By using the technique of real analysis, the author studied the structural characteristics of Hilbert’[KG-*5]s type integral inequalities with homogeneous kernel and the necessary and sufficient condition for obtaining the best constant factor, and obtained the analytical expression of the best constant factor.

We gave some basic properties of the generalized derivation algebra GDer(L), quasiderivation algebra QDer(L), centroid C(L), quasicentroid QC(L) and central derivation algebra ZDer(L) of a HomLeibniz algebra L. We also proved that QDer(L) could be embedded and become a larger derivation of HomLeibniz algebra.

Let p,q be odd primes such that p≠q, and G be p⁴q order groups. With the help of local analysis method of finite groups, we discussed the complete classification of G and obtained their whole structures whenever their Sylow -psubgroups had a nonabelian maximal subgroup with nilpotent class 2.

We considered skew constacyclic codes over the ring R=F_q+vF_q+v²F_q, where q=p^m, p was an odd prime and v³=v. According to the structure of the ring, we obtained the generating polynomial of skew constacyclic codes over R was the right divisor of xⁿ-λ, where λ was a unit element and proved that skew constacyclic codes were generated by the principal ideal, when λ²=1, we gave the necessary and sufficient condition for the dual code of a liner code to be skew constacyclic code, and discussed generating polynomials of the dual codes.

By using LusternikSchnirelmann category theory, the author considered a class of cooperative elliptic equations involving parameter and gradient term, and obtained the multiplicity of nontrivial solutions of the equations under certain conditions.

When the linear impulsive differential equations had nonuniform (μ,ν) dichotomy, the author obtained the existence of invariant manifolds under sufficiently small perturbations by using the contraction mapping principle.

Using the energy comparison method and comparison principle, we considered the global existence and blow up properties of the homogeneous Dirichlet problems in exterior domain of coupled nonlinear diffusion systems with reactions and convections, determined the critical Fujita curve and established the Fujitatype blow up theorem. The results show that the critical Fujita curve depends on the spacial dimension, convection and reaction terms of the systems.

By constructing a homotopy equation of the implicit linear complementarity problem, we gave a new condition for the existence of homotopy path, proved the boundedness and convergence of the homotopy path and obtained the condition for the existence of a solution of the implicit linear complementarity problem.

By using the function construction method and mathematical induction, we considered adjacent vertexdistinguishing I-total coloring of graphs P_m∨S_n,F_m∨W_n and W_m∨W_n, and gave the adjacent vertexdistinguishing I-total chromatic number of them.

By using methods of truncation and largeblocks or smallblocks, we considered the asymptotic properties of the wavelet estimator for ρmixing sequence in the nonparametric regression model, and obtained the strong consistency and the asymptotic normality of the wavelet estimator of g(·).

We proposed the inverse probability weighted (IPW) estimation of regression parameters and the empirical likelihoodbased weighted (ELW) estimation for varyingcoefficient quantile regression model with partial missing covariates, and discussed the large sample properties of these two estimations. The ELW estimation is more efficient than the IPW estimation by the asymptotic variance.

By using the maximum likelihood estimation (MLE) method , we considered the parameter estimation problem of a class of nonlinear stochas tic differential equations with small perturbation. We discussed the properties of the esitmator as the small perturbation parameter ε→0 or ti me T→∞, and proved that the estimator of unknown parameter had unbiasedness and asymptotic consistency as ε→0. When ε took a fix ed value and ε→0, we gave the asymptotic distribut ion of the estimator α^^ε as T→∞ respectively. Finallay, we gave the numerical simulation results to veri fy the unbiasedness and asymptotic normality of estimator.

The author proved that a monomial derivation, which was constructed by Moulin Ollagnier and  Nowicki in the polynomial algebra of four variables, has no Darboux polynomials if and only if its ring of constants was trivial.

The author considered the nonexistence of positive stable solutions of the LaneEmden systems. By using elliptic methods and derivation techniques of Farina on the JosephLundgren index, the author obtained a Liouville theorem about general stable solutions, and extended the study of a stable solution of a single equation to the study of equations.

By gaving the concept of graceful tree, bipartite graceful tree, bipartite oddgraceful tree and oddelegant tree, we constructed a coral tree by using the method of treeaddvertex (TAV), and proved that it had the oddgraceful and oddelegant labelling.

By using some limit properties for trimmed sums of independent identically distributed random variables with medium tailed distribution, we obtained the asymptotic distribution for product of the sum of trimmed sums.

We proposed an attack path generation method based on a ttack feasibility analysis to solve the problem of attack path exist ing redundancy caused inaccurate calculation of nodes confidence in attack graph. By further improving likelihood weighting algorithm based on Bayesian inf erence, the algorithm could calculate the nodes confidence more accurately. Expe rimental results show that the improved algorithm effectively eliminates the red undant paths in the attack graph, thereby improvin g the accuracy of nodes confidence, and realizing the effective predictive analy sis of the attack path.

We proposed an improved particle swarm optimization (PS O) algorithm. The algorithm used reasonable balance between the global explorati on and local development, which reduced the possibility of premature convergence of PSO. Firstly, the Beta distribution was used to initialize population. Secon dly, the inverse incomplete Γ function was used to update the inertia weig ht. Thirdly, a new operator based on differential evolution was introduced to ad just the velocity. Finally, we used the method based on boundary symmetry ma pping to deal with the cross boundary of particles. Numerical simulation results show that the improved algorithm is obviously superior to the common PSO algori thm, differential evolution algorithm, artificial bee colony optimization algorithm and an t colony optimization algorithm.

Aiming at the local convergence problem of particle swa rm optimization algorithm, we proposed a particle swarm optimization algorithm b ased on the inertia weight adjustment and group best position variation. In this algorithm, the state information of individual particles was introduced into th e inertia weight strategy. The inertia weight of each particle was adjusted inde pendently, which reflected the difference of individual particles to the weight demand. In the mutation strategy of the best position, the classification idea w as used. According to the searching state of the particle swarm, the correspondi ng extreme mutation mode was selected, which made the mutation operation more ta rgeted. The experimental results indicate that the new algorithm shows good opti mization performance for several test functions, which can effectively avoid local convergence problem and improve the global sea rch ability of the particle swarm.

Aiming at the defects of the current radio frequency identification system, such as the complexity of the authentication process , poor security and so on, we proposed a mutualauthentication scheme based on Hash function and elliptic curve cryptography, which improved the security of radio frequency identification system. Firstly, ellipti c curve cryptography was used to authenticate the reader of ra dio frequency identification system. Secondly, lightweight Hash function was used to authenticate and verify the identity of radio frequency identificat ion system, the length of public key and key could be reduced greatly, and compu tation overhead could be reduced. Finally, the feasibility of the scheme was tes ted by experiment. Test results show that compared with other mutualauthenti cation schemes, the proposed scheme can effectively resist all kinds of attacks, and the security is high, at the same time, it reduces the memory and communica tion overhead.

Aiming at the problem that the existing cross modal Has h retrieval method could not effectively eliminate the semantic differences betw een the different modal data, we proposed a new retrieval method based on spar se coding Hash. The semantic differences between the lowlevel visual featur es and highlevel semantics were solved, and the effect of cross modal retr ieval was improved. Cross modal similarity retrieval by using sparse coding. Firstly, we used sparse coding to obtain salient features and implicit concepts of images and texts. Secondly, we mapped the latent semantic f eatures of learning to a common abstract space, and then we found correlation between features of the multimodal data by the iterative mechanism . Finally, we obtained the uniform Hash coding by the quantization of highleve l semantic abstract space.

In order to ensure the security of image effectively, a nd aiming at the deficiency of current image encryption algorithm, we designed a n image encryption algorithm based on combined chaotic syst em. Firstly, logistic chaotic system was used to process original plaintext image and scramble pixel position of imag e to carry out image block scramble processing, and then Henon chaotic sys tem was used to encrypt image pixel after block processing, thus realizing the p ixel value scrambling. The performance of image encryp tion was tested by simulation experiments. Test results show that, using the enc ryption algorithm, the correlation of adjacent pixels is small, and it has reliable transmission security. It can encrypt the image information, increase the ke y space, and improve the image of various anti attack ability.

In order to get better result of image classification a nd improve the efficiency of image classification, we proposed image classificat ion algorithm based on kernel principal component analysis and relevance vector machine (RVM). Firstly, a large number of images were collected to establish the image database, and features were extracted. Secondly, kernel principal compone nt analysis was used to select features and reduce dimension of image to reduce the number of image features and eliminate some small features. Finally, image c lassifier was constructed by training of releva nce vector machine, and 3 kinds of standard image databases were used to pe rform image classification experiments. The experimental results show that, for 3 kinds of standard image databases, the image classification accuracies of the proposed algorithm are more than 95%, which is much higher than that of oth er classification algorithms, and the image classification speed can meet practi cal requirements of the image.

We analyzed and constructed Thangka domain ontology to r ealize semantic annotation and retrieval based on Thangka image. We analyzed the classification systems of Thangka under the guidance of expert s in this field, and gave the related definitions and axioms of Thangka ontology, and defined the ontology concept, object attribute, instance and constraint con ditions, then constructed the Thangka domain ontolog y based on Protégé. Finally, we carried on the analysis of the con sistency to realize the semantic query based on the Thangka knowledge base , and further verified the rationality of the construction of Thangka domain ontology.

Aiming at the lack of personalized music recommendation and collaborative filtering method based on music information, t hrough the analysis of the user’s listening to music data and download data, co mbined with LDA(latent Dirichlet allocation) theme mining model, we proposed a recommendation algorithm based on the LDAMURE model. Experimental results show that, compared with collabora tive filtering algorithm based on user of music works and collaborative filterin g algorithm based on music attribute item, the LDAMURE algorithm can be more effecti ve to music users recommend music works of interest.

Based on the introduction of image entropy into the den sity peaks clustering algorithm to determine the information quantity of spectra l band, we proposed a method for density peaks clustering band selection based o n image entropy. By constructing the measuring score of bands signif icance， we solved the problem of the band selection in the traditional density peaks clustering method without considering the info rmation quantity of the bands. The experiment al results show that the classification accuracy of the proposed method increase s by an average of 2.12% than that of the traditional density peaks clustering method.

The concept of intraclass dispersity and interclass concentration was proposed based on the traditional information gain feature se lection algorithm. Combined with the traditional information gain algorithm, i t solved the problem of performance degradation caused by ignoring the distribut ion of the characteristic items and improved the efficiency of the information g ain algorithm. The improved feature selection algorithm was applied to the spam filtering experiment. Compared with the traditional feature selection algorithms under different classifiers, the experimental results show that the improved fe ature selection algorithm has better performance.

Aiming at the disadvantages of current task scheduling alg orithms in distributed system, such as node load imbalance and low resource util ization ratio, we proposed a novel task scheduling algorithm in distribu ted system based on load balancing. Firstly, the rese arch status of current task scheduling optimization algorithm in distributed sys tem was analyzed. Secondly, realtime performance of the node was estimated, a nd assigned different tasks according to the estimated results. Finally, the s imulation experiment was compared with other algorithms. Experimental res ults show that compared with the current classical task scheduling algor ithms in distributed system, the proposed algorithm reduces task completion ti me, makes load of each node more balanced, and improves the utilization ratio of node resource.

We proposed a forecasting model of shortterm unoccupi ed parking space by using the method of combining wavelet transform with extr eme learning machine(ELM). Firstly, the time series of the effective parking spa ce were decomposed and reconstituted by wavelet function. Secondly, ELM was used to forecast the decomposed time series respectively. Final ly, the prediction results of each neural network were combined to get the final prediction results. The prediction instance results show that the method shorte ns the training time and improves the prediction results.

Aiming at the problem that cloud computing resources we re limited, and the solving efficiency of exhaustive search algorithm was low, w e proposed a cloud computing service deployment optimization method ba sed on improved particle swarm algorithm. Firstly, the problem of clou d computing service deployment was analyzed, and it was transformed into a mult iobjective combinatorial optimization problem, and the corresponding mathemati cal model was established. Secondly, the particle swarm algorithm with global se arching ability was used to solve mathemati cal model, and the slow convergence rate of standard particle swarm algorithm an d premature convergence were improved. Finally, the feasibility was verified by simulation test. Experimental results show that the proposed method can quic kly find the best scheme for cloud computing service deployment.

We calculated the electronic properties of the crystal structures of multiferroic materials BiNi_xFe_1-xO_3(x=0,0.125,0.167,0.25,0.5) using the firstprinciples based on de nsity functional theory. Calculation results of band structures, Mulliken charge s and spin magnetic moments show that partial doping of Fe ions by Ni ions can m ake the system change from antiferromagnetic order to local ferrimagnetic order, and the total spin magnetic moments increase with the increase o f concentration of Ni doping. Ni doping significantly i nhibits the magnetic moment of Fe ions at specific sites, this is due to the electronics states of minority spin of Ni-e_g orbitals occupied by 50% and the superexchange interaction betwe en Fe and Ni ions.

Based on the cavity quantum electrodynamtics (QED) syst em, two atoms were simultaneously sent through one vacuum cavity field to realiz e the fusion of two W states based on resonant interaction between the two atoms a nd the cavity field. One of the two atoms was from the Natom W state, and the other one was from the Matom W state. The cavity field was detected after the atoms and the cavity fie ld was resonant. The results show that if only one photon in the cavity is detec ted, an (N+M)atom W state can be genera ted with some probability. If no photon is detected in the cavity, the two atoms are detected. If only one excitation is detected between the two atoms, an (N+M-2)atom W state can be generated with some probability. If no excitati on is detected between the two atoms, the left (N-1)atom W state and ( M-1)atom W state can be refused by the same scheme.

We obtained the ground states geometry, dipole moment and total energy of C₅H₈O under different intense electric fields rangin g from -0.006 to 0.006 by using density functional theory DFT/B3P86 at the 6-3 11++G(-d,p-) basis set level. The calculation results show that the geomet ric configuration of C₅H₈O molecule is affected by the electric field intensity . The dipole moment of the molecule increases with the increase of electric fiel d intensity. The total energy of the molecule is -271.481 6 as F=0. The tota l energy of the molecule decreases with the increase of the electric field intensity. The total energy of the molecule reaches the maximum -27 1.475 2 as F=-0.006. The total energy of the system decreases with the incre ase of the electric field intensity.

We presented a circuit structure and realization me thod of the currentcontrolled selftracking filter which based on the design of LC ladder network. The input voltage signal was firstly processed by the amp lifying circuit, and then the frequency selftracking circuit was composed of a mplitude limiting circuit, shaping circuit and bro adband frequencycurrent conversion circuit. The amplified voltage signal was c onverted into the current signal which was used as the bias current control end of the log domain filter circuit to adjust the cutoff freq uency or central frequency of the filter. Therefore, frequency of the fi lter could automatically track the input signal frequency. Simulation experiment results show that the highest central frequency of the bandpass filter and lowpass filter is 30 MHz, and the tracking ra nge of input frequency is from 1 MHz to 30 MHz. Simulation results verify the effectiveness and feasibility of the proposed method.

Using density functional theory B3LYP, we investigat ed the chiral transition mechanism of the leucine (Leu) molecule in the non\|confined m onomer and water at the level of 6-311+G(d,p) basis sets. We drawed a Leu mo lecule chiral transition path reaction potential energy surface by finding struc tures of the extreme value points including the transition st ates and intermediates, and analyzed the geometric and electronic structure prop erties of extreme value points. The results show that the hydrogen atom o n the chiral carbon atom of SLeu molecule can transfer to the other si de of the carbon atom via the oxygen atoms of carboxyl atoms as a bridge, and ach ieve the chiral transition of Leu molecule from Stype to Rtype. On t his path there are four intermediates and five transition states. The maximum re action energy barrier is 57235 9 kJ/mol, which comes from the first transition state TS₁-S-Leu&1H₂O-1. The maximum reaction energy barrier of the first transition state TS₁-S-Leu of monomer Leu molecule is 145452 7 kJ/mol. As a result, a single water molecule as the H transfer bridge can reduce the reaction barrier.

We studied the mechanism of interaction and binding con stant between Eu(Ⅲ) complex with methaerylic acid8hydroxyquinoline （Eu(MA)2(hq)） and her ring sperm DNA by using spectroscopic methods, viscosity and thermal denatur ation method of DNA. Results show that the absorption peak has obvious hypochrom ic effect, but red shift phenomenon of peak is not obvious after the complex add ing herring sperm DNA. The complex can quench the fluorescence of neutral redDNA system. The binding ratio of n(Eu(MA)2(hq))∶n(DNA) is 1, and the binding cons tants are K₂₀= 5.91×10³ L/mol, an d K₃₅=7.70×10³ L/mol. The thermodynamic functions between complex and herring sperm DNA are Δr H_m=1.34×10³ J/mol, Δr G_m=-2.12×10⁴ J/mol, and Δr S_m=76.41 J/(mol·K) . The relative viscosity and melting point of herring sperm DNA ar e increased with the addition of complex, and the interaction mode of the Eu(MA)₂ (hq) with herring sperm DNA belongs to intercalation.

Using the ONIOM methods by combining quantum mechanics and molecular mechanics, we studied the reaction mechanism of the chiral transition of lysine (Lys) molecules conf ined in the armchair single walled boron nitride nanotube (SWBNNT). Using atom centered density matrix propagation (ADMP) molecular dynamics methods, we studied Lys molecules in the SWBNNT(5,5) dynamic reaction path in the inlet and outlet of the potential energy surface in chiral transition reaction channel, and gave images of the microscopic dynamic reaction of intermediates and products. The results show that with the decrease of diameter of nanotube, the bond angle between the skeletal carbon atoms of Lys molecules confined in nanotubes increases obviousl y, and the distance between H and amino N on chiral carbon gradually becomes sma ller. The chiral transition of Lys molecules is achieved by a two\|s tep elementary reaction in SWBNNT(5,5), whereas it is achieved by the three\|ste p and four\|step elementary reactions in SWBNNT(6,6) and SWBNNT(7,7), respective ly. The free energy barrier of the rate\|determining step of Lys molecule chiral transition reaction is reduced to a minimum value of 190.1 kJ/mol in SWCNT(5,5) . The energy barrier of the rate\|determining step is similar to that of bare reaction in SWBNNT(7,7).

Based on the fluorescence quenching effect of CdTe quan tum dots by amaranth, we used fluorescence quenching method of CdTe quantum dots to detect the concentration of amaranth, and analyzed its reaction mechanism. T he results show that the linear range of detection is from 4.14×10^-6 mol/ L to 9.10×10^-5 mol/L, and the minimum detection limit is 4.81×10^-9 mol/L. The fluorescence quenching constant is 1.91×10¹² L/(mol·s) , the slope of SternVolmer curve at high temperature is lower than that of l ow temperature, and UVVis absorption spectra show that the process is a static quenching process. According to thermodynamics calculation, the thermodynamic p arameters Δ H=1.063 kJ/mol, Δ S=91.36 J/(mol·K) and Δ G=-26.62 kJ/mol, i.e., and the process is an endothermic and spontaneous proc ess.

Using Dongmu 70 ryegrass seedlings as experimental mate rial, we investigated its physiological response mechanism under the single artificia l simulated freezingthawing stress (10,5,0,-5,0,5,10 ℃) and combined with NaH CO₃ stress. The results show that the content of proline and malondialdehyd e (MDA) and the activity of catalase (CAT) and superoxide dismutase (SOD) in the leaves of ryegrass seedlings increased firstly and then decreased significantly under a single freezingthawing stress, the activity of peroxidase (POD) increa sed firstly and then decreased slowly, except for CAT, other physiological index es reach the maximum value at -5 ℃, which compared with other temperatures ther e are significant differences (P<0.05). Under the condition of combined stre ss treatment, physiological indexes show the rule of combined stress>single stre ss>control. The mass ratio of protein in the leaves of ryegrass seedlings raech the maximum value at 0 ℃, and combined stress and single freezingthawing gro up are higher than those in control group. Thus, the ryegrass seedling under the single freezingthawing stress and combined with NaHCO₃ stress can rapidly i mprove the activities of antioxidant enzymes and the mass ratio of osmotic adjus tment substances to alleviate damage caused by stress, and the effects of combin ed stress on seedlings are greater than the single stress.

We investigated the effects of adding ionic state, complex state and oxidation state of iron o r manganese on generation of H₂O₂ and degrada tion of sodium dodecyl benzene sulfonate (SDBS) in natural water biofilm systems under illumination via the simulation experiment, and analyzed the mechanism of degradation of SDB S in the system. The results indicate that different forms of iron or manganes e can promote degradation of SDBS in the system, and the concentration of H₂O ₂ decreases firstly and then increases in the system. Effects of different for ms of iron or manganese are small. The effect of ionic state is relatively str ong, and the effect of oxidation state is relatively week. The effect of adding iron is more obvious than that of adding manganese.