Using the fixed point theorems of increasing operator and the fixed point theorem of cone expansion and cone compression, we studied the positive solutions of a class of  multi-order fractional differential equations, and obtained the existence of positive solutions of the equations.

Using the  fixed point theorem of cone expansion and cone compression, we investigated threepoint boundary value problem for a class   of RiemannLiouville fractional differential equation with two disturbance parameters. We established and proved the  existence theorem and nonexistence theorem of positive solutions of the problem. The results show the  parameters affect the existence of positive solutions.

Using the calculus theory on time scales and the Riccati transformation and the inequality technique, we studied the oscillation for a class of secondorder nonlinear neutral variable delay damped EmdenFowler functional dynamic equations on time scales, and established some new oscillation criteria for the equations.

We considered a class of nonlinear fractional differential equations with infinitepoint integral boundary conditions. By calculating the Green’s function, we transformed the differential equation into integral equation. On the basis of analysis of the properties of Green’s function, we used the indexed fixed point theorem to obtain the existence and multiplicity of solutions of the boundary value problem.

We discussed the integral expression of a kind of generalized hypermonogenic function vector in Clifford analysis by using the properties of some Cauchytype singular integral operators. Then  we proved the solvability of the nonlinear boundary value problem for the kind of generalized hypermonogenic function vector by using the Schauder fixed point theorem, and gave the expression of the solution.

We considered TD soliton hierarchy. Firstly, based on a Loop super Lie algebra and super identity, the super TD soliton hierarchy was constructed on the basis of the equivalence of the TD spectral problem, and the super Hamiltonian structure was obtained. Secondly, the super TD soliton hierarchy with selfconsistent sources was constructed. Finally, the infinite conservation laws for the super TD soliton hierarchy were obtained by introducing two variables F and G.

By using an isotropic Homideal J of Hom-Jordan Lie algebra L, we obtained that L contained a maximally isotropic Homideal I of J, then L was isometric to a T*extension of L/I or a nondegenerate  Homideal of codimension 1 in a T*extension of L/I, moreover, we gave structure characteristics of Hom-Jordan Lie algebra L
.

The author considered the Bousfield equivalence relationship of the stable module category for a finite group, and proved that, if H was a strongly pembedded subgroup of G, then two finitely generated indecomposable kGmodules(kHmodules) were Bousfield equivalent if and only if their Green correspondents were Bousfield equivalent, in addition, Green correspondence induced a onetoone correspondence between Bousfield equivalence classes of Stmod(kG) and those of Stmod(kH).

By introducing assistant set into function Psets to expand the function P\|sets, we gave the concept and construction of function P(σ,τ)sets, and obtained the generation theorems, dynamic change theorems depending on attributes and threshold value, identification theorems  for function P(σ,τ)sets.

We described bounded derived category D^b(A ) of Abel category Avia precovering class and gave the corresponding applications. The results show that the bounded derived category of the module category can be described by the Gorenstein flat modules and the cotorsion pairs.

We defined a class of Finsler metrics which could be expressed by a Euclidean metrics and two 1forms. By using dually flat equations, we obtained the equivalent condition for those Finsler metrics to be dually flat, and obtained a solution satisfying the dually flat equivalent condition.

The parallel lattice Boltzmann algorithm was used to calculate the flow around twodimensional square cylinder, cylinder, and NACA0012 airfoil. We obtained the flow results at different Reynolds numbers and different time steps. The calculation results show that the parallel algorithm can increase the computational region of flow field.

Based on the properties of Hardy operators and BMO functions, together with the definition of HerzMorrey spaces with variable exponent, and by using the Hlder inequalities, we established the boundedness of the higher order commutators generated by fractional Hardy operators with variable index and BMO functions on the HerzMorrey spaces with variable exponent. The result generalized the boundedness of the higher order commutators of the classical fractional Hardy operators to the higher order commutators of fractional Hardy operators with variable index. When the variable exponent β(x) was a constant, the fractional Hardy operators  were the classical fractional Hardy operators.

Aiming at the problem of low matching rate of traditional feature matching algorithms, we proposed an improved algorithm based on enhanced image gradient information for scaleinvariant feature transform （SIFT） feature matching algorithm. Firstly, a gradient image was obtained by proper gradient operator. Secondly, the gradient image and the original image were fused with the specific weight, and after normalization, the fused image was blurred by Gauss. Finally, the traditional algorithm was used for feature extraction. Experimental results show that the visual angle and invariability of rotation of the i
mproved algorithm are obviously better than those of the original algorithm, and the matching rate of the images with larger brightness or noise is also slightly improved, which effectively improves the accuracy of the SIFT feature matching algorithm.

We used two types of depth textures called dynamic depth texture and static depth texture to improve traditional shadow mapping method. When rendering complex scenes, the static depth texture was applied to the static objects, and the dynamic depth texture was applied to the moving objects. The minimum value of two depth textures was compared with the current depth when calculated shadows. The method required real\|time monitoring of the motion and static states of the objects in the rendering process, and recording depth information of different states of objects into different kinds of depth textures. The experimental results show that this method improves the rendering speed obviously in a complex scene, thus improving the fluency of virtual reality scene rendering.

The improved artificial colony optimization algorithm was used to solve the combinatorial optimization problem of parameters and features in density clustering anomaly intrusion detection. Firstly, the parameters and characteristic values were encoded by the different encoding methods in the initial honey source stage. Secondly, two search strategies were used to search the parameters and characteristic values in the neighborhood search stage. Finally, in order to satisfy the requirement of low false positive rate for anomaly intrusion detection, an influence factor of false positive rate was added into the new fitness function. The experimental results show that the improved algorithm not only improves the accuracy of normal behavior profiles, but also reduces the computational cost and storage space. It can eliminate the noise characteristic interference to some extent and improve the detection performance.

The author proposed a bearing fault detection algorithm based on Morlet wavelet and multimode kernel optimized by genetic algorithm. Firstly, the algorithm extracted the characteristics of Morlet wavelet transform under conditions of multiscale and multiple displacement for the fault signal of original
 bearing. Secondly, the author designed a multimode kernel method, including linear kernel and radical basis function (RBF) kernel. Finally, the genetic algorithm (GA) was used to optimize parameters of multimode kernel in the support vector machine (SVM) training process, and the  optimizing multimode kernel for bearing fault detection was carried out. The ball fault, inner ring crack fault and outer ring crack fault were tested on the data set of UoCn intelligent maintenance center, and the error rate and efficiency of singlemode kernel and multimode kernel were compared. The experimental results show that the improved algorithm can get the robust features for bearing fault detection, and the multimode kernel can converge quickly and get optimal results under the optimization of GA, the accuracy of bearing fault detection is greatly improved by sacrificing a small amount of time efficiency.

Aiming at the problem that  the streaming data were constantly changing, fast and potentially unlimited features, and it was more difficult to protect than static data privacy. Based on streaming data, we proposed a new data information anonymous algorithm to solve the problem of sensitive value and its sensitivity level  changing with data transformation. It could  effectively prevent  anonymous streaming data from being  linked attacks, similarity attacks and threat attack  based on sensitive classification. The  results of simulation experiment show that the new data anonymous model can effectively protect the anonymous information of the data.

By improved SinglePass incremental text clustering algorithm, we organized news information with granularity of topics, and achieved the discovery of network news topics. Considering the dynamic and time characteristics of news, the position information of terms in the headlines and texts and the frequency of incremental documents of terms in the feature terms weight calculation were optimized, meanwhile, time factor was added in similarity calculation and the topics centroid vectors were updated dynamically in clustering. Through the topicbased Web crawler to construct news corpus as the test data set, the experimental results show that, compared with  the traditional algorithm, the improved algorithm reduces the cost and fallout ratio by 0.34% and 1.57% respectively, which verify the validity and accuracy of the improved algorithm.

Aiming at the problem that the accuracy of credit risk evaluation of supply chain finance mode was affected by credit feature subset and model parameters, we proposed a credit risk evaluation model with particle swarm cooperative optimization. On the basis of fully demonstrating the characteristic index system of supply chain financial risk, we used the binary particle swarm algorithm to optimize the feature subset and optimize parameters of support vector machines. We carried out an experiment on the risk evaluation of supply chain financial credit, and compared it with traditional radial basis support vector machines and feature extraction method of principal component analysis.  The results show that the selected feature subset and SVM parameters of the proposed model can significantly improve the accuracy of credit risk evaluation.

Aiming at the shortcomings of current bank card number recognition algorithm, we proposed an improved feature matching algorithm based on pattern recognition technique, and applied it to bank card number recognition. The improved feature extraction algorithm transformed feature vectors and increased the number of feature learnings,  solved the problem of traditional method identifying bank card number with low accuracy, and ensured the recognition efficiency. Simulation experimental results show that the improved feature extraction algorithm can effectively improve the correct rate of bank card number recognition.

Using the method of density functional B3LYP, we optimized ground state stable geometries of the gas phase cysteine (Cys) molecules and charged ions at the level of the 6-311++G(-d,p-) basis set. At the same time, the method of time dependent density functional theory (TD-DFT) was used to study the
low excited state properties of the gas phase Cys molecules and ions. The results show that the energy of the system increases gradually, the difference between S1 excited state energy and ground state energy decreases, molecular fluorescence wavelength increases from 239.35 nm to 1 895.82 nm, and the number of electronic transition orbit of S7 excited state decreases with the increases of the number of electrons obtained by molecules.

The author obtained the ground states geometry of C₈H₁₄O molecule 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 author studied the effect of the same electric field intensities on the excitation energies and oscillator strengths of the optimized C₈H₁₄O molecule by using the timedependent density functional theory (TD-DFT) method. The calculation results show that the molecular geometry is influenced by the electric field intensity. The excitation energies decrease as the increase of the electric field intensity, indicating that the C₈H₁₄O molecule is easy to be dissociated and excited under the action of electric field intensity.

Using the WKB approximation and paraxial model, we investigated the effect of electron temperature on interaction of 527 nm intense laser and plasmas. The results show that, the electron temperature presents an oscillation variation, and dielectric constant also presents an oscillation variation and leads to laser width presents steady separation, oscillation separation and selffocusing in plasmas.

A Hamiltonian of threemode system was derived based on secondorder nonlinearity. Using this Hamiltonian and conventional nonHermitian Hamiltonian method, we obtained the optimal analytical conditions for unconventional photon blockade under the condition of dual mode drive. And then, by solving the steady state solution of the master equation and secondorder correlation function, we obtained the numerical solution for unconventional photon blockade.

The complexity of radix4 algorithm was reduced by optimizing the traditional radix-4 fast Fourier transform (FFT) algorithm, which retained the butterfly structure of radix-2 algorithm. The optimized mixed radix-4/2 and pipeline radix-2² singlepath delay feedback (R2²SDF) structure were adopted to design the variable points FFT processor, and the output results were verified by the function and signal simulation. The results show that the FFT processor is excellent in validity and efficiency.

The author studied the mechanism of Cucatalyzed three\|component decarboxylative coupling reaction of glyoxylic acid, an amine and an alkyne by using the density functional theory methods. First, the reaction  mechanism proposed in experiments was calculated, and then a new reaction mechanism was proposed and calculated involving the coordination of the iminium salt, in situ formed from the glyoxylic acid and the amine, decarboxylation, alkyne coordination and insertion, protonation, nucleophilic addition, ligand exchange steps. The results of theoretical calculation show that the ratedetermining step of the mechanism is the insertion of the alkyne, and the energy barrier of reaction is 129.8 kJ/mol, which is in agreement with the result of experimental reaction temperature of 110 ℃.

We synthesized visible light catalyst Ag₃PO₄ under different temperatures in the hydrothermal reaction system. It was characterized by Xray diffraction (XRD), scanning electron microscopy (SEM) and Fourier transform infrared spectrum (FTIR), and the photodegradation experiments were carried out. The results show that with the increase of the hydrothermal reaction temperature, the partical size of Ag₃PO₄  increases gradually, and the morphology tends to rule; when the temperature is 110 ℃, a small amount of Ag₃PO₄ primitives are found on the surface of the photocatalyst Ag₃PO₄ , and the surface primitives increase with the increase of temperature; efficiency of Ag₃PO₄ degradation of  cationic dye—rhodamine B (RhB) is higher than that of degrading anionicdye—methyl orange (MO); the degradation rate of 180-APO is the highest after 20 min exposure to visible light, and the degradation rates of MO and RhB are 96.45% and 99.73%, respectively; the hole positive ions h⁺ and superoxide anion ·O^-₂ are the main active groups in the catalytic system.

We synthesized poly(methyl acrylate) by the method of single electron transfer living radical polymerization (SETLRP) and the method of atom transfer radical polymerization (ATRP). The properties of products were detected by ¹H-NMR, FT-IR and Ubbelohde viscometer. The results show that the molecular structure of the products synthesized by the two methods is similar, and the specific viscosity of the final product has little difference; in the same reaction time, the monomer conversion rate of SET-LRP method is much higher than that of ATRP method, and the SET-LRP reaction process  accords with the firstorder reaction kinetics.

Using the fermentation broth of the endophytic fungus FSN002 as material, we studied the adsorption process of resins in static test, and established dynamic model of adsorption of resins. The effect of varieties of resins on characteristics of adsorption and desorption were investigated through
the model analysis. The results show that the adsorption of resins to catalitaxol fits firstorder dynamic model, and the average maximum adsorption capacity of reversedphase resins is 3939 mg/mL, 138 times of ionexchange resins.  However, it is difficult to elute the catalitaxol after being adsorbed by the reversedphase resins, and the average elution rate is 122%. While the average elution rate of ion exchange resins is 466%,
and the elution rate of catalitaxol under the anionexchange resin D201 is the highest, which can reach 830%. The adsorption rate is faster, and the comprehensive performance is the best.

We investigated the effect of field decay biochar on the stability of phytoplankton community in the simulated wetland system of Iris wilsonii. Experimental results show that the biochar can maintain the stability of ketone in the simulated wetland system by adsorptiondesorption when the mass ratio of biochar is 5 g/kg in wetland matrix. The stability can make the phytoplankton community under a relatively stable intensity of allelochemical stress, which make the small succession of the community normal.