We considered a class of nonlinear fractional differential equations with integral terms, and the corresponding Green’s function of equations was obtained by computing. We used the increasing operator fixed point theorem and the method of upper and lower solutions to prove the existence and uniqueness of extremal solutions of the equation, and gave the display iterative format of the approximate extremal solutions.

We considered the periodic solutions for second order nonautonomous differential system with partially periodic potential and sublinear nonlinearity. Some sufficient conditions for the existence of multiple periodic solutions are obtained by using critical point theory.

In this paper, we obtained a geometric inequality for doubly warped product submanifolds in a Riemannian manifold of nearly quasiconstant curvature by using algebraic lemma and fundamental equations. We also established an inequality involving Ricci curvature and mean curvature, and discussed the equality conditions of the inequalities.

The topologically conjugate classifications for holomorphic automorphisms on unit disk and upper half plane were considered. By rotation theory and some constructions of homeomorphisms, we prove that all holomorphic automorphisms on upper half plane without fixed points are topologically conjugate; two holomorphic automorphisms f and g with fixed points are topologically conjugate if and only if ρ(f)=±ρ(g), mod Z; a holomorphic
automorphisms without fixed points and a holomorphic automorphisms with fixed points on upper half plane are not topologically conjugate.

By giving definition of Hom \%δ\%\|Jordan Lie color algebra, we studied  its algebraic structure and Hom\|Nijienhuis operator. The results show that a Hom-Nijienhuis operator and a bilinear operator can get a deformation of the regular Hom δ-Jordan Lie color algebra under appropriate conditions. Furthermore, this deformation is trivial.

Using the strictly generalized Kato decomposition property of operator, we investigated the stability of the single valued extension property of the operator and the Weyl type theorem under compact perturbations. In addition, we also discussed the relation between the Weyl type theorem and the single valued extension property under compact perturbation. Then we obtained the sufficient and necessary conditions for the equivalence of the perturbation of Weyl type theorem and single valued extension property.

We considered the problem of parameter identification of the fractal interpolation functions (FIFs) with function vertical scaling factors in the restricted domain, and gave some of sufficient conditions that function vertical scaling factors should be satisfied, so that the corresponding FIFs were restricted to a given range. Furthermore, we gave some numerical examples to illustrate the relationship between the graphs of the FIFs and the variable parameters in the restricted domain.

The author proposed an optimal perfectly matched layer (PML) method with a small parameter ε₀ for solving scattering problem in twolayered media. By introducing a small parameter ε₀ in the absorption function, the calculation of the scattering problem to optimize the PML method did not depend on the thickness δ of the PML layer. The results show that the numerical solution converges exponentially to the original problem as long as the parameter ε₀ is sufficiently small.

We considered the ε-strict efficiency of setvalued optimization in Hausdorff locally convex topological linear spaces. When ordered pair mapping consisting of the object function and constrained function was near conesubconvexlikeness, under the assumption of weaker constraint qualification, with the help of separated theorem of convex sets, we obtained Lagrangian type optimality conditions for ε-strictly efficient solutions of setvalued optimization.

We gave an iterative scheme for the numerical solution of butterfly option price by the implicit difference method, and proved the stability of numerical approximate iterative scheme.

Using the bifractional jumpdiffusion stochastic analysis theory and the actuarial approach, we set up the financial market model in bifractional jump-diffusion process and gave pricing formula of the minimum or maximum option in bifractional jumpdiffusion process.

We proposed a weighted composite quantile regression method based on empirical likelihood in linear model with some covariates missing at random, and proved the large sample properties of the proposed method under the missing at random mechanism. The results show that the proposed method is computationally simple and the estimation efficiency of the regression parameters is higher than that of the inverse probability weighted method.

By using the weak convergence theorem and the moment inequality of nonstationary martingale difference sequence, we obtained a general form of precise asymptotics in complete moment convergence for sums of movingaverage process for more general boundary function and quasi weight function.

By using the theory of α-chain diagonally dominant matrices and some techniques for Hlder inequalities, we obtained some new criteria for nonsingular H-matrices, and thus the corresponding results improved and generalized the existing determination methods for H-matrices. The validity and superiority of the determination methods were illustrated by numerical examples.

By using the method of combinatorial analysis, we considered the vertex strongly distinguishing total coloring schemes of complete bipartite graph K_6,8, and gave a feasible coloring scheme. The results show that the vertex strongly distinguishing total chromatic number of complete bipartite graph K_6,8 is equal to ten.

We considered representations for Drazin inverses of the sum of two matrices,  under the condition of A^DB=0, AB^D=0, B^πABAA^π=0, B^πAB²A^π=0 for the n order matrix [WTHX]A[WT] and B. We gave representations for Drazin inverses of A+B by using the corenilpotent decomposition of matrices.

Let {X_n, n≥1} be a sequence of i.i.d. positive square integrable random variables with continuous and independent medium tail distribution function. For a fixed constant a>0, T_n(a)=S_n-S_n(a) denoted the trimmed sum, we proved the almost sure central limit theorem for the product of trimmed sums under the general weight by using the limit properties of the trimmed sums and the law of large numbers.

We obtained a new Jacobi elliptic function periodic solutions of generalized Zakharov equations by using improved Jacobi elliptic function method. The results show that some of these solutions can be degenerated into the corresponding soliton solutions and triangular function solutions in the limit cases. This method can also be used to solve the exact travelling wave solutions of other nonlinear equations.

We proposed an operation sharing optimization algorithm based on the location aware according to the data flow in large scale, and the basic data processing operations had overlapping features. We assumed that the operations had assigned the resources of compute nodes in advance, in guaranteed the stream processing realtime and dynamic state, to take advantage of the similarity between topologies and operational functions of multiple stream data operations. We established an operation sharing revenue optimized model based on the DAG matching method on the constraint of output bandwidth. This method tackled the insufficiency consideration of traditional operation for operation sharing method to the cluster of output bandwidth. Simulation experiment results show that this method has fuller consideration in the calculation of the node constraints and improves the benefits of sharing, thereby saving the computing resources of the system effectively.

Aiming at the problem of vehicle tracking in real scene, we proposed an improved particle filter for vehicle tracking algorithm. By using the framework of immune resampling, it reduced particle degeneracy and ensured the effectiveness of particle filter. Meanwhile, a memory base was established which refers to the idea of artificial immune algorithm, so that the algorithm could track targets for a long time. The background weights histogram and subblock identification mechanisms were used to reduce occlusions which caused by offtracking. Moreover, the adaptive learning parameters were added to the movement model and antibody mutation, which could improve the robustness of the algorithm. The experimental results show the algorithm has ability of stable tracking under the different conditions of illumination change, sudden movement or target occlusion, which verifies the validity of the proposed algorithm.

To minimize and balance the energy consumption in the process of data transferring in wireless sensor network (WSN), we proposed a data gathering algorithm based on topology (DGAT) by dynamically constructing minimum spanning tree with communication energy consumption as the weight and a
djusting node communication probability. DGAT changed the mode of communication and energy consumption of nodes in the network service process. Simulation results show that DGAT algorithm not only greatly improves the network lifetime, but also makes the network energy consumption more balanced.

Aiming at the problem of content authentication for Chinese text document, combined with the characteristics of Chinese characters, we proposed an authentication scheme of text zerowatermarking based on structure knowledge of Chinese characters. In this scheme, the authentication information was embedded in the constructed binary pattern, but not in the host itself, so it was applicable to short or long text documents simultaneously. The certification process did not need to participate in the third party, the scheme was practical. The binary pattern was constructed by using the structure knowledge of Chinese characters and chaotic encrypting algorithm in the process of watermarking construction and text authentication, and the security of this scheme was better.

In order to find the best cloud computing task scheduling scheme and shorten task completion time of cloud computation, by a comprehensive consideration of advantages of genetic algorithm and ant colony algorithm, we proposed a new cloud computing task scheduling and optimization algorithm based on genetic algorithm and ant colony algorithm. Firstly, genetic algorithm was used to search feasible scheme of cloud computing task scheduling. Secondly, feasible scheme was used to initialize pheromone distribution of ant colony algorithm, to solve problem of lack initial pheromone, to speed up convergence speed and search ability, and to improve the efficiency of cloud computing tasks. Finally the experimental results on CloudSim platform show that compared with genetic algorithm. The proposed algorithm is more suitable for solving the problem of largescale cloud computing tasks, which shortens task scheduling time, and user satisfaction is higher.

Aiming at the problem that non marking software metric metadata was easy to fall into the local optimum of the K-means process in the spectral clustering algorithm, we proposed a new algorithm of chaotic immune clustering algorithm. Under the framework of the immune clonal selection algorithm, the method of antibody affinity calculation was designed for the evaluation of immune clonal clustering center, and the hierarchical chaotic mutation operator was given, which further improved  prediction performance of non marking software metric metadata. Simulation results show that the algorithm is effective.

Aiming at the problem of multimodality images fusion, we proposed an image fusion method based on boundconstrained optimal projection gradient for nonnegative matrix factorization (NMF) in translation invariance nonseparable shearlet transform (TINST) domain. The problem of low fusion accuracy in some existing typical fusion methods was solved effectively. Images were decomposed to some subbands by translation invariance nonseparable shearlet transform. The lowfrequency subband coefficients were regarded as original observed data, and the lowfrequency subband coefficients were obtained by boundconstrained optimal projection gradient for NMF algorithm. Highfrequency directional suband coefficients were used as external input excitation and edge intensity was served as linking strength of each neuron in pulse coupled neural networks (PCNN) and after the fire processing and compareselection computing, fused highfrequency directional suband coefficients were obtained. Finally, all the fused subbands were reconstructed to an image by translation invariance nonseparable shearlet inverse transform. In order to verify the efficiency of the proposed method, some compared fusion experiments were implemented on several sets of different modality images. Subjective and objective evaluation on fused image indicates that the proposed method is better than a few existing typical fusion techniques based on multiscale decomposition (MSD).

In order to distinguish different kinds of heart sound signals accurately and obtain better recognition effect, we proposed a heart sound signal recognition model based on Gauss mixture model. Firstly, wavelet transform was used to denoise original heart sound signal, [JP+1]and the interference of noise to feature extraction of heart sound signal was eliminated. Secondly, heart sound signal was extracted while model of classification and recognition of heart
sound signal was constructed by using Gauss model. Finally, the performance of the model was verified by using heart sound signal data. The results show that the average recognition rate of heart sound signal for the proposed model is more than 95%, and recognition result of heart sound signal is superior to other models.

Aiming at the problem that the current active contour model was sensitive to noise, and it was difficult to realize accurate segmentation for weak boundary image, we proposed a new active contour model based on gradient vector flow. Firstly, contourlet transform was used to denoise image, and interference of noise to image segmentation was solved. Secondly, an instruction function was introduced to active contour model, which was used to describe the relationship between the vector field and the contour curve, and image was segmented by contour curve evolution. Finally, experiments were carried out to verify the performance of the proposed image segmentation model. Experimental results show that the proposed method can achieve fast and accurate segmentation for many kinds  of images, and segmentation accuracy and anti noise ability are better than other active contour models.

Aiming at the problem of optimal deployment of nodes in three dimensional sensor networks, we proposed a deployment strategy for the target point on a three dimensional curved surfaces. The proposed algorithm improved the deployment efficiency of the network nodes by using differential evolution (DE) algorithm to optimize the position coordinates of sensor nodes. The algorithm used the least sensor nodes to achieve the full coverage of the target point on the curved surfaces, and solved the problem of three dimensional perception blind spot in the process of monitoring target of sensor nodes in three dimensional space. The simulation experiments verify the feasibility of DE algorithm in solving the coverage problem of three dimensional space. It shows that DE algorithm has a certain degree of fault tolerance and can effectively improve the deployment efficiency of network nodes.

In order to improve utilization ratio of virtual machine resource scheduling, and to realize reasonable scheduling of virtual machine resource, we proposed a method based on cat swarm optimization algorithm for virtual machine resource scheduling optimization. Firstly, mathematical model was built according to the virtual machine resource scheduling optimization objective. Secondly, considering the shortest time and optimal load, the fitness function of cat swarm optimization algorithm was constructed, and the optimization of the optimal scheme of virtual machine resource scheduling was realized by simulating the daily behavior of the cat. Finally, the effectiveness of the proposed algorithm was tested on CloudSim platform. Test results show that the proposed algorithm can obtain a better virtual machine resource scheduling scheme, which can ensure load balance of virtual machine resource, and  meet the user’s preferences.

Aiming at the problem of  thyroid nodule segmentation of ultrasound images, we proposed the new segmentation algorithm combining kernel fuzzy Cmeans (KFCM) clustering with    improved distance regularized level set evdution (DRLSE) model. The algorithm solved the problem that the DRLSE model was sensitive to initial contour, and the evolution parameters needed to be manually set, and the ability of segmentation for weak edges was poor. Firstly, the KFCM clustering algorithm was used to segment the nodule region coarsely which was regarded as the initial evolution contour after binaryzation. Secondly, the evolution parameters of the level set were calculated automatically using the region surrounded by the initial evolution outline. Finally,  the region of thyroid nodules was segmented by Gaussian regularization rule evolution level set. Comparative experimental results show that the proposed algorithm can improve segmentation accuracy of thyroid nodules, and the nodule area can be segmented accurately even in the presence of noise.

We studied the problem of finitetime chaos synchronization control of a class of threeorder multiscroll systems based on sliding mode control method. We gave the sufficient conditions for quick synchronization of errors systems based on Lyapunov stability theory. Simulation results show that the proposed method is feasible.

Using density functional B3P86 and timedependent density functional theory (TDDFT) methods, the author calculated the excitation energy, wavelengths and oscillator strength of C₁₀H₁₄N₂ from ground state to tenth excited states at basis sets 6311++G(2df) level, and studied effect of external electric fields on the excited states of C₁₀H₁₄N₂. The results show that the HOMOLUMO gaps become smaller, and the excitation energies of the excited states of C₁₀H₁₄N₂ decrease sharply as the external electric field intensity become strong. So the C₁₀H₁₄N₂ molecules are easily excited and dissociated under the action of external electric field.

With polyvinyl alcohol (PVA) and acrylamide (AM) as raw material, PVA/PAM hybrid doublenetwork hydrogel was synthesized by onepot twostep polymerization method combined UV irradiation and freezingthawing technology. We tested and analyzed the mechanical property, swelling property, water loss property and selfhealing property of hydrogels. The results show that PVA/PAM hybrid doublenetwork hydrogel has high mechanical strength, its tensile strength is 428 kPa, the water loss rate is slower than the single network hydrogel. The hybrid doublenetwork hydrogel possesses selfhealing property.

Using B3LYP methods of density functional theory, we investigated the chiral transition process of nonrestricted area monomer isoleucine molecule
at the 6-311+G(-2df-) basis set level. A complete chiral transition path reaction potential energy surface was drawn by looking for the extreme value point structures including the transition state and intermediate, and the geometry and electronic structure properties of extreme value points were also analyzed. The results show that the H atom on the chiral C  atom of Sisoleucine molecule can transfer to the other side of the C atom via the O atoms of carboxyl atoms as a bridge, to achieve the chiral transition of isoleucine molecule from Stype to Rtype. There are four intermediates and five transition states on this path under the condition of nonrestricted area. The biggest reaction energy barrier is 325.824 6 kJ/mol derived from the second transition state TS₂-S-Ile.

We studied the chiral transition mechanism of lysine molecules and the catalysis of water molecules and hydroxyl radicals on the hydrogen transfer reaction based on amino as proton transfer bridge by using the B3LYP methods of density functional theory and the MP2 methods of perturbation theory. The results show that there are two channels a, b in the chiral transition reaction of lysine. The channel a is the dominant reaction channel, where the Gibbs free energy barrier of naked reaction of rate determining step is 252.6 kJ/mol. Besides, the chain composed of two water molecules and the chain composed of
 hydroxyl radicals and water molecules have a better catalysis in hydrogen migration, which make the free energy barrier be reduced to 1195 kJ/mol and 98.5 kJ/mol respectively. So the water molecules and hydroxyl radicals have good catalysis on the hydrogen transfer in lysine molecules and  this is the main reasons of leading to the heterogeneous of Llysine that there is hydroxyl radical in life body.

We studied the catalytic synthesis of isoamyl butyrate and isoamyl propionate by using the selfmade bis(1pyridine) butylidene double bissulfate (［Py-HSO₄］₂). The esters were characterized by FTIR and refractive index measurement. We determined the optimum reaction conditions for synthesis of esters by changing n(acid)∶n(alcohol), the amount of catalyst and reaction time, investigated the reuse performance of ionic liquid, and discussed the different reasons both of the esterification rate by quantum chemistry calculation and thermodynamic theories. The results show that the esterification rates of isoamyl butyrate and isoamyl propionate are 9594% and 9578% under the optimum conditions of esterification, respectively.

A polyimide containing fluorene group was prepared by 9,9-bis(3-fluoro-4-aminophenyl) fluorene and 4,4′(hexafluoroisopropylidene) diphthalic anhydride as a monomer. The structure of polyimide was characterized by Fourier transform infrared spectoscopy (FTIR) and nuclear magnetic resonance hydrogen spectrum (¹H NMR). Experimental results show that the structure of FFDA-6FDA is the same as the expected results, and the imidization reaction between monomers is conducted completely. FFDA-6FDA has good solubility in most common organic solvents at room temperature. FFDA6FDA has high thermal performance: its glass transition temperature is 370 ℃, the temperature at 10% weight loss is 582 ℃ and the weight maintenance rate in 800 ℃ is beyond 61% in nitrogen atmospheres. Furthermore, the thin film of FFDA6FDA has good optical transparency with 294 nm UV cutoff wavelength.

We studied the effects of ultrasonic pretreatment power, pretreatment temperature, ultrasonic pretreatment time, and the reaction conditions of water activity and pH on the enzymatic resolution of ibuprofen, and obtained the optimum reaction conditions for the enzymatic resolution of ibuprofen. Experimental results show that the cataytic performance of enzyme can be greatly improved by ultrasonic pretreatment.

We peeled fresh Aloe chinensis Baker, extracted and diluted with PBS buffer. The nematodes were cultured on nematode growth medium containing with different mass concentrations of D-glucose, which was used to evaluate the optimal mass concentration by conventional physiological index such as lifespan, athletic ability of nematodes. And the effect of aloe extract on reducing fat accumulation was showed by oil red O staining and Image J software analysis. Experimental results show that the 2%(2 gD-glu/100 mL NGM) is the optimal induced mass concentration to establish the Caenorhabditis elegans fat accumulation model, and aloe extract has excellent effect on reducing fat accumulation model of C. elegans.

We studied the effect of tubificid density and overlying water pH on the behavior of tubificid bioturbation and on migration of Cu and Cd from overlying water to the sediment through laboratory simulation of sediment/water system in tubificid bioturbation processes. The results show that bioturbation can significantly increase the migration rate of both Cu and Cd to the sediment, and the effect increases with increased density of tubificid. The influence of bioturbation on migration rate of Cu is greater than Cd. Acid and alkali induced stress can enhance the bioturbation. This enhancement of bioturbation is more significant under alkaline conditions. The presence of tubificid bioturbation can significantly enhance the acidbase buffering capacity of the experimental systems, and make the pH  of systems to be uniform and neutral. Both the changes of pH and the bioturbation in the systems affect the migration rate of Cu and Cd.
 Generally, the migration rate of the metals increases with the increase of overlying water pH. The promotion effect of bioturbation on migration rate of Cd is greater than Cu.