By using the method of energy estimates and the comparison principle, we studied the long time asymptotic behavior of solutions to the Cauchy problems of a class of coupled semilinear diffusion systems with firstorder terms. We gave the Fujita critical curves which described the global existence and blowup properties of solutions, and established the theorems of Fujita type.

The author considered the primitive equations of largescale moist atmosphere defined  in cylindrical region. By using the technique of differential inequality and the method of energy estimation, the author gave the prior bounds of the solutions of the equations, and proved the continuous dependence of the equations on the viscosity coefficient.

We considered a class of fourthorder low curvature equation related to image processing, and proved the existence and uniqueness of the weak solution of the equation by using the method of half difference.

We considered the boundary value problem for a class of coupled system of nonlinear Caputo fractional differential equations, and proved the existence of two positive solutions of the coupled system by using properties of Green’s function and the fixed point theorem of GuoKrasnosel’skii’s.

By using  the weight estimation of A_p and the function decompositions method, and by means of the weighted estimation on the  L^p spaces, we proved the weighted boundedness of the intrinsic square functions, intrinsic Littlewood-Paley  g and g^*_λfunctions on the generalized fractional  Morrey spaces, and gave the weighted boundedness of the corresponding BMO commutators.

By using hierarchical decomposition of function and the weighted inequalities, and by means of the boundedness of Hardy operator on variable Lebesgue spaces and the properties of bounded mean oscillation function space (BMO) functions, the author gave the boundedness of the higher order commutators generated by fractional Hardy operators with variable index and BMO functions on weighted HerzMorrey spaces with variable exponent.

Let B(X) be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space. We study the structure of the surjective additive maps on B(X) preserving parts of normal eigenvalues, and prove that the map is either an isomorphism or antiisomorphism.

Using representations and cohomologies of HomJordan Lie superalgebra T, we gave  that the necessary  and sufficient conditions for constructing HomJordan Lie superalgebra TV and proved that equivalent abelian extensions of Hom-Jordan Lie superalgebras gave the same representation. Then, we obtained a 2-cocycle by means of representations and abelian extensions.

By introducing the concept of (σ,δ)-SILS weak Armendariz rings, we investigated the weak Armendariz properties of general skew inverse Laurent series rings. By using the itemized analysis method on series, we prove that if R is weak -(σ,δ)-compatible and nil(R) is a nilpotent ideal, then R is (σ,δ)-SILS weak Armendariz ring.

By using the special vector field in space forms and the basic formulas on submanifolds, the almost Yamabe solitons on Euclidean space were extended to space forms, we obtained a necessary and sufficient condition for the submanifolds in space forms to be the almost Yamabe solitons, and that any almost Yamabe solitons on a hypersurface in space forms were totally umblical.

Firstly,  we give the notion of Hom-δ-Lie supertriple systems and prove that generalized derivations, quasiderivations, derivations Der(T), central derivations ZDer(T), quasicentroids QC(T) and centroids C(T) are Lie superalgebras in a Hom-δ-Lie supertriple system T. Secondly, we prove that  ZDer(T) and C(T) are ideals of Der(T) and ZDer(T)=C(T)∩Der(T).  If T is centerless, then ［C(T),QC(T)］={0}.

Firstly, we discussed vertex-distinguishing general total chromatic number of complete tripartite graphs K_3,5,p(p≥5) by using the method of distributing the color sets in advance and contradiction, and gave special proofs when p was small and regular proofs when p increased gradually. Secondly, we used the methods of constructing the colorings to dye the complete tripartite graphs K_3,5,p, and gave a  coloring scheme. The success of the coloring verified the correctness of the color number proved by the contradiction method, thus we solved the problem of vertex-distinguishing general total coloring of complete tripartite graphs K_3,5,p.

Bayesian genetic algorithm was used to solve the heat source parameters of twodimensional heat conduction equation. Firstly, the posterior probability density function of the heat source parameters was obtained by Bayesian inference and twodimensional heat conduction equation. Secondly, combined with the genetic algorithm, according to maximum likelihood principle, we gave the posterior probability distribution and statistical results of the location and the time parameters of the heat source. Numerical experiments show that when the iteration number reaches 50 times, the relative error of the parameters converge stably within 1%. Adding 5% and 10% noise to the observation data respectively, and the relative error of the parameters is controlled within 5% and 9% respectively.

Using the Armijolike search and strongly positive bounded operator to improve an extragradient method of monotone variational inequality problem. We discussed the feasibility of the Armijolike search in a Hilbert space, and established strong convergence theorems to approximate the solution of monotone variational inequality problem.

We considered a zeroandoneinflated Poisson (ZOIP) regression model with general linear constraints, and gave an EM (expectation maximization） algorithm to estimate the parameters of the model. The flexibility and feasibility of results are verified by numerical simulation and a real data analysis.

The perfect matchings of  2-2nP₅ and 2-nK_1,1,1,3 graphs were classified according to the edges that matched a fixed vertex. First, we found out  the recurrence relations of each kind of  perfect matching number, and obtained a set of recurrence relations 
which were related to each other. Then we used the  correlation between these recurrence relations to give the  counting formula of the perfect matching mumber  of these two graphs.

We considered the lower bound for the lifespan of the solutions to a class of fourthorder nonlinear coupled hyperbolic systems. 
By constructing the appropriate control function, using the energy estimate method and Sobolev embedding theorem, we  gave the firstorder differential inequality satisfied by the control function, and gave the estimate of the lower bound for the lifespan of the solution of the problem by analyzing  the properties of differential inequalities.

Aiming at the problem that the acceleration strategy of the traditional random walking algorithm had some limitations when dealing with large-scale power grids, we proposed a random walking acceleration algorithm based on variable step size. Firstly, based on the experimental comparison of different number of nodes and threshold size, the time efficiency of traditional random walking acceleration algorithm and variable step size random walking acceleration algorithm was analyzed, then it was proved that the variable step size random walking acceleration algorithm could greatly improve the efficiency of power grids analysis. Secondly, we proved that the random walking algorithm had spatial local characteristics, which could further release the running space. Experiments on power grids of different scales show that the method can optimize the running space of the algorithm.

Aiming at the problem that the structural information were easily lost in the process of decolorization, we proposed a decoloriz
ation algorithm based on structural information similarity. Firstly, the contrast image was constructed in RGB color space by using the average and standard deviation of pixels to keep the contrast and brightness information of the color image. Secondly, the similarity between each RGB channel image and contrast image was measured by structural similarity index. Finally, the structural similarity indices were taken as the weights in the global weighted mapping function to obtain the final grayscale image. This algorithm effectively solved the problem that the objective function needed to be solved in other typical decolorization algorithms, which resulted in the defects of high complexity and unnatural structural information. The experimental results on Cadik and CSDD database show that the proposed  algorithm is superior to some existing typical grayscale algorithms, which can effectively preserve the contrast and structural information of the original image and improve the computational efficiency. The visual perception is natural for the grayscale image, whose subjectivity and objective evaluation results are optimal.

Firstly, based on the combination of sentence organization information and the influence of rules, partofspeech and word order on the syntax analysis system, we proposed a rulebased sentence analysis and recognition algorithm, which could quickly identify correct sentence patterns in large amounts of text. Secondly, based on the sentence analysis and recognition algorithm, we proposed a hierarchical sentence analysis and recognition algorithm based on the combination of rules and syntax to improve the accuracy of the hierarchical sentence recognition error detection. The experimental results show that the average accuracy rate and average recall rate are 8465% and 7715%, respectively, compared with the rulebased sentence recognition algorithm respectively improve 11.79% and 14.48%. It proves the feasibility of the analysis and recognition of hierarchical sentence combining rule and syntax.

Aiming at the problem that it was difficult to recognize the fovea of color fundus image with traditional algorithm, we proposed  a fovea automatic detection algorithm based on fully convolutional networks (FCN). Firstly, we mined global context information through the local context environment of color fundus images, and constructed an FCN model to realize local pixel-level classification. Secondly, the local pixel\|level features were extended to the global pyramid pooling module, so that the spatial statistical data could provide a better description and expression for the global context understanding, thus effectively obtain the highly differentiated global context information. Finally, the global and local features were fused to achieve accurate detection of the central fovea. The experimental results show that the algorithm improves the specificity of detection of dark fundus lesions, and provides an effective basis for the detection of serious fundus lesions.

Aiming at the shortcomings of the current image retrieval algorithm, such as low accuracy, poor realtime performance, in order to obtain more ideal image retrieval results, the author proposed an image retrieval algorithm based on support vector machine and user feedback mechanism. Firstly, the author collected large images, extracted the relevant features of image retrieval, and established image retrieval feature library. Secondly, the author used support vector machine to calculate the similarity between the features of the image to be retrieved and the features of image retrieval library, determined the image category, and realized the preliminary image retrieval. Finally, the author introduced the user feedback mechanism to refine the preliminary image detection results, and compared with the classical image retrieval algorithm. The experimental results show that the image retrieval accuracy of the proposed method is more than 90%, the image retrieval error is much smaller than that of the classical image retrieval algorithm, and improves the image retrieval efficiency.

Aiming at the problem of the low efficiency of coarse granularity data in specific operation mode, the author proposed a data distributed algorithm based on convolutional neural network. Firstly, the convolutional neural network model for coarse granularity data processing was constructed. The connection structure and weight proportion of the neural network in the basic connection layer of the model were given, and the coarse granularity data were trained and pooled. Secondly, the result of training
 pooling was used to solve the minimum loss function of the model and improve the distributed computing ability of the model for coarse granularity data. The experimental results show that in the single machine and cluster mode, the convolutional neural network model has better computing efficiency and data generalization ability.

Firstly, based on the convolutional neural network, we proposed a remote sensing image fusion model that used crosslayer copy connection operations to fuse feature maps of different scales, and solved the problem that traditional remote sensing image fusion methods needed to manually select different decomposition and fusion rules for different types of remote sensing images, w
hich led to the problem that the fusion image quality was greatly affected by selected rules. Secondly, the effectiveness of the method was verified by the Deimos satellite and QuickBird satellite data, and the fusion image quality was evaluated by the subjective and objective methods. Experimental results show that the proposed model can effectively combine the spatial information of panchromatic image with the spectral information of multispectral image, and control the spectral distortion.

We proposed a short text classification model based on improved convolutional neural network. Firstly, different coding methods were used to map short text to distributed representation in different spaces, and digital features of different granularities were extracted as multi-channel inputs of short text classification model. Extracting concept features from standard knowledge base as prior knowledge to improve the semantic representation ability of short text. Secondly, the selfcoding learning strategy was added to the full connection layer, on the basis of approximate identity, the digital features were further combined to simulate the relevance within the data. Finally, the principle of relative entropy were used to increase the sparsity limit of the model, reduce the complexity and improve the generalization ability of the model. The effectiveness of the proposed model was verified by short text classification experiments on the open source dataset.

Aiming at the problem that singlemodality medical images could not provide comprehensive and complementary information for clinical diagnosis, the author proposed a multimodal medical image fusion method based on nonsubsampled shearlet transform (NSST) and improved sparse representation (ISR). Firstly, the NSST tool was used to decompose the source image into a low frequency subband and several high frequency subbands. Secondly, the ISR method was used to fuse the lowfrequency subbands, and the details of the lowfrequency subbands were removed by the sobel operator and the guided filter, thereby improving the fusion efficiency of the lowfrequency subbands. At the same time, the highfrequency subbands were fused by using the maximum absolute value fusion rule. Finally, the final fused image was obtained by the inverse NSST transform of the fused lowfrequency and highfrequency subbands. Experimental results show that proposed method is superior to other fusion methods in subjective visual performance and objective evaluation.

In order to improve the accuracy of security risk assessment of wireless sensor network, we proposed a model of security risk assessment of wireless sensor network based on index selection and weighted fusion. Firstly, the index system of security risk assessment of wireless sensor network was established, and some indexes with important contribution were selected by grey relation analysis method. Secondly, according to the correlation degree, the security risk assessment indexes of important wireless sensor network were weighted,  support vector machine was used to fit the characteristics of security risk change of wireless sensor network, and particle swarm optimization algorithm was introduced to optimize the parameters of support vector machine. Finally, the results were compared with other models. The results show that the proposed model obtains better security risk evaluation results than the comparison model. The accuracy of the assessment is more than 95%, and the efficiency of the security risk assessment of wireless sensor networks is improved.

The quantum selforganizing network method was used to solve the problem of water-flooded layer identification in oil field logging interpretation. Firstly, the reservoir feature indicator set was constructed, including sequence indicators from the log curves and some single numerical indicators. For the sequence indicators, the discrete Walsh filtering method was first used to remove the noise in sequence indicators, then the average was taken, and then the reservoir feature vector was constructed together with other single numerical indicators. Secondly, the reservoir feature vectors were transformed into quantum state descriptions, and the quantum self-organizing networks were implemented clustering. Finally, the converged network was used as a mathematical model for waterflooded layer recognition in similar blocks of oil fields. The simulation results show that the accuracy of the proposed method is 6% higher than that of the traditional selforganizing clustering method.

In view of the diversity of sensor data, we proposed an improved method based on wavelet and neural network data fusion. Firstly, the sensor data was preprocessed. Secondly, wavelet and BP neural network were combined to optimize the data. Finally, the data was fused by calculating the credibility of the sensor. The experimental results of the sensor data fusion effect show that  the algorithm is stable and effective for data processing and data fusion. The degree of dispersion of the fusion result is better than that of weighted data fusion, Kalman data fusion and other methods.

Firstly, we selected the world ocean atlas 2013 (WOA13) ocean data  as the experimental data, the unequal distance differential method and vertical gradient method were applied to the preprocessing of ocean data, the division of ocean area and analysis of thermocline. Through the performance analysis of various neural networks based on the threedimensional WOA13 ocean data in the binary classification experiment, we chose the residual network as the network model of the binary classification experiment, and added the Dropout retention layer on the basis of the threelayer residual network model to prevent over-fitting. Secondly, the residual network model was used for thermocline analysis and determination, and the comparative tests such as the super parameters optimization, the residual unit improvement and  the retention rate adjustment were carried out for the improved model. The experimental results show that the improved ResNet26 network is effective for the thermocline data classifica
tion of WOA13 ocean area data, and the classification accuracy is more than 94%.

Firstly, by introducing adaptive strategy, we proposed a selfadaptive nonnegative matrix factorization based on gradient descent. Secondly, by comparing the distance between reconstructed nonnegative matrix and selfadaptive regulation, the problems of 
randomness and the number of basic vectors validation for traditional nonnegative matrix factorization were solved, and the basic vectors generated by the algorithm were more representative. Finally, taking the analysis and validation of undergraduate achievement of a college of Jilin University as an example, we investigated effectiveness of the proposed algorithm. The experimental results show that  compared with the traditional nonnegative matrix method, the selfadaptive nonnegetive matrix factorization method has better robutness and reduces the error rate by 20.16%.

Firstly, the quantum transmission matrix, quantum dispersion relation, quantum transmittance and reflectivity of onedimensional photonic crystals were given based on the quantum wave theory of light. Secondly, the curves of quantum dispersion relation, quantum transmissivity and reflectivity of onedimensional photonic crystals were given respectively by numerical calculation, and it was compared with the classical dispersion relation, transmissivity and reflectivity. The results show that the calculation results are consistent. This method can be used to further study the quantum topological properties of photonic crystals, such as quantum Zak phase, quantum Chern number and quantum edge state.

We built the supercell model of single layer monovacancy graphene with hexagonal structure. Based on the first-principles of density functional theory, we studied the adsorption energy of O₂ and the desorption energy of H₂O and OH on Pt graphene. We investigated the intermediate reactant and the corresponding energy change of Pt2graphene and Pt₄ graphene in oxygen reduction reaction (ORR), and gave the optimal path of ORR.

Using the B3P86 method of density functional theory, the author optimized the ground state stable geometric configuration of S-Serine (S-Ser) molecules and charged ions at the level of 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 S-Ser molecule and ion. The results show that the structural parameters of the SSer molecule and S-Ser-2- change with the increase of the number of electrons captured in the molecular system, such as the bond length R is the most obvious change. The molecular orbital (MO) combined with natural transition orbital (NTO) characteristic analysis method can better describe the electronic excitation characteristics of each excited state of S-Ser system, and the identification effect for Rydberg excitation characteristics is better.

Monte Carlo program was used to simulate the shielding effectiveness of different adulterants and mass fraction of adulterant for a X-ray spectrum at low energy. The simulation results show that the alloy shielding effectiveness has a positive correlation with atomic number of adulterant, and a positive correlation （ΔZ>0） or a negative correlation （ΔZ<0） with mass fraction of adulterant. With the increases of the absolute value ΔZ, the variation of shielding effectiveness is getting lager, and the variation range has a positive correlation with mass fraction of adulterant. The shielding effectiveness of TaW alloy is the best and is nearly not affected by the variation of mass fraction of adulterant. The transmission rate of different low energy X-ray obtained by MCNP simulation shows good agreement with the experimental value.

ZnO particles was prepared by hydrothermal method and ZnO photoanode was prepared by solgel method. Through X-ray diffraction (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM), ultraviolet visible absorption spectrum (UV-Vis) and photocurrent densityvoltage curve, we analyzed the influence of ZnO photoanode with different thickness on quantum dot sensitized solar cells. The results show that increasing the adsorption area of quantum dots can make red shift of the absorption edge of the ZnO photoanode to the visible light region, and then improve the photoelectric conversion efficiency of solar cells.

Using the 3-(1H-tetrazole-1-acetic acid amido) pyridine (TAAP）, Andersontype polyoxoanions and copper chloride as raw materials, we synthesized a new Anderson-type polyoxometalate-based copper complex {H₂Cu₁₂(Trz)₁₂［CrMo₆(OH)₆O₁₈］₂(OH)₈(H₂O)₄}·12H₂O. (HTrz=1Htetrazole). The crystal structure analysis shows that the complex is a twodimensional metalorganic layer formed by Trz ligand and Cu²⁺ ions. The terminal oxygen atoms of the［CrMo₆(OH)₆O₁₈］-3- polyoxoanions is connected to the Cu²⁺ ions to further form a threedimensional coordination framework. In situ conversion of TAAP ligand to Trz during the hydrothermal synthesis. The synthesized complex has good electrocatalytic reduction effect on H2O2, and good catalytic degradation effect on methylene blue and crystal violet under ultraviolet light.

The prepared copperdoped silica adsorbent was used to enrich luteoloside in Coreopsis tinctoria, and the adsorbents enriched with luteoloside were determined by nearinfrared spectroscopy. After the pretreatment of nearinfrared spectra, a quantitative correction model of luteoloside was established by partial least square regression method for determination and validation. The results show that the adsorption efficiency is 89.7% when the mass of copperdoped silica adsorbent is 0.25 g and the adsorption is oscillated at room temperature for 20 min. The adsorbents enriched with luteoloside can be directly detected by nearinfrared spectra without desorption. After the NIR spectral data are processed with multiple scattering correction and first derivative,  the correlation coefficient between the reference mass concentration and the predicted mass concentration of luteoloside is 0.975 0, the root mean square error of cross validation is 0.959 8 mg/L, within the lower mass concentration range of 1.5—19.5 mg/L, and the recovery rate of luteoloside in prediction set can achieve 82.6%—111.4% in the calibration model.

Using 1,4-dichloro-2,5-dinitrotoluene as bridging agent, H-2MHTPP porphyrin dimer was prepared by one-step synthesis. The structure of porphyrin dimer was characterized by MALDI-TOF mass spectrometry. The electrochemical and photochemical properties of the porphyrin dimer and the surface photovoltage spectrum (SPS) of the porphyrin dimer were studied. The results show that the H2MHTPP porphyrin dimer is a p-type semiconductor.

The 3,5dicarboxy1Hpyrazole reacted with Cu(NO₃)₂ in the mixed CH₃CN/H₂O solvents at 120 ℃ for 72 h, and blue crystals were obtained. The molecular formula of the compound was {［Cu₃(pdc)₂(H₂O)₇］·2H₂O}_n. The compound was characterized by elemental analysis, IR spectrum, single-crystal X-ray diffraction, powder Xray diffraction and thermal analysis. The results show that three Cu²⁺ ions and two pdc^3- anions interconnect to form the neutral molecule Cu₃(pdc)₂, which is further joined to form a onedimensional (1D) puckered chain by coordinated H₂O molecule as bridging ligand, then 1D chains are further joined into a three-dimensional supramolecular network through hydrogen bonding. The coordinated H₂O molecules of Cu²⁺ ions and lattice H₂O molecules form one-dimensional metal-water chain through hydrogen bonding.

The effective components of Perilla stem were extracted by ethyl acetate, chloroformane, nbutanol and water respectively, the organic acids, triterpenoids and flavonoids were obtained, and its antioxidant effect was studied. The results show that the gallic acid is 0.6 g/kg in n-butyl alcohol of Perilla stem, and the oleanolic acid is 0.9 g/kg in chloroform of Perilla stem. There are lots of brass compounds in Perilla stem, and the hyperin are 1.2 g/kg in ethyl acetate and 1.1 g/kg in chloroform. All of the Perilla stem extracts have certain ability to remove ·OH, the super oxygen free radical (·O-2) and DPPH·. The removal ability of acetic ether and chloroform in 1 mg/mL are best, which reach 79% and 73%, 62% and 59%, 83% and 80% respectively. Acetic ether and chloroform have strong ability to remove ·OH radicals and DPPH·. Therefore Perilla stem extract has obvious antioxidant effect.