By using the method of upper and lower solutions and the monotone iterative technique, we solved the initial value problem of a class of nonlinear fractional differential equations by establishing a new comparison principle, and obtained the result of the existence of extremal solutions of the initial problem.

We considered  the existence of travelling wave solutions of a class of space- time Whitham-Broer-Kaup (WBK) equations with modified RiemannLiouville fractional derivative. First, we turned the WBK equations into the ordinary differential equations, and then got analytical expressions of some travelling wave solutions of this equations by using the first integral method.

We considered a class of integral boundary value problems of RiemannLiouville fractional differential equations with parameters in the infinite interval. By using cone compression and cone expansion fixed point theorem, we established and proved the existence and nonexistence theorems of positive solutions for the boundary value problems in the infinite interval, and gave an application example.

Using the classical Uzawa method and modified Hermitian and SkewHermitian splitting (MHSS) iterative method, we proposed a new Uzawa-MHSS iterative method for solving a class of complex singular saddlepoint problems. We obtained the semiconvergence theroem of the new method, and analyzed its semiconvergence. Numerical experiments show that the new iterative method is more effective than the classical Uzawa method and MHSS method to solve the saddlepoint problems.

We used the homotopy method to solve the linear complementarity problem. By constructing a new homotopy equation for the linear complementarity problem corresponding to the R₀matrix, we gave a new condition for the existence of homotopy path. Under this condition, we proved the boundedness and convergence of the homotopy path, and obtained a condition for the existence of a solution of the linear complementarity problem.

We considered the generalized centrosymmetric solution (generalized anticentrosymmetric solution) of an inverse quadratic eigenvalue problem and its optimal approximation problem. By using the orthogonal projection methods of matrix, we gave the solution of matrix equation AX+BY+CZ=0and its optimal approximation problem. According to the properties of generalized centrosymmetric matrices (generalized anti-centrosymmetric matrices), we derived the conditions for the problem with a generalized centrosymmetric solution (generalized anticentrosymmetric solution) and the expression of general solution. We proved the existence and the uniqueness of solution of the optimal approximation problem, and obtained the expression of the optimal approximation solution.

We gave a new criterion for Htensors by constructing different positive diagonal matrices combined with scaling techniques of inequalities, and gave new practical criteria conditions for the positive definiteness of an evenorder real symmetric tensor, i.e., an evendegree homogeneous polynomials.

By using the timefrequency analysis method and the Plancherel theorem, the author obtained necessary conditions for wavelet and Gabor systems
 which could be made frames in Sobolev space, respectively. This generalized some results in L²(L) to Sobolev space, and enriched the related theory about the frames in Sobolev space.

By using the central limit theorem and the moment inequality of the moving average process, we obtained the precise asymptotics of complete moment convergence for partial sum of a class of φ-mixing moving average process.

We gave some equivalent characterizations for the (b,c)-inverse by using invertibility of certain elements in  a ring, and gave an expression for the (B,C)-inverse of a 2×2 matrix over a ring under certain conditions.

By giving sufficient conditions and necessary and sufficient conditions for the judgment of generalized positive definite matrix, the author studied HSS iterative algorithm for solving linear equations of generalized positive definite matrix, analyzed convergence of the algorithm and gave numerical experiments.

For common string matching problem in information processing, we analyzed the classical algorithms as Brute Force and KnuthMorrisPratt. According to the distribution characteristics of GPU heterogeneous parallel computing task, we designed a parallel scheme for data overlapping partition based on KnuthMorrisPratt algorithm, and proposed a heterogeneous parallel string matching algorithm KMP_MOP based on mobile platform. We tested the algorithm performance in PowerVR mobile platform by using strings with lengths of tens of millions. Also we compared execution of algorithm running on
other platforms, verifying the portability of the parallel algorithm. The experimental result indicates that the KMP_MOP algorithm can make full use of the GPU performance in mobile platform, and effectively improve the string matching efficiency of mobile platform devices with GPU.

Based on the features of gestures and regression algorithms, by improving the defects of the traditional 3D gesture cascading regression algorithm, we proposed a new operator of handstructure features based on the gestural variations. This operator efficiently reduced the dimension of handfeature operators. We adapted to the structural improvement of traditional cascading regression in terms of the changes of gestures, so that it significantly improved the recognition efficiency aiming at the handy structures. The experiments were carried out on the public databases and selfbuilt databases, and the experimental results indicates that the algorithm can successfully improve the execution efficiency while maintaining the accuracy of gesture recognition.

By modifying the data structure of arc consistency algorithm of Knapsacks constraints, we transformed the bitmap to a directed graph, which solved the problem of redundant computation and invalid operation in the arc consistency algorithm of the original knapsack constraint, and accelerated the algorithm to solve the problem of efficiency. Comparative experimental results show that in the face of the same kind of problem, the initialization time of the improved algorithm is increased because the data structure is more complex, but the solution time is improved by 20%—50%. The improved algorithm can reduce the time of solving the problem in the face of the high difficulty of solving the problem.

Using spherical projection model of fisheye image, we proposed a realtime correction method based on spherical projection. The method made the fisheye image map in 5 image plane, so as to solve the problem of serious distortion and poor visual effects for fisheye video. According to the layout of 2D image data allocations in memory, the space mapping calculation and memory management were optimized in the correction algorithm. The efficiency of the algorithm was improved and the memory consumption of the algorithm was reduced. The experimental results show that the method can significantly improve the visual effects of fisheye images, and the running time of single frame image is only 18.37 ms, which can satisfy the need of realtime fisheye video image correction.

We proposed a distributed K-Means clustering algorithm based on sampling under MapReduce framework, in order to solve the problems of high time cost of parallel execution of K-Means algorithm in the massive data environment. The algorithm used sampling algorithm to reduce the original data size on the premise of ensuring the invariant data distribution, and the clustering algorithm was optimized under the MapReduce framework. The experimental results demonstrate that the algorithm can effectively reduce the clustering time while maintaining good clustering effect, and it has high execution efficiency and good scalability for large scale datasets.

In order to reduce the computational complexity of image stitching method, we proposed a fast image stitching method based on scale invariant feature transform (SIFT) feature vector image. Firstly, the method combined the phase correlation algorithm to determine the overlapping regions of the images to be stitched, and the detection range of the SIFT feature points was defined. Then we considered the spatial location information of feature points,  constructed the SIFT feature vector images in order to limit the searching ranges in the feature matching, and got the matching points quickly. Experimental results show that the new method reduces a lot of unnecessary search, and improves the speed of image stitching.

We set up a simulation model of the unmanned surface vehicle in defending target. We first made digital and non\|dimensional processing of the target threat index, and then calculated the weighted correlation degree of each suspicious object. We used the grey correlation algorithm to sort multiple suspicious targets, and then determined the degree of threat about each suspicious target. Unmanned surface vehicle based on the degree of threat to intercept priority to solve the uncertainty of the threat degree of multiple suspicious targets in the simulation environment of the security target. The simulation results show that this method is more accurate than the traditional threat assessment method, and improves the reliability of the unmanned
surface vehicle defending the goal.

We calculated the enthalpies of γ′-Fe₄N doped by different transition metals M (M=Mn,Co,Ni) by using first principles density functional theory. The results show that the energy of MnFe₃N/Fe₂,CoFe₃N/Fe₂ and NiFe₃N/Fe₁ are the most stable structures, and all of them are ferromagnetic materials. The energy of the system decreases with the decrease of the atomic numbers of the doped transition metal elements, and the structures of the material are more stable. With the increase of pressure, the substitution of doped elements for facecentered non equivalent Fe positions can effectively reduce the effect of pressure on the magnetic properties of the material, the material maintains strong ferromagnetism in a larger pressure range, and the decay rate is relatively low.

We obtained the ground states geometry, dipole moment and total energy of C₈H₁₄O under different intense electric fields ranging from -0.008 0 to 0.002 5 based on the method of density functional theory DFT/B3P86, at the 6-311++G(2-df) basis set level. The calculation results show that the geometric configuration of the molecule affected by the electric field intensity. The dipole moment of the molecule first decreases and then increases with the increase of electric field intensity. The total energy of the molecule is -389.881 8 as F=0. The total energy of the molecule increases with the increase of the electric field intensity, the total energy of the molecule reaches the maximum -389.879 9 as F=0.002 5. The total energy of the system increases with the increase of the electric field intensity.

Using the theory of fractional calculus, we studied the problem of observer chaos synchronization of two kinds of fractional\|order systems. We gave the sufficient conditions for chaos synchronization of observer of masterslave systems of fractional-order system by designing appropriate observer and controller. Numerical simulations result show that the proposed method is effective.

ZnO thin films were deposited on SiO2 substrate by magnetron sputtering technique. The crystal structure, surface topography, band gap width and photoluminescence properties of the thin films were characterized by X-ray diffraction, atomic force microscope, UV\|Vis spectrophotometer and fluo
rescence spectrometer. The third\|order nonlinear optical properties of the thin films were measured by Z-scan method using femtosecond laser （wavelength of 800 nm, pulse width of 50 fs）. The results show that the third order nonlinear refractive index and nonlinear absorption coefficient of the film are all positive, the values are 3.50×10^-18 m²/W and 2.88×10^-11 m/W.

We designed onedimensional photonic crystal with a complex refractive index defects layer and calculated the transmissivity of light waves by using the quantum transfer matrix. The results show that the number of defect modes increases with the increase of the thickness of the defect layer and the positions of the defect mode move towards the direction of the smaller wavelength as the thickness of the conventional medium increases.

Using density functional theory B3LYP, the author investigated the chiral transition process of the asparagine molecule under the complex condition of double water at the level of 6-311+G(2-df). The author drawed a complete asparagine molecule chiral transition path reaction potential energy surface by finding structures of the extreme value points including the transition states and intermediates, and analyzed the geometric and electronic structure properties of extreme value points. The results show that the hydrogen atom on the chiral carbon atom of Sasparagine molecule can transfer to the other side of the carbon atom via the oxygen atoms of carboxyl atoms as abridge, and achieve the chiral transition of asparagine molecule from Stype to Rtype. On this path there are four intermediates and five transition states. The maximum reaction energy barrier is 317.948 1 kJ/mol, which comes from the fourth transition state TS₂-R-Asn&2H₂O₁.

A new porous cobalt compound ［Co(L)_1.5(BDC)(H₂O)₃]_n(1) (L=N,N′-bis(3-pyridyl)adipamide, H₂BDC=1,2benzenedicarboxylic acid) was prepared by the selfassembly process of hydrothermal synthesis by selecting the mixed ligands of the flexible bis(pyridyl)bis(amide) L and the aromatic dicarboxylate H₂BDC. The crystal structure of the compound was characterized by the element analysis, IR and the single crystal Xray diffraction technique. Experimental results show that the compound belongs to   triclinic system, P1 space group, a=1.097 87(10) nm, b=1.213 82(11) nm,c=1.429 40(13) nm, α=72.788(2)°, β=75.235(2)°, γ=72.127(2)°, V=1.703 3(3) nm³, M_r=575.43, Z=2, Dcal=1122 g/cm³, μ=
0.549 mm^-1, F(000)=598, S=1.064, R₁=0.054 3, ωR₂=0.151 8. The metal cobalt ions are bridged by the bidentate L ligands to form a onedimensional ［Co(L)_1.5］²ⁿ⁺_n chain structrue, and the carboxylate ligand BDC is suspended on both sides of this chain with a monodentated coordination mode.
A threedimensional supramolecular porous network with large pore structure is expanded by the hydrogenbonding interactions among onedimensional chains. This porous cobalt compound shows the remarkable photocatalytic degradation ability to the organic dye molecules methylene blue or congo red under the UV light.

A 76mer seleniumcontaining peptide (SeCuZn76P) with double glutathione peroxidase (GPx) and superoxide dismutase (SOD) activity, which was embedded in a sequence of membranepenetrating domain, was designed according to the principles of module enzyme, and was expressed by the method of cysteine auxotrophic expression in a single protein production (SPP) system, then the cellpenetrating effects of Se-CuZn-76P were identified. Experimental results show that the method can successfully express the high purity of SeCuZn76P, and demonstrate GPx activity (109 μmol/min) and SOD activity (1 218 μmol/min) per mg of protein. The GPx activity and the SOD activity in hepatic L02 cells are increased by 1.65 and 4.12 times respectively, when L02 cells are cultured for a period of time in the presence of SeCuZn76P, and SeCuZn76P can be successfully entered into L02 cells.

By using the method of light irradiation in the biofilm system, we investigated three kinds of bioactivity inhibitors with different inhibitory effect on generation of H₂O₂ and degradation of typical organic pollutants of sodium dodecyl benzene sulfonate (SDBS) in natural biofilm/water simulation systems. The results show that inhibitors of photosynthesis and respiration have a significant inhibitory effect on the generation of H₂O₂ and degradation of SDBS, and the inhibitory effects of both of them are almost the same. The photo expiration inhibitor has little or no effect on the generation of H₂O₂ and degradation of SDBS. Therefore, the biological photosynthesis is the main reason for the generation of H₂O₂ and other reactive oxygen species, as well as the degradation of organic pollutants. Whereas, the contribution of other physiological role is relatively small.

By using the balance method, we investigated the effects on the adsorption\|desorption characteristics of phosphorus in black soil with the biochars from different addition mass fraction  and different sources (corn stalk, husk, pine). The results show that with the increase of the addition mass fraction of biochars, the amount of phosphorus adsorption in the black soil increase first and then decrease. When the mass fraction of 1.2% is added, the phosphorus adsorption capacity of black soil is maximum. The  adsorption capacity of different biochars on phosphorus in black soil is as follows: pine>corn stalk>husk. The black soil mixed with pine biochar on phosphorus adsorption capacity is the largest, which value is 0.697 mg/g. Phosphorus adsorption and desorption capacity is increased with mass concentration of phosphorus solution increased, but the rate of increase is gradually smaller. The isothermal adsorption curve of phosphorus in block soil conforms to the Langmuir adsorption equation.