs.

We presented a family of modified ChebyshevHalley iterative methods for nonlinear equations, the methods avoid calculating the second derivative, and have thirdorder convergent at least, if we choose some values of the parameters, these methods will be of order four. Several examples were given to illustrate the efficiency and stability of the new methods.

The almost sure and moment exponential stability of the Milstein scheme for stochastic differential equations were studied. We focused our attention on these stability properties in the limit as the timestep tends to zero and we proved that under proper conditions, explicit and semiimplicit Milstein methods maintain these stability properties.

Let R be a retract of k［x,y,z］ with a retraction φ. It is proved that there exist p,q∈R such that R=k［p,q］ if
 the transcendental degree of R over k is 2 and either of the following  conditions holds: 1) R is an inert subalgebra containing no coordinates andφ is the gradient of a polynomial; 2) R is a 2valuation algebra.

A method about testing variance differences of a single population was constructed based on Ustatistics. This method, compared with the χ² testing, can be applied to more general situations, and its asymptotic relative efficiency is 1.

According to the problem of the traditional information content method depending on WordNet structure, only the Hypernym/Hyponym relation is considered in this method. However, the Holonym/Meronym relation which is also important has not been considered. Therefore, a method based on extending relations was given in this paper. According to the experiments, the method is better.  The result of the semantic similarity between words or concepts can be improved according to the method.

Based on the high degree of flexibility and the functions of find automatically of Spread, a business support system was constructed. We made detailed researches of the topology construction of the business support system, for the four common conditions: the joining of a serve node, the leaving of a serve node, the dynamic increase of topology and the dynamic reduce of topology, we gave the detailed algorithm. Simulation shows that the system has better stability, extensibility and a better capability to resist disaster and destruction.

The convergence of the kernel based fuzzy cmeans clustering algorithm (KFCM) was established by applying the Zangwill’s convergence theorem. The result shows that when the distance matrix induced by kernel function satisfies the given conditions, the iteration sequence produced by the KFCM algorithm terminates at a local minimum or a saddle point, or at worst, conta
ins a subsequence which terminates at a local minimum or saddle point of the objective function of the KFCM clustering model.

Unidirectional synchronization for neurons via  terminal sliding mode control was realized. Simulation made us know that desynchronized neurons because of parameters changing or external disturbance can be changed into synchronized neurons by this control method. The simulation experiments prove the feasibility and the validity of this control method.

The authors proposed a combination of Fourier descriptors with the least square method for iris localization. On locating the inner boundary of iris, an improved tracking algorithm was introduced to obtain pointsequences by tracking the edge of the binarization pupil. After Fourier descriptors transforming, the least square method was finally used to fit the inner circle. On locating the outer boundary, the gray gradient information on the left and right parts of the iris was appropriately used. Based on this information, the outer boundary pointsequences were extracted. Similarly, the outer circle can be fitted by the least square method at last. Experimental results show that the method can overcome the eyelashes and eyelid occlusion, and also improve the loc
alization speed and accuracy. The results can meet the requirements of realtime iris recognition system.

An improved support vector machine recursive feature extraction (SVM-RFE) algorithm was used to screen the disease resistance genes. In the 20 important genes, we found that 3 of them have strong relation to the disease resistance as reported and 2 of them have relation to the stress response. It shows that this method can find out which genes could impact the rice growth status (normal/disease). It might provide a guide on finding other unknown rice disease resistance/sensibility genes in biology.

In view of the accuracy of the service node weight in weighted least connection algorithm directly affects the load balancing efficiency and the integer cluster system performance. We proposed a new improved algorithm: priority processing capacity weights distribution scheduling algorithm, described the work process and algorithm thought in the improved algorithm, analysed and designed the improved algorithm’s main technology, main module and principle. The improved algorithm solves the LVS load imbalance problem; the LVS performance and stability are improved to some extent. The experiment comparative analysis shows the improved algorithm is more optimal than weighted least connections algorithm in dynamic balance.

Mn doped nanocrystalline ZnO was synthesized at different temperatures by means of self\|assembly growth method. The structure, morphology and optic properties were characterized by  X\|ray diffraction (XRD), transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS), X\|ray photoelectron spectroscopy (XPS) and photoluminescence spectroscopy (PL). The results show that ZnMnO was in the shell of ZnMnlowO/ZnMnhighO structure. A large number of Mn on the surface played a role in surface passivation at 250 ℃ and 300 ℃. 

The authors presented alternating direction implicit multiresolution time\|domain (ADI-MRTD) formulation, and  implemented  perfect matched layer (PML) as absorbing boundary conditions of ADI\|MRTD method. The application of the ADI\|MRTD method  to the calculations of asymmetrical coplanar waveguide (ACPW) and ultra\|wideband ACPW filter. The  numerical and measured results show the advantages of ADI-MRTD over conventional FDTD method with respect to memory and mesh requirements and execution time, and the numerical result of ADI\|MRTD is in agreement  with FDTD and measured result.

A simple and efficient method for patterning poly(3,4\|ethylenedioxythiophene)∶poly(styrene sulfonate) (PEDOT∶PSS) electrodes for application in the field of organic electronics was proposed. The entire PEDOT∶PSS layer, except  the desired pattern, was selectively detached from a flat substrate surface by an epoxy resin mold with a relief pattern.  Epoxy mold has a high  work of adhesion with polymer could make selective detachment occurrence, thereby the thin films can be rapidly patterned with large area.

TiO₂ nanotube arrays  were prepared by means of anodizing method on the surface of titanium films. The packed n\|type TiO₂ tubes have  an inner pore diameter of 60—90 nm, a wall thickness of approximately 15 nm and a length of 600 nm. The NiO/TiO₂ heterojunction electrode was synthesized by means of electroless plating and annealing which resulted in TiO₂ nanotube arrays coated with a layer (about 200 nm in thickness) of NiO particles (20—40 nm). The results show that  NiO/TiO₂ heterojunction electrode  enhanced photoelectrochemical property under 100 mW/cm2 irradiation. The photocurrent density is 3.05 mA/cm2, and photoelectricity conversion efficiency is 1.41％ at a bias voltage of 0.65 V.

A 3D structure of thermostable esterase (EstTs1) was built by means of the protein homology/analogy recognition engine (Phyre) program and further refined via unrestrained dynamics simulation. The docking results reveal that p-nitrophenyl butyrate （C₄） is the best substrate of EstTs1,  which has the adaptive size to the EstTs1. In addition, the key bindingsite residue of Thr111 plays an important role in the catalysis of EstTs1 for it made a hydrogen bond with p-nitrophenyl butyrate. One important finding was that the identification of the key binding site： residue of Ser85 which plays an important role in the catalysis of EstTs1.

According to the SQS gene of Panax ginseng, the authors designed a sense primer and an antisense primer to construct a SQS interference expression vector. The ginseng callus was transformed by agrobacteriummediated methods, and the selected resistant callus was assayed by PCR and realtime PCR, and the ginsenosides of resistant callus was analyzed by HPLC. Compared with the nontransformation ginseng callus, the SQS gene’s expression of positive callus decreased, and the ginsenosides also had certain changes. SQS is a critical biosynthetic enzyme of ginsenoside. To inhibit the expression of SQS can mediate the change of the content of the ginsenosides of ginseng.

The Pleurotus ostreatus were used as the raw material for extracting polysaccharide by means of smashing extractor, ultrasonic extraction, ultrasonicassisted complex enzyme extraction. The results indicate the  optimal extraction conditions of the smashing extractor were extraction temperature 90 ℃, extraction rate 11 350 r/min, extraction time 20 min, extraction 3 times, and the yield of polysaccharide extracted was 11.20%. The optimal extraction conditions of ultrasonic extraction were extraction temperature 60 ℃, extraction time 60 min, ultrasonic power 450 W, extraction 3 times, and the yield of polysaccharide extracted was 9.75%. The optimal extraction conditions of ultrasonicassisted complex enzyme extraction were extraction temperature 30 ℃, extraction time 60 min, ultrasonic power 350 W, extraction pH 5, the yield of polysaccharide extracted was 1205%. In comprehensive consideration of the yield of polysaccharide extracted, saving energy, simple operation, the smashing extractor was considered as an ideal method.

We extracted total RNA from human embryonic lung fibroblast cells and obtained cDNA by means of RTPCR. Then the PCR products were inserted into pET3c that was transformed into BL21 (DE3) host cells, which was induced to develop solubility protein products. Highdensity culture was conducted  in fedbatch mode under the control of fermentation conditions. Purification was carried out by cation exchange chromatography and heparin affinity chromatography. And the effect of rhKGF2 on proliferative activity was tested via transferring receptor FGFR2Ⅲb of the BaF3 cells. We constructed gene engineering bacteria of recombinant human keratinocyte growth factor2 (rhKGF2), studied the highdensity culture of recombinant engineering bacteria and purification process and established the method of activity determination. Total protein is more than 30.0% of the total bacterial protein over consecutive three batches of fermentation. The purity of rhKGF2 was higher than 99.0% after twostep column chromatography. We built a new way to test its biological activity. The result shows that it seemed obviously curved letter S, which had some relation with the dose in some extent.

We investigated the photoconversion laws of α-naphthol in laboratory simulation experiments in ice under UV irradiation, studied the impact factors, analyzed the photoproducts, and deduced reaction mechanisms. The results show that α-naphthol could be photoconverted under UV irradiation in ice, and the conversion rate increased with the decreasing of initial concentration of α-naphthol, and increased with the increasing of light intensity and ultrasonic time. The photoconversion rate of αnaphthol in natural Songhua River water was faster than that in distilled water. Strong acidic or basic conditions were beneficial to the photoconversion of αnaphthol. Added NO^-₃,NO^-₂,HCO^-₃,Fe²⁺,Fe³⁺, and Mn²⁺ all promoted the photoconversion of α-naphthol. Cl^- had no significant impact on the photoconversion of α-naphthol. Four photoproducts were determined by GC-MS in the photoconversion of α-naphthol, and the proposal photoconversion pathways of α-naphthol were condensation, oxidation and reduction reactions.

The doublechamber microbial fuel cell (DCMFC) with landfill leachate from some refuse dump of Siping City of Jilin Province as fuel was designed in the  system with the bacteria in the titanium anode chamber separated from the titanium cathode chamber by a salt bridge. The effects of cathode chamber solution parameters on the electricity generation performance of DCMFC were
 researched. The results show that the DCMFC output power density is 12.074 W/m², opencircuit voltage is 1.13 V, internal resistance is 76.868 Ω under cathode chamber solution optimum conditions of 30 ℃, 1.0 g/L  H₂O₂, pH=2.5, and 0.5 g/L  Na₂SO₄. After the DCMFC was continuously running for 30 days, the COD removal rate of landfill leachate reached to 95%, the adjust of cathode chamber operational parameters can improve the microbial fuel cell electricit generation.