By using the technique of real analysis and the method of weight function, the author discussed Hilberttype multiple series inequalities with homogeneous kernel, obtained the necessary and sufficient condition for obtaining the best constant factor, and gave its applications.

We defined a new spectrum of operators based on the single valued extension property of bounded linear operators on a Hilbert space. Using the spectrum, the single valued extension property and Kato property of bounded linear operators, we obtained a new judgement method for the property (ω₁) and the property (ω) of bounded linear operators on a Hilbert space.

We considered submanifolds in statistical manifolds of constant curvatures by using Oprea’s optimization method, and obtained some geometric inequalities involving the generalized normalized δ-Casorati curvatures. We gave the upper bound and the lower bound of the normalized scalar curvature of the submanifolds, respectively, and the properties of submanifolds satisfying the equality cases.

Using the Schauder’s fixed point theorem and the Banach contraction mapping principle, we discussed a class of integrodifferential equation with the KurzweilHenstockStieltjes integral, and proved the existence and uniqueness of their solutions.

We considered the existence of positive solutions for a class of nonhomogeneous integral boundary value problems of fractional differential equations with sign changing nonlinearities. By using fixed point theorems of cone expansion and cone compression, we established and proved the existence theorems of positive solutions for the boundary value problem, and gave some examples to illustrate the rationality of the conclusions.

By using the fixed point theorem of ksetcontraction mapping and a new estimation of the measure of noncompactness, we proved the existence of the solution for the initial value problem of ordinary differential equations with noninstantaneous impulses, and then obtained the existence of the solution for the initial value problem of ordinary differential equations with noninstantaneous impulses under the assumption that the nonlinear term satisfied some weaker growth condition and noncompactness measure condition, and the noninstantaneous impulsive functions satisfied some Lipschitz conditions.

We considered a dynamic behavior of a class of  tuberculosis transmission model with immigration and treatment mechanism under random perturbations.  Firstly,  the existence and uniqueness of a positive solution of the model were obtianed by Lyapunov analysis method. Secondly, it was proved that the model had unique  stationary distribution by using  Has’minskii theory. Finally,  the conditions for extinction of the disease were obtained by stochastic analysis method.

Let m,n be two arbitrary  positive integers. By introducing the concept of (m,n)hereditary rings, and using the exact method of functor, we gave some characterizations of (m,n)projective modules and (m,n)hereditary rings.

Some properties of restricted HomLie algebras were extended to restricted Hom-Lie superalgebras.  We gave  definitions and some properties of semi-simple elements and toral elements of restricted Hom-Lie superalgebras, and definitions and some properties of  Hom-Lie Cartan-subsuperalgebras. The necessary and sufficient condition for characterization of Hom-Lie Cartan-subsuperalgebras  restricted by Hom-Lie superalgebras could be described  by its maximal torus, and  some properties of its maximal torus of the restricted Hom-Lie superalgebras were given.

We first pointed out that the product of two latticevalued filters was not necessarily  latticevalued filters by a counterexample. Then we defined inverse operation and multiplication for latticevalued filters on groups, and characterized the results of inverse operation and multiplication.

We presented a new smoothing Newton method for solving the linear circular cone complementarity problems. Firstly, based on  the smoothing function of the circular cone complementary function, the linear circular cone complementarity problem was transformed into a system of equations, which were solved by the smoothing Newton method. Secondly, under suitable assumptions, we proved that the algorithm had the global convergence and local quadratic convergence. The numerical results show that the CPU time and iteration times of the algorithm for solving linear circular cone complementarity problems are less, and the algorithm is relatively stable, which proves the effectiveness of the algorithm.

Firstly, the author gave properties of three uniform smooth approximation functions for absolute value function from above, and demonstrated their approximation effect with images. Secondly, a new method for solving linear programming problems was given. First, the linear programming problem was transformed into nonlinear equations, then the smooth 
nonlinear equations were obtained by uniform smooth approximation function, and then solved by high order Newton method. Numerical experiments show that approximation degree of uniform smooth function from above adopted in this method is superior to the existing algorithms, and the computational time is less under the same conditions.

Using the lattice Boltzmann method, we considered  Maxwell’s equations without source terms in space. We first constructed a lattice Boltzmann model for Maxwell’s equations and performed numerical experiments. Then we compared the numerical solutions obtained by lattice Boltzmann method with those obtained by other traditional methods. The results show that the lattice Boltzmann method is an effective method for solving Maxwell’s equations.

Firstly, aiming at the high rigid characteristics of bending resistance of combined rotating members of  turntabledrum mixing rotor in large rotating machinery, the turntable-drum mixing rotating members were approximated to a rigid cylinder, and the  dynamic model of thickness-disk rotor system was established. Secondly, considering the bending characteristics of the rotating shaft and the stored elastic potential energy bending shaft, and the bending  stiffness of the rotating shaft was calculated  by Hermite interpolation method and curve fitting method. Compared with traditional Jeffcott rotor systems, the results of numerical examples  show that the thickness of turntable is one of the main factors which affect the inherent dynamic characteristics of rotor system.

Firstly, the perfect matching of the graph 2-nZ₆,2-nXT₃ was classified by matching a certain vertex, and a recursive relation of a
 set of perfect matching numbers was obtained. Then the  formulas for calculating the perfect matching numbers of two types of graphs were given by these recursive relations.

Using a lattice Boltzmann model in spherical coordinate system, we solved the Giere-Meinhardt equation on spherical surface, and obtained the Turing patterns on spherical surface. Compared with the classical difference method, the model could be used to simulate the Turing pattern on the spherical surface.

By using the Markov inequality, under exponential moment condition, we gave the complete convergence and complete integral convergence of sequence of negatively dependent (ND) random variables with the same distribution in the sublinear expectation space. Thus, the complete convergence and complete moment convergence in probability space were exten
ded to the sublinear expectation space, and similar results were obtained.

Using the method of weighted estimation equation, under the generalized casecohort design scheme, we gave the estimation of regression coefficients in Cox’s model for lengthbiased data. Under appropriate conditions, we proved that the obtained estimators were consistent and asymptotic normality, and the asymptotic variance was explicit expression. It could be estimated by the plugin method in practical application.

By using Bernstein inequality  and BorelCantelli lemma of  negatively superadditive dependent (NSD) sequence, we gave  the (weak) strong consistency, uniform strong consistency and (uniform) strong consistency rate for the nearest neighbor estimator of density function and failure rate function of NSD samples.

We considered estimate of a  lower bound of blow-up time for solutions to  a class of nonlinear viscoelastic hyperbolic equations involving  supercritical source terms. By constructing the control function with damping term, using the mehtod of energy estimate  and Sobolev embedding theorem, we obtained an explicit estimate of lower bound of the blow-up time  for the solutions to the problem.

Firstly, LogGabor filter was used to extract the iris amplitude features, according to the type of iris library the filter parameters were optimized by the improved genetic particle swarm optimization algorithm. Secondly, principal component analysis was used to reduce dimensions, thereby reducing noise and redundancy. Thirdly, a dynamic radial basis function (RBF) neural network was constructed and iris recognition was performed by the Euclidean distance between iris amplitude features. Finally, we compared a variety of small iris libraries with other iris recognition algorithms. The experimental results show that the algorithm has higher accuracy in onetoone iris recognition, the ROC curve is closer to the coordinate axis, and filter is more versatile, which improves the recognition rate of the small iris library. It solves the problem of slow learning convergence speed and poor structural universality of traditional algorithms.

Aiming at the detection problems of advanced persistent threats, we proposed a detection method based on the attributes of network connection. Through four steps of data acquisition, characteristic extraction, anomaly detection and realtime alarm, we selected 12 kinds of attributes of network connection and applied machine learning methods to analyze attribute feature data set, and  established detection model of advanced persistent threat attacks. Experimental results show that the proposed method has good detection performance for advanced persistent threat attacks, high detection rate and low false alarm rate.

We proposed a multiobjective particle swarm optimization algorithm based on selfadaption partition of searching space, according to the search capability and scale of particles, it was transformed into a multidimensional standard normal distribution with the volume of subsearch space, which finely partitioned search spaces and optimized the distribution of particles in the divided subsearch spaces, and the partition continued during iteration until an optimal solution set was obtained. The experimental results show that the algorithm effectively solves the problem that multiobjective particle swarm optimization algorithm is easy to fall into local extremum, compared with some typical multiobjective particle swarm optimization algorithms, the algorithm has significant advantages in diversity of population and convergence of solution on the performance index of inverted generational distance.

We proposed an improved weighted centroid algorithm based on setting the received signal strength indication reference value. First, the relevant data packets such as the coordinates were diverted from the anchor node to the surrounding area. Then, assuming that a reference node was an unknown node, the signal intensity loss value in the process of propagation with the surrounding anchor node was measured, the minimum received signal intensity indication value was judged, and the sample set was optimized. The parameters of the revised signal indication value were taken as the weights of the corresponding new table nodes, and the location error was obtained. The simulation results of MATLAB show that, compared with the traditional algorithm, the algorithm has higher location accuracy, smaller fluctuation of location error, and strong mobility and adaptability.

We proposed a new routing algorithm for doublelayer networks based on low earth orbit(LEO) and geostationary earth orbit (GEO) constellations. The algorithm used the mesh topology of LEO satellites and their intersatellite links to calculate routing. The mechanism of congestion avoidance and packet classification was used to optimize the algorithm. It solved the problem of network congestion caused by large traffic in satellite networks. The simulation results show that the proposed method reduces the average endtoend delay and average packet loss rate, so network performance is improved.

Aiming at the shortages that current routing algorithms for wireless sensor backbone networks could not balance the contradiction between energy consumption and data transmission, which led to large data transmission delay and low throughput of routing of wireless sensor backbone networks, in order to improve the overall performance of wireless sensor networks, we designed a new routing algorithm for wireless sensor backbone networks. Firstly, the working principle of wireless sensor networks was analyzed, and the corresponding routing model was established. Secondly, machine learning al
gorithm was introduced to predict the energy of wireless sensor nodes in the routing of wireless sensor backbone networks in real time. The energyintensive wireless sensor nodes were selected for data transmission, and the wireless sensor with the least energy consumption was constructed. Finally, the algorithm was compared with other routing algorithms for wireless sensor backbone networks. The test results show that the energy consumption of the routing algorithm for wireless sensor backbone networks is small, the reliability of data transmission in wireless sensor networks is high, and the speed of data transmission in wireless sensor networks is accelerated. The overall performance of the routing algorithm in wireless sensor blackbone networks is obviously better than that of comparative algorithms.

Aiming at the problem that the traditional single color image enhancement algorithm based on multiscale Retinex did not consider the brightness component and local contrast when image enhancement was performed, which led to the image enhancement not reaching the optimal scale value, and the obtained enhanced image had the distortion and fog film, we proposed a single color image enhancement algorithm based on the improved multiscale Retinex. Firstly, the Gaussian environment function was used to convolve the three grayscale images and perform grayscale correction. The three corrected grayscale images were combined to obtain a preliminary single color image enhancement result. Secondly, we improved multiscale Retinex single color image enhancement algorithm to enhance the average brightness of single color image pixels. Finally, local contrast enhancement processing of color image after brightness enhanced was performed by nonlinear function, and image color after local contrast enhancement was restored by linear adjustment method to obtain   the best image enhancement results of single color image. The experimental results show that the proposed algorithm can obtain single color
 image enhancement results with good brightness and contrast.

Firstly, based on the pointwise mutual informationinformation retrieval (PMIIR) algorithm, we proposed Laplace smoothing
sentiment opinion (LSSO) algorithm, which automatically expanded the emotional dictionary and the emotional dictionary of emotive symbols. A certain scale and high quality emotional dictionary was obtained, including basic 
emotional dictionary, target emotional dictionary, online emotional dictionary, emotional dictionary of emotive symbols, negative dictionary, interrogative dictionary, degree adverb dictionary, conjunction dictionary. Then, the emotional value of text was calculated by refining the rules of text semantic analysis. The experimental results verified the effectiveness of the proposed method.

Aiming at the shortcomings of current resource allocation strategy of multiuser system, such as poor user fairness and small system throughput, we designed a resource allocation strategy of multiuser system based on artificial fish swarm algorithm. Firstly, by analyzing the working  principle of resource allocation of multiuser system, we constructed the corresponding mathematical model. Secondly, we introduced the artificial fish swarm algorithm to solve the mathematical model of the resource allocation of multiuser system, and improved the limitations of the standard artificial fish algorithm. Finally, the simulation and comparative test experiments were carried out  with other resource allocation strategies of multiuser system. The experimental results show that the artificial fish swarm algorithm can quickly and accurately find the optimal allocation scheme of multiuser system resources. It can effectively protect the fairness of the users, and greatly improve the communication ability of the multiuser system. The overall performance is superior to the other resource
 allocation strategies of multiuser system.

Aiming at the problem that the current spatial database clustering method did not consider the inverse result of the distance feature after dimensionality reduction, which led to the distortion of spatial data components, the clustering accuracy was low and the timeconsuming was long, the author proposed a reverse nearest neighbor clustering method of spatial database. Firstly, the feature decomposition of the kernel matrix was realized by selecting the training sample set, and the distance 
feature correction value was obtained to remove the influence of initial value. Secondly, according to dimensionality reduction of kernel principal component analysis (KPCA) combined with the inverse result of distance feature after dimensionality reduction, the inverse nearest neighbor clustering method was combined with the extended partial distortion search method to realize spatial data clustering. Finally, the data set was calculated by using the selected clustering center, the distortion between the first dimension component of the data set and the first dimension component of the clustering center was calculated, the reverse nearest neighbor was obtained until all spatial data found the category, and the reverse nearest neighbor clustering of spatial database was completed. The experimental results show that the method improves the clustering accuracy of spatial data and reduces the time used for spatial data clustering.

Aiming at the problem that the current computer generated image identification algorithm had poor precision in image texture feature identification, the author proposed a computer generated image identification algorithm based on longterm control plan (LTCP) features. Firstly, the color image was transformed into the color model, and the image was sampled to obtain higherscale texture information. Secondly, using the computer generated image blind identification algorithm based on LTCP features and cooccurrence matrix, LTCP features of texture images with different scales and adjacent pixel consistency cooccurrence matrix features were collected. Finally, the LTCP features and the adjacent pixel consistency cooccurrence matrix features were classified and predicted by discriminant classifier, and the computer generated image was identified a
ccording to the classification prediction results. The experimental results show that the proposed algorithm generates images on the computer with low feature dimension, high resolution and accuracy, which can accurately identify computer generated images.

We considered the entanglement properties of multiphoton transition in the linear and nonlinear Kerr medium with JaynesCummings (J\|C) model. We gave the analytical relationship between the transition photon numbers, detuning quantity, initial photon numbers, initial state parameter, nonlinear coefficient and the entanglement degrees of atoms and light fields, and analyzed its effect on the entanglement degrees of atoms and light fields with time evolution. The results show that when the initial state is close to the maximum entangled state in the nonlinear Kerr medium, and the transition photon numbers are large, the entangled state is more stable near the maximum entangled state, which is beneficial to the longdistance transmission of quantum entangled states.

We used relativistic mean field theory (RMFT) to describe hadronic matter, MIT bag model to describe colorflavorlocked (CFL) color superconducting quark matter, and the GL85,GL1,NL3 parameter groups to investigate the effect of the energy gap (Δ) of the CFL color superconductivity on the property of hybrid star. The results show that with the increase of the Δ, the maximum mass and radius of hybrid star is distributed in three regions: hadron star region （Δ<76 MeV）、 intermadiate transition region （76 MeV≤Δ<160 MeV）、 CFL color superconducting quark star region （160 MeV≤Δ≤200 MeV）. With the increase of Δ, the phase transition density of hardonCFL quark transition in hybrid stars decreases, and phase transition region narrows, the equation of state (EOS) softens first, then stiffens, and the maximum mass of stars decreases firstly and then increases. The influence of the energy gap of CFL color superconductivity on the properties of hybrid stars studied by GL85 and GL1 parameter groups is consistent. The neutron star PSR J16142230 can be obtained by NL3 parameter group in small energy gap （Δ<30 MeV）.

The band gap structure, defect mode and intrinsic field distribution of the twodimensional function photonic crystals with point defects were studied by COMSOL Multiphysics simulation software. The linear function form of dielectric constant of dielectric column was ε(r)=k·r+b, according to the photoelectric effect and the Kerr effect, and  the refractive index of the dielectric column was changed by applying external electric field and light field.   The calculation results show that the band gap structure, the position of band gap, and the intrinsic field distribution of defect mode can be adjustable by changing the parameters and the number of point defects.

Using the CAMB3LYP method of density functional theory, we optimized the geometric configuration of S-phenylalanine (S-Phe) molecule at 6-31G(d) basis set under different conditions. The results show that, under the conditions of implicit methanol solvent and the gas phase,  the qualitative results of charge transfer in S-Phe molecular system are basically consistent, the quantitative results are slightly different, the S2 excited states of each fragment are basically consistent, only the difference of S2 excited state of COOH fragment is 2.2%, and the difference of S4 excited state is 0.4%—2.8%. The qualitative analysis lacks an S5 excited state in different environments. The difference of charge transfer of S2 and S4 excited states calculated by Becke method is about 2.5%—8%.

The author designed a superimposed elliptic ring tri-frequency monopole slot antenna and analyzed the effects of the size 
change of elliptic ring on the antenna performance. The antenna consisted of a superimposed elliptic loop feed terminal, coplanar waveguide feeder and rectangular wide spot floor, and coplanar waveguide was used to feed the antenna. The results show that the designed antenna has trifrequency characteristics, effective working bandwidths are 3.2—3.8 GHz, 5.1—6 GHz and 7.8—12 GHz, the size is 25 mm×25 mm, the radiation characteristics and gain characteristic are good, so it is suitable for small multiband wireless communication system of integrated WiMAX,WLAN and X bands.

Using electrospinning technology, N,Ndimethylformamide as solvent and polyacrylonitrile (PAN) as carrier, we prepared PAN/CNC/Ag composite nanofibers. The chemical structure, morphology, thermal stability and crystal structure of composite nanofibers were characterized by Fourier transform infrared spectroscopy (FT-IR), transmission electromicroscopy (TEM), scanning electron microscope (SEM), thermal gravity differential thermal gravity analysis (TG\|DTG) and X-ray diffraction (XRD). The results show that PNC,CNC and Ag nanoparticles combined form PNC/CNC/Ag composite nanofibers. The composite nanofibers are uniform in size with average diameter of (214±12)nm, and the Ag nanoparticles are uniformly distrib
uted in the composite nanofibers with particle size of 5—25 nm. The composite nanofibers have excellent antimicrobial properties against grampositive Staphylococcus aureus (S.aureus) and gramnegative Escherichia coli (E.coli).

Firstly, ZSM-5 zeolite with microporous structure by alkali treatment for different time was mixed with mesoporous template hexadecyltrimethylammonium bromide (CTAB) to prepare microporousmesoporous ZSM-5 molecular sieve by hydrothermal method. The physicalchemical properties of the microporousmesoporous ZSM-5 molecular sieve were characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR) and N₂ adsorptiondesorption and transmission electron microscopy (TEM). Secondly, the microporousmesoporous ZSM5 molecular sieve was used as catalysts for alkylation reaction of phenol with tertbutanol. The catalytic properties of the materials were tested by the conversion of phenol and the selectivity of 2,4ditertbutylphenol. The results show that ZSM5 with good composite of micropore and mesopores can be obtained after alkali treatment for 1 h,  the catalyst has better catalytic performance for phenol with tertbutanol, the highest conversion of phenol is 86.2%, and the selectivity of 2,4ditertbutylphenol is 57.9%.

The hypoglycemic active ingredient in the ethyl acetate layer of rhizome of Acanthopanax senticosus was separated and purified by normal phase silica gel column chromatography, C-18 reverse phase column chromatography and semipreparative high performance liquid chromatography (HPLC). Ten compounds were obtained, and the structures of the obtai
ned compounds were determined by analyzing spectral data of nuclear magnetic resonance hydrogen spectroscopy (1HNMR), nuclear magnetic resonance carbon spectroscopy (13C
NMR), distortionless enhancement by polarization transfer (DEPT), mass spect
rum (MS), and compared with the relevant literatures. Their activities were tested. The results show that compounds 〖STHZ〗1
〖ST〗—〖STHZ〗5〖ST〗 are kauranetype diterpenoids, compounds 〖STHZ〗6〖ST
〗—〖STHZ〗8〖ST〗 are turpentinetype diterpenoids, and compounds 〖STHZ〗9〖
ST〗,〖STHZ〗10〖ST〗 are lignin compounds. Compounds 〖STHZ〗1〖ST〗,〖STHZ〗5〖ST〗,〖STHZ〗7〖ST〗,〖STHZ〗8〖ST〗 h
ave significant specific inhibitory activity on protein tyrosine phosphatase 1B (PTP1B), 
compounds 〖STHZ〗2〖ST〗,〖STHZ〗4〖ST〗,〖STHZ〗9〖ST〗 have  good inhibitory effects on 
protein phosphatase 1 (PP1), and compounds 〖STHZ〗9〖ST〗,〖STHZ〗10〖ST〗 have a low inhibitory effect on
 vaccinia H1 related (VHR) phosphatase.

Using laboratory simulation method, soil was soaked and leached with sodium chloride (NaCl) and calcium magnesium acetate (CMA), respectively, we determined the variation of mass ratio of binding states of Zn and Cu in soil by Tessier sequential extraction procedure, and investigated  the effects of two deicing salts on binding states of typical heavy metals in soil. The results show that NaCl has more obvious effect on heavy metals in soil than CMA, and the higher the concentration of NaCl, the greater the difference. Both Zn and Cu in soil tend to be converted into exchangeable state under the action of immersion of deicing salts, and exchangeable state of Zn increases by 115% at most. The leaching effect of deicing salts has a great effect on binding state of Zn, compared with distilled water leaching, the exchangeable and carbonate   states of Zn are reduceed by 30% and 20%, respectively, the effect on binding state of Cu is minor. The organic/sulfide binding state and residual state of Zn and Cu are little affected by immersion and leaching of deicing salts. CMA is more environmentfriendly than NaCl deicing salts.

Aiming at the problem of groudwater pollution caused by trinitrogenous compound antibiotics(NH⁺₄N,NO^-₂N,NO^-₃-N)  in agricultural areas of China, the effects of sulfanilamide degrading bacteria on the degradation of trinitrogen by nitrogen bacteria in the process of microbial remediation was studied by experimental simulation. The results show that sulfanilamide de
grading bacteria promote the degradation of NH⁺₄-N and NH⁺₂-N, and inhibit the growth of nitrogen bacteria and the degradation of NH⁺₃-N. Sulfanilamide degrading bacteria are bacilli, belonging to Grampositive bacteria and the nitrogen bacteria are cocci and bacilli, belonging to Gramnegative bacteria, indiciting that sulfanilamide degrading bacteria can promote nitrification and inhibit denitrification.