We computed the HaezendonckGoovaerts risk measure of the sum of random variables with Pareto and exponential marginal distributions on different Young functions, using the inverse function of the distribution function and the properties of upper comonotonic random vector. The upper comonotonic thresholds of the portfolio risks were given. We established a transparent expression for the stoploss premium and HaezendonckGoovaerts risk measure of the total claim. We also analyzed the properties of the natural estimators of HaezendonckGoovaerts risk measures by means of numerical simulations with the help of R.

The authors  gave representations for the Drazin inverses of some antitriangular block matrices M under the condition BCAⁱB=0（i=0,1,…,n）.

Based on the properties of the rank of the matrix polynomial, the necessary and sufficient conditions of generalized m involutory matrix and (m,l) idempotent matrix were obtained so as to generalize and improve the corresponding results  of m- involutory matrix and m-idempotent matrix.

Based on  the singular value decomposition (SVD) and quotient singular value decomposition (QSVD) of a matrix and matrix pair, the necessary and sufficient conditions were established for the existence of the symmetric solutions and the expressions for the inverse problem of a matrix  X^TAX=Bunder a submatrix constraint. Moreover, the optimal approximation problem to a given matrix in the solution set was considered, and the optimal approximation symmetric solution was obtained.

With the help of the way of weight coefficient and Hadamard’s inequality, a halfdiscrete Hilberttype inequality with a best constant factor was given. We also considered its more accurate extension form with multiparameters as well as the equivalent form.

A global exponential stability judging theorem was given via  topological degree technique, Mmatrix theory and variational methods, in which the reactiondiffusion item is considered. Our estimation of the convergent rate is more accurate than that of traditional estimation, and a numerical example  shows the efficiency of the theorem.

We studied the collocation method for numerically solving a class of delay Volterra integrodifferential equations (DVIDEs). Uniform convergence and global superconvergence of the collocation method were discussed, and local superconvergence on the collocation points was also presented under a weak assumption. Results of the numerical experiments  demonstrate our theoretical analysis.

The lattice Boltzmann method was used to simulate the solitary waves of the coupled nonlinear Schrdinger equations. We constructed a lattice Boltzmann model for the coupled nonlinear Schrdinger equations, and conducted some numerical tests. The numerical results show that the lattice Boltzmann method is an effective method for simulating the solitary waves of the coupled nonlinear Schrdinger equations.

Using upper and lower solution method and the monotone iterative method, we studied the existence and uniqueness of the solutions of nth-order differential equations boundary value problems with integral boundary conditions. We obtained the sufficient conditions of the existence and uniqueness of solutions, and  gave the iterative sequence for solving the solutions and its error estimation formula under satisfying the conditions of uniqueness of solutions.

The authors investigated the global existence and blowup properties of nonnegative solutions for a class of nonlocal parabolic systems
with nonlocal boundary conditions. With the help of  the super and subsolution methods, the critical exponent of system was gained. And it’s proved that if p=(p₁+q₁)…(p_k+q_k)-1,p≤0 and 0≤∫_Ωψ_i(x,y)dy<1, every nonnegative solution is global, whereas if p>0, then the solution blows\|up in finite time if the initial data is sufficiently large. Moveover, the exact rate of the blow\|up is obtained. The results show that the size of initial values and exponents play an important role in the properties of the solutions.

The contingent claim method was used to solve the problems of both the debt value and the optimal capital structure of the corporate in the jumpdiffusion model. By this way, we got the debt value, the equity value and the total value expression of the corporate. Meantime, we  discussed  the influence of Poisson jump.

The multiple scattering problem was solved by means of a boundary integral equation method and regularization method, the inverse problem was solved by virtue of optimization method. The introduction of auxiliary obstacle makes scattering information richer and  reconstruction better. Numerical results show the advantages of the method.

As a generalization of the homogeneous funiction, a quasihomogeneous function was defined and a HardyHilbert type integral inequality with a quasihomogeneous kernel was given, and its application was discussed.

Under some suitable assumptions, we proved the almost sure central limit theorem for the products of sums of partial sums for ρ^-mixing sequences using the central limit theorem of weighted sums and the moment inequality.

The parameter estimator of generalized random coefficient autoregressive model was studied and a class of estimators of unknown parameter was presented. We proved the consistency and the asymptotic normality of the estimators among the class of estimators and obtained the smallest asymptotic variance estimator. Furthermore, some simulation studies were conducted to investigate the finite performances of the proposed estimators.

This paper deals with  the consistency of nearest neighbor density estimator for negatively dependent samples by using Bernstein inequality,and presents some sufficient conditions for weak and strong consistency.The therom in this paper extended the consistency to the case of negatively dependent samples.

In normed linear spaces, the super efficient solutions of set-valued optimization were investigated with generalized higherorder conedirected adjacent derivatives. Under the assumption of near conesubconvexlikeness, with the help of separate theorem for convex sets and the properties of Henig
dilating cone, the type of Fritz John necessary optimality condition was established for setvalued optimization problem to obtain its super efficient elements.

The authors  discussed the mathematical description of electromagnetic scattering problems of the diffraction grating in the homogeneous medium. With the help of the cylindrical coordinates and artificial boundary conditions introduced, the authors showed that  the mathematical description of diffraction grating scat
tering problem was feasible, and gave the variational problem equivalent to the scattering problem.

A new principal component analysis particle filter algorithm  proposed in this paper combines principal component analysis method with the traditional particle filtermethod.  The proposed method avoids undue resampling and improves the accuracy of object tracking.  Experimental results demonstrate that this algorithmcan acquire better precision in single object tracking and multiple\|obstacle object tracking, and this algorithm could track human face accurately in complex backgrounds.  Compared with present particle filter algorithm, this algorithm performs better in robustness and accuracy and avoids particledegeneration and particle impoverishment.

The authors proposed a multiagent cooperation method to solve heterogeneous resource allocation problem in a distributed way. When the problem is put into the architecture of distributed generalized assignment problem, the large problem is separated into many small ones and each agent is responsible for a part of the solution. By means of the knowledge from their previous communication searches, agents are able to predict how to deploy their future similar searches more efficiently. Therefore, if an agent can solve some parts well, similar searches will be sent to it. Using this method, we may avoid the shortcomings mentioned above in the traditional ways. The experiment shows that the proposed method is feasible.

The thesis brought up a scale\|free model based on community and hierarchy in the light of the complex network node degree distribution obey power law distribution. The  preferential attachment mechanism of BA model was improved via turntable technique and restrictions on node degree, and the searching in scale-free networks was optimized by bringing in hierarchical structure. The new model not only introduces the concept of local world but also solves the uncertainty problem in local\|world model  via the community structure. Theoretical analysis proves that this model’s degree distribution obeys power\|law distribution and the power\|law index is adjustable. Simulation experiment shows that the new model has a smaller average path length and a larger clustering coefficient. While searching the network, two\|layer network is much more efficient than single-layer network. 

In view of the requirement of flight simulation, we presented a largescale terrain rendering method with dynamic error metric, which is based on restricted quadtree. By means of error saturation, the error metric of our method meets the requirements of parallel computing that can be used to select terrain grid points, which makes the error metric and triangulation executed by GPU. It improves the rending efficiency of image hardware, and saves the running time of CPU. The algorithm can be used for realtime rendering of large scale terrain in highspeed flight simulation.

On the condition of losing less information and retaining less data,  the data were refined by the data reduction technique. The proposed approximation algorithm for fuzzy c-means clustering was used to estimate the cluster centers. Combined with validity indexed and estimated centers, FCM can execute unsupervised clustering. The proposed algorithm improved the computational efficiency and performance of the conventional unsupervised fuzzy c-means clustering algorithm. The contrast experimental results with conventional algorithms show that the proposed algorithm has a relatively high precision and efficiency. It can obtain the cluster number more accurately than the conventional algorithm.

Based on the  two basic features of advertisements: frequent shot changes and apparent brand information, the curve of histogram difference was obtained via histogram difference between two adjacent frames, and four common shot changes such as cut, dissolve, fade\|in/out and wipe were analyzed so as to  recognize shot change detection. As for those advertisements with low shot change frequencies, the text detection method based on maximum gradient difference was employed to extract the brand information. According to the above ideals and algorithms, a video advertisement retrieval system was designed and realized. A general precision rate of 8332% in about 15 min of video frames indicates the system could preliminarily satisfy the performance requirement according to video consecutive sequence.

Function perturbation was applied, on the basis of the researches on feature selection for high\|dimensional data, to integrating the results of four different feature selectors in order to get a subset which has good classification accuracy and stability. The former algorithm and the new algorithm were compared on five gene datasets. The experimental results demonstrate that the new algorithm  is able to make the effects of different feature selectors complementary, and thus it effectively improves the stability of feature selection and has a good classification accuracy.

An improved algorithm of Web structure similarity based on tree path matching was proposed, which defines the sequence similarity and position similarity of the tree path, finds out all the Web tree paths, and calculates the structural similarity by best tree path matching between two Web pages. Experiments show that the proposed algorithm to calculate the Web structure similarity is more realistic and effective than the original algorithm.

The authors analyzed the security in WSNs, proposing a novel security algorithm based on biological immune principles. Intrusion characteristic library was established, so as to provide security system  with the functions of memory and learning. Uncertainty and imperfection of information are solved by  using the rough set in WSNs. The simulation results show that the proposed algorithm is feasible and superior to the existed others.

We extended 4intersection matrix model to 8-intersection matrix model to solve the representation for topological relations between a region with a hole and a simple region. We obtained 17 topological relations of a region with a hole and a simple region by means of this model. And it was proved that 8-intersection model intersection model is more expressive than the extended 4intersection model and 8intersection model is complete and mutually exclusive.

Most existing outlier detection algorithms ignore local information of data sets, they are of low accuracy. We adopted a twophase algorithm based on k-means clustering algorithm, defined a new local stray factor as the standard to judge whether data objects are outliers. We also improved the process of detecting outliers and solved the above problem. Experiments show that our algorithm overcomes the shortcomings of existing methods, ensure the algorithm has linear time complexity and is able to find outliers in data sets more accurately and effectively.

With the help of  FFmpeg technology, the author designed a management sysytem of media assets involving  various types of video data, audio data, text, pictures, and other media digital data storage, inventory management, query, edit material transcoding, information dissemination, and equipment and fixed assets to conduct a comprehensive management. The results show that the media asset design solves the media transmission and conversion and  guarantees  effective and complete data.

On the basis of analyzing  the commonalities between the correlation of Traditional Chinese Medicines and the relationship of data nodes of the graph structure, we  transfered the links of the drugs in a prescription into the graph structure data according to the rules. Dealing  the structured prescription data with CloseGraph, an efficient frequent closed subgraph mining algorithm, we  got frequent closed graph with a specific function of the graph structure. And then we obtained the core drug combinations and the forms of the combinations with a decisive effect on a specific disease for Traditional Chinese Medicines, providing a valuable scientific basis on figuring out the principles among diseasesyndromeformula. We successfully introduced the graph mining strategy into the field of Chinese Medicine research, providing a new idea and a more solid scientific theoretical foundation for both the prescription study and the future development of Traditional Chinese Medicines.

On the basis of the analysis of historical data on the stock sample, we proposed an algorithm for the prediction of stock data to find the abnormal data to detect the abnormal data, with the introduction of Gaussian process machine learning method. The adaptive mechanism for the parameters of the Gaussian process was also solved with ant colony algorithm. Finally, some experiments show that the proposed algorithm can improve the accuracy and enhance customers’ satisfaction.

 Stabilizing unstable periodic points and bifurcational points of a chaotic electricaloptical bistable system were studied by means of  the feedback method. Based on the relations between state and the eigenvalue of Jacobi matrix of system, the coefficient can be ascertained,  and then the chaos control can be achieved. The   numerical calculation result shows that this method can fulfill the stable control of different periodic points and bifurcation points. Simultaneously, with the same method we can realize the stable control of different periodic states, such as periodic points of four, eight and the others.

The crystal structure, mechanical, thermodynamic, and electronic properties of the high pressure phase R3m  in BaC₂ were investigaed by means of first\|principle method of the density functional theory. The calculation results show that R3m  phase is a more ionic semiconductor material, compared with the I4mmm phase in BaC₂. The phase transition pressure from I4mmm to R3m  is 3.6 GPa, and agrees with experimental result. The elastic constants of R3m  structure meet the Bonn\|Huang Kun criterion, and thus its lattice is dynamics stable. The population analysis shows that the electron transfer from Ba atom to C atom under high pressure plays an important role in the transition from I4mmm to R3m  phase in BaC₂.

 The authors introduced the principles of lifertime measurement, and  measured  the natual radiative lifetime of   Mo atom at 5 odd\|parity highly\|exited levels by means of  the time-resolved laser-induced fluorescence and laser ablation techniques.

The growth of wurtzite indium nitride (InN) films was investigated by means of radio\|frequency plasma-assisted molecular beam epitaxy (RF\|MBE) on 6H\|SiC substrates.  In\|situ X-ray photoelectron spectra were used to determine the Wagner plot of InN. The auger parameter α′ is 85276 eV. The mass radio of In to N in InN is  1.19; the sample surface of InN/6H\|SiC, observed by an scanning electron microscope and atomic force microscope, is  reticular structure  without indium droplets; X-ray diffraction results show that the films have a preferential c-axis orientation normal to the substrate surface, FWHM of InN (0002) rocking curve is 326 arcmin; and the room temperature photoluminescence peak is at about 1 575 nm.

A series of mesoporous aluminosilicate catalysts was synthesized from the synthesizing system with different amounts of citric acid (CA) as poreforming agent and  NaOH as pH adjusting agent. XRD, TEM and N2 adsorption characterization results confirm the presence of interconnected wormlike meso
porous structure in the mesoporous aluminosilicate catalysts. The effect of different amount CA on the porous structures of the mesoporous aluminosilicate materials was investigated. NH₃TPD characterization suggests that most of Al was introduced into mesoporous framework and imparted acid sites. Catalytic test shows that the mesoporous aluminosilicate catalyst with  n(CA)∶n(Al)=13 exhibits higher catalytic activity than the other catalyst for the alkylation of phenol with tert\|butanol. The excellent catalytic activity and high 2,4-diTBP selectivity are mainly assigned to the acidity together with the large pore size of the mesoporous aluminosilicate catalyst.

A full length leucinerich repeat receptorlike protein kinase （LRR-RLK） was obtained from a fulllength Atriplex canescens cDNA library, named as
AcLRR (GenBank accession number: JN974247). To investigate the stress tolerance of AcLRR, the recombinant plasmid pYES-AcLRR was constructed by inserting the AcLRR gene into the yeast expression vector pYES\|DEST52 via LR recombination. The recombinant plasmid pYES-AcLRR that was transformed into yeast Saccharomyces cerevisiae INVSc1, and the INVSc1 strain transformed with empty pYESDEST52 was used as the control. The recombinant yeast INVSc1 harboring pYES-AcLRR and the control INVSc1 harboring empty pYESDEST52 were treated with salinealkali, drought, high temperature, frezzing and paraquat, respectively, and their survival rates were compared under these stress conditions. The results show that the survival rates of the recombinant yeast INVScl (pYES-AcLRR) were higher than those of the control strain under these stress conditions, indicating that the AcLRR was tolerant to NaCl,KCl,NaHCO₃,Na₂CO₃, drought, high temperature, frezzing stresses, which exhibits that AcLRR may play an important role in stress tolerance of A.canescens.

In order to understand the migration and transformation of heavy metal pollutants in the soil covered by different road area vegetation in the Changchun area, the thermodynamics and kinetics of the adsorption of Cu²⁺ and Pb²⁺ in these soils were studied with the batch equilibration method. The results show that the adsorption isotherms of the two heavy metals in different soil both fit the Langmuir equation and Freundlich equation, but both  better fit  the Langmuir equation, which shows that the adsorption process was closer to the monolayer adsorption model. For the  soil covered with the bush vegetation, the saturation adsorption capacities of the Cu²⁺ and Pb²⁺ were the largest, respectively reached 3 429,5 311 mg/kg. Elovich equation can describe the adsorption kinetics processes of the Cu²⁺ and Pb²⁺ in these different soil better, the adsorption rate of the heavy metals into the soil covered with  bush vegetation  was the largest. The adsorption of these metals into the different soil was related to high pH value, CEC, organic matter content, clay content and other physical and chemical
 properties. The results show that  Pb²⁺ was easier to be absorbed by the soil than Cu^2+, which was related to the physical and chemical properties of the heavy metals.