The author considered mathematical problem of a class of optimal investment. By variable substitution, the author transformed this mathematical problem into the initial boundary value problem of a class of parabolic MongeAmpère equation. Firstly, the author established a series of a priori estimates, and then using some analytical techniques including the continuity method, the author obtained the existence and uniqueness of the smooth solution of the
 initial boundary value problem.

A class of diffusion equation for dust plasma in atmosphere was considered. Firstly, we took a travelling wave transformation for equation, and turned into a travelling wave equation. Secondly, we introduced a functional,  set variation was zero, and determined the Lagrange operator. Then we constructed a generalized variational iteration and determined the zeroth order approximate soliton solution, and derived the any order approximate soliton solutions by iterative. Finally, we used the travelling wave transformation to obtain the any order approximate travelling wave solutions of the soliton for the original equation.

We extended c-supplemented subalgebras, E-algebras and Frattini theory of Lie superalgebras and Lie supertriple systems for δ-Lie supertriple systems, obtained some important properties and gave a necessary condition for solvable δ-Lie supertriple systems. Moreover, we gave a necessary and sufficient condition for the judgement of c-supplemented δ-Lie supertriple systems and E-δ-Lie supertriple systems, respectively.

We consider and construct a Grothendieck spectral sequence on the Ext groups to reveal the cotorsion dimensions of weak HopfGalois extensions. Let H be a finite dimensional weak Hopf algebra and A/B  a weak H-Galois extension, we give the relationship between the left cotor
sion dimensions of A,B and the right global dimensions of H, and discuss the properties of the left cotorsion dimensions of A,B when B is commutative or H* is semisimple.

By giving some basic properties of the generalized derivation algebra GDer(L), quasiderivation[JP] algebra QDer(L), centroid C(L), quasicentroid QC(L) and center derivation algebra ZDer(L) of a Leibniz algebra L, we  proved that QDer (L) could be embedded and become a derivation for a larger Leibniz algebra.

We gave the definition of Relative Hom-Rota-Baxter operators, and constructed Hom-Dendriform algebras and Hom-Tridendriform algebra
s by using Relative Hom-Rota-Baxter operators.

Let W be a class of modules that contained all injective modules. By introducing the cover W-Gorenstein flat dimension of modules over associativering, we described that a class of  W-Gorenstein flat modules was projectively resolving, and proved that for every Rmodule M and every positiveinteger n, if the cover 〖WTHT〗W〖WT〗Gorenstein flat dimension of Rmodule M was n, then there existed an exact sequence of Rmodules 0→K→H→M→0 such that fd(K)=n-1 and H was W-Gorenstein flat module. At the same time, we proved that the W-Gorenstein flat dimension was less than the cover W-Gorenstein flat dimension and they were equivalent when the cover W-Gorenstein flat dimension was finite.

Let G be a finite group. If G has at least one conjugacy class C  such that  |C| is divisible by at least two distinct primes, then we define ccl2(G)=max{|C||C| is a conjugacy class of G such that |C| is divisible by at least two distinct primes}. The purpose of this paper is to  discuss the influence of a given upper bound of ccl2(G) on the structure of a  nonsolvable group G when ccl2(G)≠0.

Using algebraic techniques, we established Chen inequalities for submanifolds of generalized Sasakian space forms with a semi-symmetric metric connection, and gave relationships between the mean curvature associated with a semisymmetric metric connection and certain intrinsic invariants involving the sectional and scalar curvatures of submanifolds.

By using the methods including Weyl’s difference principle, large deviation theorem, avalanche principle and so on, we considered the problem of the Lyapunov exponent positivity and continuity of the discrete analytic Schrdinger operator defined by the high order skew shift T_ω. We proved that if the potential energy factor was big enough, then the Lyapunov exponent of the system was positive and week Hlder continuity. This results extended the conclusion about the Lyapunov exponent positivity and continuity with the lower order skew shift to the one with the high order skew shift.

Using particle swarm optimization algorithm with inertia weight exponentially decreasing, we solved a class of nondifferentiable NPhard problem of absolute value equations. This method could effectively overcome the shortcomings of the local search ability of basic particle swarm algorithm  was weak in the late and easy to fall into local optimal solution by adjusting the dynamic changes of the inertia weight. Numerical experiments show that the proposed algorithm has high precision and less number of iterations for solving absolute value equations with unique solution or multiple solutions.

Using matrix analytic method, we proved that scalar tripotent matrices were generalized quadratic matrices. For scalar tripotent matrices, we gave necessary and sufficient condition of them to be essential, explicit expression of their generalized quadratic matrices form, and relatedproperties of them based on generalized quadratic matrices.

By constructing a homotopy equation for the generalized linear complementarity problem, we gave a new existence condition of homotopy path, under this condition. We proved the boundedness and convergence of the homotopy path, and obtained existence condition of a solution of the generalized linear complementarity problem.

Using the information of known sample points to construct simplex gradient and interpolation function, we proposed a local search algorithm based on the simplex gradient. The algorithm combined the effective sample point set Ω with a hybrid selection strategy, and improved the multistart clustering global optimization algorithm (GLOBAL). Experimental results show that the new algorithm has great improvement in efficiency and stability, and can effectively deal with the problem of high evaluation of the original algorithm for the “narrow valley” function.

With the help of existing conclusions of vertex distinguishing IEtotal colorings of complete bipartite graphs K_2,n and K_3,n, we discussed the question on general vertexdistinguishing total colorings of complete bipartite graphs K_2,n and K_3,n by using the method of combinatorial analysis and constructing the specific colorings, and determined the general vertexdistinguishing total chromatic numbers of K_2,nand K_3,n.

By using the way of weight function and the real analysis technique, and introducing the extended ζfunction to describe the constant factor, the author obtained a multiparameters Hilberttype integral inequality and its equivalent formula, and discussed the problem of their optimal values.

We further studied the conditions to ensure the existence of fuzzy bases for ［0,1］-matroids, and to ensure that the fuzzy bases have equicardinal property and exchange property. We gave the relations between boundedness and closedness, between saturation and regularity, between strongly goodbase property and goodbase property by introducing the notions of boundedness, saturation and strongly goodbase property.

We considered a finite volume method for pricing European options with stochastic volatility. We first simplified the corresponding BlackScholes equation to the equivalent conservation form. Then, we constructed backward Euler and CrankNicolson finite volume schemes based on barycenter dual partition and a linear finite element space. Numerical experiments show that the proposed finite volume schemes are effective.

We proposed an induced smoothingbased weighted estimator of regression parameter and an estimator of its asymptotic covariance in quantile regression model of partial covariates with random missing mechanism. We showed that the induced smoothingbased weighted estimator and empirical likelihoodbased weighted estimator had the same asymptotic covariance and the estimator of the asymptotic covariance of the induced smoothingbased weighted estimator was also consistent. We gave an efficient algorithm for calculating the induced smoothingbased weighted estimator of regression parameter and the estimator of its asymptotic covariance. Simulation results show that the proposed method performs well in finite samples.

We obtained a complete convergence theorem for maximum of weighted sums of arrays of rowwise asymptotically linear negative quadrant dependent (ALNQD) by using the moment inequalities for maximum of ALNQD sequences, and proved a MarcinkiewiczZygmund type strong law of large numbers for maximum of weighted sums of ALNQD sequences by using the proposed theorem.

For a fairly wide range of boundary function and quasi weight function, the author obtained a general form of precise asymptotics in complete moment convergence for the largest eigenvalue by using the weak convergence theorem and the small deviation conclusion for largest eigenvalue of β-Hermite random matrix and tail probability inequality of the general β-Tracy-Wisdom distribution.

The author gave the definition of stochastic processes in the probability distribution of almost automorphic. Using Yoshida approximation approach of bounded linear operator, the author proved that if the coefficients of a class of nonautonomous stochastic differential equations satisfied some dissipative conditions, it must exist only in accordance with the probability distribution of stochastic almost automorphic solutions.

We prove that  K₄-P(n,2),K₃-P(n,2) and I(K_1,1,n) are graceful graphs by using the constructive method, which
gives the  graceful labeling of graphs K₄-P(n,2),K₃-P(n,2) and I(K_1,1,n).

By using generalized (G′/G)expansion method and MATLAB software, we investigated the exact solutions of variablecoefficient Sharma-Tasso-Olver (STO) equation. The results demonstrate that the proposed  method can  obtain the exact solutions of variablecoefficient STO equation.

The conformal invariance and Mei symmetry of the gradient system under infinitesimal transformations were considered. The author gave the definition and determining equations of Mei symmetry and Mei conserved quantity of the gradient system. The necessary and sufficient condition that conformal invariance of the gradient system would be Mei symmetry was given. Mei conserved quantity deduced from conformal invariance was obtained by making use of Mei symmetry.

Aiming at the problem that single neuron PID controller contained output noise, which resulted in degradation of the control performance, we proposed an improved single neuron adaptive PID control algorithm based on Kalman filtering theory. By introducing the concept of state space, the algorithm used recurrence method in the time domain to filter data. The output value of the controlled object was processed by Kalman filtering algorithm and then returned to closed loop control system. The experimental results show that the improved algorithm can effectively reduce output noise of the control system, which is close to an ideal state without noise, and improve the control performance.

In large geographic information system (GIS), it was necessary to store massive vector data and grid data to provide efficient response for users’ data query of high concurrency. The traditional design scheme was difficult to meet the demand. We proposed a distributed database HBase to store spatial data, which
 was based on memory storage, and designed the distributed spatial index based on GeoHash, realized distributed storage and fast query of vector and grid spatial data. Experimental result shows that this method improves the query speed of massive spatial data.

Aiming at the problems that palmprint acquisition was influenced by external factors and noise, palmprint recognition rate of traditional method was low and robustness was poor, we proposed a new palmprint recognition algorithm based on feature weighted and kernel principal component analysis. Firstly, palmprint image was decomposed by Curvelet transform, contour coefficients of different scales and angles were obtained, and Curvelet coefficients were weighted by the fusion operation. Secondly, feature extraction was realized by using kernel principal component analysis to reduce dimension of palmprint feature. Finally, relevance vector machine was used to realize palmprint matching, and the performance of the algorithm was tested by using PolyU palmprint image. The test results show that, compared with other palmprint recognition algorithms, the proposed algorithm has higher palmprint recognition rate, and palmprint matching time is the shortest, which can meet the requirements of realtime palmprint recognition.

According to the need of realtime video splicing, we proposed a method of realtime video splicing based on small region fusion and lookup table mapping. Firstly, we used color correction algorithm to deal with color correction of the mosaic camera video. Secondly, we estimated the image transformation parameters and the small region fusion weights at the initialization stage and stored image in the form of index tables. Finally, we used lookup table method for realtime video splicing in the video mosaic stage. The experimental results show that this method can well eliminate ghosting and splicing gap, meanwhile, the average splicing time of each frame is reduced to about 0.03 s. The method has good performance in speed and effect of video splicing.

Aiming at the problem that distribution of nodes was not uniform and energy consumption of nodes was too fast and current routing algorithms seriously affected the survival time of wireless sensor networks, we proposed a wireless sensor network routing algorithm based on node clustering and optimal distance. Firstly, the algorithm simulated the connection process of biological cells to realize clustering process of sensor network nodes, then balanced the relationship between network survival time and energy consumption, and determined optimal path of data routing according to distance between cluster
 head and base station. Finally, the routing algorithm was realized by using MATLAB R2014b toolbox. Compared with other algorithms, experimental results show that the proposed algorithm can prolong the survival time of the whole sensor network, effectively reduce energy consumption, and improve the utilization rate of energy.

Through the analysis of MPI parallel program which was used to transmit information in uncertain way, we gave the mathematical modelof automatic generation of test data, put forward the concept of similar path, then integrated crossidea and coevolutionary mechanism into artificial bee colony algorithm, and proposed a test data generation algorithm: cross coevolutionary artificial bee colony algorithm. We used the proposed algorithm to solve
the test data of parallel programs, and compared with the results of artificial bee colony algorithm and random method. Experimental results show that the method can solve the test data and reduce time consumption.

Aiming at the problem that Range partition algorithm could not optimize two table join efficiency, which contained heavily skewed data, we proposed an improved algorithm for the data skew connection. The algorithm took different treatment for skew data and nonskew data,  sent data to each Reduce node by using the methods of replicating and broadcasting,  and completed all the connection operation through a round of Map/Reduce tasks. The algorithm could effectively balance processing of each Reduce, which solved the impact of the heavily skewed data on the performance of two table join. The results show that the algorithm is effective by comparing with the traditional partition join algorithm.

In order to avoid the energy hole problem in wireless sensor networks (WSN), and to prolong the lifetime of WSN, we proposed a new non\|uniform clustering algorithm for WSN based on double cluster heads. The algorithm considered the node residual energy and the distance from node to the base station to elect the clustering, and the WSN was divided into clusters of different size. In order to reduce the burden of cluster  head node collection of large scale clusters and transmitting the data, the data transmission path was constructed based on the improved minimum two fork tree in the data transmission phase. Experimental results show that the algorithm can effectively reduce the node energy consumption, and effectively prolong the service life of WSN.

Aiming at the problem of outliers and noise in credit evaluation data, we proposed a support vector machine (SVM) credit risk evaluation model based on eliminating outliers. This model used Fuzzy c-means clustering algorithm to eliminate the outliers. The classification performance of SVM was impro
ved by optimizing the SVM classification parameters by using the particle swarm optimization algorithm. The results of applying the proposed method to the credit risk evaluation show that the classification accuracy is higher than other models. 

Aiming at the problem of large data acquisition and high cost of microarray chip, we proposed a new algorithm for generation of simulated microarray data based on grey value interval. The algorithm simulated differential expression of genes in microarray data by means of grey value measurement, combined with cluster analysis method to create a cluster tunnel, and then generated simulation data with similar mathematical distribution and biological significance of the original data. The algorithm was verified and analyzed by simulated data and real biological data. Experimental results show that the simulation data generated by the concept of grey value interval and the generation mechanism of cluster tunnel is effective and reliable.

Aiming at the defect that the annulus intersection and grid scan algorithm required the number of beacon nodes to meet the size of a certain scale, the author proposed an improved algorithm based on annulus intersection and grid scan for unknownbeacon iterative. The algorithm took the localized unknown nodes as the known condition. The algorithm solved the problem of low localization precision of a small number of beacon nodes and increased the recycling utilization of the localized nodes in the unknown nodes by introducing the beacon node iterative method. Experimental results show that the improved algorithm can improve the localization precision and reduce the dependence on the scale of beacon nodes.

The corresponding Raman spectra were obtained by using λ=532 nm laser excitation with the incident laser beam direction parallel to the baxis and caxis of the single crystal material WTe₂, respectively. Based on the firstprinciples calculations, we studied the Raman spectra of the single crystal material WTe₂ under two excitation conditions. We gave a tentative assignment on the Raman spectra of the single crystal material WTe₂ based on the theoretical calculation and the polarized Raman spectra of WTe₂. Experimental results show that the Raman spectra of the single crystal material WTe₂ excited by the incident laser beam direction parallel to the baxis  have more significant changes than those obtained by the excitation along the caxis.

We gave topology and preparation process of a 2.45 GHz and 5.8 GHz flexible wearable monopole dualband antenna based on polydimethylsiloxane (PDMS) flexible substrate and organosilicone conductive silver adhesive. The structure of the flexible dualband antenna was optimized and the performances of the antenna were characterized. The results show that the experimental results are in good agreement with simulation results. The return losses of the dualband antenna at the center frequency of 2.45 GHz and 5.8 GHz are -26 dB and -28 dB, respectively.

In view of the semiconductor laser as a backlight source of liquid crystal display (LCD) backlight module, we used TN type liquid crystal E7 to construct speckle suppression device, and analyzed the effects of frequency and voltage on speckle suppression. The results show that the speckle contrast is reduced from 6.52% to 2.80%, which makes the human eye can not detect speckle.

Using selfassembly polystyrene microspheres monolayer template and pulse electrodeposition method, we assembled a twodimensional silica/gold spherical cavity microelectrode array, and used square wave pulse voltammetry method to test its performance. The results show that when the mass concentration of Pb(Ⅱ) is 0—100 μg/L, the response of the electrode and the ion mass concentration  is linear, the sensitivity of detection is 0.070 35 μA·L/μg (S/N=3), and a limit of detection (LOD) is 0.3 μg/L. The ability of the array to resist interference of Cu(Ⅱ) is stronger.

Based on density functional theory at the level of B3LYP/6-311+G(2df), we investigated the chiral transition process of the phenylalanine molecule under the cooperative action of monoH₂O. Further more, we drew a complete chiral transition path reaction potential energy surface of phenylalanine molecule  by searching for the extreme value point structures including 5 transition states and 4 intermediate, and analyzed the geometric and electronic structure properties of extreme value points. The results show that the H atom on the chiral C atom of Sphenylalanine molecule can transfer to the other side of the chiral C atom via the O atoms of carboxyl as a bridge under the cooperative action of monoH2O, to achieve the chiral transition of phenylalanine molecule from Stype to Rtype. On this path there is 4 intermediate and 5 transition states. The maximum reaction [JP+1]energy barrier is 200.588 2 kJ/mol, which comes from the fourth transition state TS₂-R-Phe&1H₂O-2.

We studied confined catalysis of the MOR molecular sieve 12ring pore on the chiral transition reaction of lysine molecule by using the combined quantum chemistry ONIOM methods. The results show that conformations of the objects which confined in the MOR molecular sieve 12ring pore are different from that in nude environment, the 1C—5N bond length of transition state a_TS2@MOR has been shortened and the distances of the intermediate SINT1
@MOR between 12H and 9O, 11H and 9O as well as 12H and 10O have also been shortened. There are three channels a,b and c in chiral transition reaction. The channel a is the dominant reaction channel of chiral transition reaction, and the Gibbs free energy barrier of the stepdetermining step is 229.7 kJ/mol, which is significantly lower than that of the Gibbs free energy barrier 252.6 kJ/mol, i.e., the MOR molecular sieve has a confined catalytic effect on the chiral transition reaction of lysine molecule.

We designed and synthesized a novel carbazolesubstituted symmetrical porphyrin derivatives, 5,10,15,20tetracarbazole porphyrins and their lanthanide acetylacetonate (Ln=Gd,Tb,Dy) complexes. We characterized the complexes by means of UVVis spectra, IR spectra, 1H NMR spectra, MS and molar conductances, and studied their fluorescence properties. Experimental results show that quantum yields of Q band fluorescence of rare earth metal porphyrin complexes are 0.007 79—0.158 at room temperature. This is due to the different property of the rare earth metal ions and difference in the intensity of the radiationless transition.

Using fluorescence staining of 4,6diamidino2phenylindole dihyodrochloride  and flow cytometry we studied protective effect of an artificial mimic 2tellurium bridged cyclodextrin (2-TeCD) with the activity of glutathione peroxidase (GPx) on UVBinduced damage in NIH3T3 cells. The results show that 2TeCD can affect DNA lysis rate, the level of lipid peroxidation, the volume fraction of ROS, cell cycle, P53 protein expression and other indicators in NIH3T3 cells caused by UVB. The 2TeCD can play a protective role against UVB damage by removing free radicals.

Using multilayer soft lithography technology, polydimethylsiloxane (PDMS) as the chip material, we made a novel microfluidic chip (60 mm×40 mm×4 mm) for single cell identification research. We enriched tumor stem cells in serumfree suspension culture of lung cancer cell A549 into single cell suspension.  RTPCR reaction liquid mixed into the chip, and cells were randomly distributed and reverse transcription PCR (RTPCR) in 2 048 micro chamber. The chip integrated in cell capture, separation, lysing and PCR reaction to achieve rapid identification of tumor stem cells. By counting the number of positive reaction, we could calculate the proportion of tumor stem cell in the total cells.

We studied the characteristics of phosphate solubilization of Pseudomonas aeruginosa JM1 and its immobilization of Pb in sediment via pure culture and simulated experiment. The results show that strain JM1 is capable of dissolving Ca₃(PO₄)₂ and AlPO₄ which leads to the mass concentrations of dissolved PO^3-₄ are 24063,9273 mg/L, and pH in culture solution decreases to 464,5 12, respectively. Meanwhile, strain JM1 can grow on lecithin but not the release phosphations. Strain JM1 makes the mass ratio of immobilized Pb in the  sterilized and without sterilized sediment increased to 1402,1183 mg/kg, which show that strain JM1 has strong ability to immobilize Pb in the sediment.

Using the  ²¹⁰Pb and ¹³⁷Cs dating technique combined with test results of polycyclic aromatic hydrocarbons (PAHs) in sediment cores on floodplain of Songhua River, we analyzed time trend of PAHs mass ratio in the past 90 years. Results show that the mass ratio of PAHs in sediment increases sharply from the 1960s to a peak in the early 1990s and subsequently decrease. The time trend of sedimentary PAHs in Songhua River is basically similar to that in Dianchi and some other urban lakes in China, but clearly different from that in developed countries. The results also show that the PAHs concentrations reach a relatively moderate level in the surface sediments compared with other domestic river sediments. The pollution characteristics of low ring compounds such as naphthalene, phenanthrene and so on are presented. According to the relative abundance of PAHs ring number and ratios of w(Ant)/w(Ant+Phe), w(Flt)/w(Flt+Pyr), the PAHs of sediment mainly comes from petroleum pollution. The stage change of mass ratio of PAHs is significantly correlated with the population and GDP in the watershed during the last 90 years, i.e. PAHs pollution of Songhua River is related to human activities.