By using the group theory and congruence theory, we calculated the number of homomorphisms between a class of metacyclic groups, which were normal cyclic groups of the order m expanded by cyclic groups of the order 4, and gave the number of endomorphisms of the metacyclic groups. The results verified that the metacyclic groups satisfied the conjecture of Asai and Yoshida.

We constructed some special homotopy categories composed of Dingprojective modules, and gave some properties of them. In addition, if ring R satisfied certain conditions, we gave a stable t-structure and its corresponding right Recollement in the homotopy categories.

Using the method and principle of fuzzy sets, we gave the concept of category Set(fL) of L-flou sets, and proved that the category Set(L )  of L-fuzzy sets was isomorphic to the category Set(fL ). According to the isomorphism relationship between the category Set (L ) and the lifting category Set_L(S H) of sheaf structures on the sets category, we obtained the category Set(fL ) was isomorphic to the category Set_L(S H).

By combining the hesitant fuzzy set and bipolar soft set models, the author gave a new concept of bipolar hesitant fuzzy soft sets, as well as some operators on the bipolar hesitant fuzzy soft sets, such as complement, “AND”, “OR”, extended union, extended intersection, restricted union and restricted intersection. By means of reduct bipolar fuzzy soft sets and level cut sets, the author proposed an adjustable method to bipolar hesitant fuzzy soft sets based on decision making, and gave the method of making the best choice.

We considered the first exit time problem in diffusion model of chemical reaction. Firstly, we transformed the problem of stochastic differential equation into a boundary value problem of partial differential equation. Secondly, we used the coordinate transformation and asymptotic expansion of singular perturbation  to obtain the first order approximate solution. Finally, we gave the results combined with the asymptotic method of Laplace integral.

The author gave  an anisotropic optimal perfectly matched layer method (PML) with a small parameter for solving the 
timeharmonic scattering problems. A continuous vector field was defined outside a rectangle domain by using  the idea of the shortest distance, and  the complex coordinate stretching transformation was carried out along the direction of the vector field. The calculation  of the optimal PML method for scattering problem was no longer dependent on the thickness of the PML  layer by introducing  a small parameter ε₀ into the absorbing function. The results show  that the anisotropic optimal PML solution converges exponentially to the solution of the original scattering problem if only the parameter ε₀ is sufficiently small. The results of numerical experiments verify the effectiveness  of the proposed method.

We considered the asymptotic structure and regularity of the timedependent attractors for the Plate equations with coefficients dependent time. Based on the existence theorem of the timedependent global attractors, we proved the asymptotic structure of the timedependent attractors, and obtained the regularity result of timedependent attractors.

Aiming at the limitations of intuitionistic fuzzy member in ranking, we proposed an intuitionistic fuzzy soft decision making method by improving the classical score function of intuitionistic fuzzy numbers, and using the expected score functions and its induced partial orders. An illustrative example shows that the proposed method generalizes the complementary operation of intuitionistic fuzzy soft sets, and can effectively solve relevant decision making problems.

We extended the nuclear design of  combinatorial design theory, and considered a more general  group divisible nuclear design. By using the method of direct construction and recursive construction, we  solved the existence problem of the group divisible nuclear design with block K₄-e and equal size group,  and proved that there existed a group divisible (K₄-e)nuclear design of type gⁿ for n≥3, g≥1.

Firstly, by using the kernel smooth method, we studied the estimation of the total quantile difference with lefttruncated and rightcensored (LTRC) data, and obtained the large sample properties of the smoothed estimators of  quantile difference with LTRC data. Secondly, in the sense of mean square error, we proved the estimation efficiency of the smooth quantile difference was higher than that of the product limit quantile difference with LTRC data. Finally, we analyzed the effect of various bandwidths with Gaussian kernel function on the improved estimation efficiency of product limit quantile difference through numerical simulations.

We established a statistical inference model of the component lifetime for the doubly typeⅡ censored cases  based on the theory and methods of Signature. By using the maximum likelihood estimation and its asymptotic theory, we derived the analytical expression for the point estimation and asymptotic confidence interval estimation of the component lifetime distribution parameters and  obtained the numerical solutions of the relevant estimation by three optimization algorithms. Simulation results show that the likelihood function statistical inference model based on Signature is effective for inference of the component lifetime under the doubly type Ⅱcensored cases.

By using the method for handling homological dimension in homological algebra and relative homological algebra, the author proved that the (left) X-Gorenstein global projective dimension of a semiprimary ring was equal to the supremum of the set of (left) X-Gorenstein projective dimensions of all simple modules, and gave some related applications.

The author considered the approximate controllability of a class of coupled degenerate parabolic equations with the gradient terms. When the control function only acted on one equation, the author proved the approximate controllability of the equation by using the unique continuation of the adjoint equations.

By using two variables (G′/G,1/G)function expansion method, and with the help of scientific computing software Mathematica, we obtained exact traveling wave solutions of hyperbolic function form, trigonometric form, rational function form for the timespace fractional nonlinear Kuramoto-Sivashinsky  equation. The results show that the (G′/G,1/G)function expansion method is simple and effctive, and is suitable for solving exact traveling wave solutions of other fractional nonlinear partial differential equations.

Firstly, based on the  cloud computing application model, we proposed a double\|layer cache technology which could efficiently utilize the cloud storage architecture. By establishing the distributed  cache between the client and the server, it could  effectively avoid users frequent access to remote data and build lightweight clients for users, which solved the problem that current geoscience data visualization software occupied a large number of user’s local storage capacity, and adapt to the rapid development of mobile devices. In the mean time, the server side  also avoided multiple access to the cloud storage file system, reducing a lot of data retrieval and loading time. Secondly, we  proposed an association rule last successor access prediction algorithm, according to user’s historical access records, the association rules were used to mine the user’s access mode, and predict their access behavior. Then the data was loaded in advance, the cache hit rate was improved, we solved  the problem of constantly moving region of interest and changing the rendering data frequently in the process of visualization, our system could effectively deal with the user’s multiple  access patterns case and improve the accuracy of the prediction. 
Experimental results show that the cloud storage architecture  significantly reduces the  local resource consumption. The accuracy rate of the  access prediction algorithm is 47.59% in the worst case, the average accuracy rate is 913%, and the average cache hit rate of distributed cache is  9561%, which can effectively support the rapid visualization of large-scale seismic data in the cloud.

We proposed an iris quality evaluation algorithm based on morphology and gray distribution of gray histogram. Through the sharpness, live detection based on binary morphology, region validity determination based on gray distribution in the gray histogram, and squint level based on ultraboundary deviation degree and strabismus eccentricity degree, it solved the problem of the low effective iris survival rate caused by  stringent discriminant index in continuous collection of sequence iris quality evaluation. While removing the unqualified images, the  proposed algorithm preserved iris which could be identified as far as possible, so as to improve the  effective iris survival rate, and time consumption was relatively short.

Aiming at the contradiction between watermark visibility and antiattack robustness in the current image watermarking algorithm, we designed an image watermarking algorithm based on singular value decomposition (SVD) and particle swarm optimization (PSO) algorithm to obtain the ideal image watermark effect. Firstly, the image of original carrier was transformed by scale invariant feature, the watermark embedding area was selected, and the watermark embedding region was divided into multiple subblocks. Secondly, the singular value decomposition algorithm was used to deal with the subblocks, and the singular value matrix was established, and the watermark and the subblock were fused into the watermark matrix. Finally, the particle swarm optimization algorithm was used to determine the intensity of watermark embedding. The simulation experiment results of image watermarking show that the algorithm can get the ideal watermark embedding effect, the wa
termark is invisible, the human eye cannot feel the effect of the watermark embedding, the watermark is robust to various attacks, and the overall performance of the watermarking algorithm is much better than other current image watermarking algorithms.

Aiming at  the diversity of multisensor data, we proposed an improved data fusion algorithm. Firstly, the wavelet technology was used to eliminate the Gaussian white noise of collected data and compress the data. Secondly, the processed data was stratified, and the coefficients were filtered by Kalman. Meanwhile,  the data was reconstructed by the Mallat fast reconstruction algorithm. Finally, the signaltonoise ratio (SNR) was calculated by maximum and minimum degree of close to the sensor data, and data fusion was carried out by SNR. Experimental results based on multisensor actual data show that the data fusion algorithm is superior to simple weighted data fusion, wavelet data fusion and Kalman filtering fusion algorithm in stability.

Using a spelling correction model based on keyboard distance and dependency parsing, the nonword errors generated in the process of text input were solved. The final spelling correction model was constructed by considering three parts: the proximity weight, the dependency weight and the word frequency. The model was validated in the Brown corpus, the Gutenberg corpus and the Inaugural corpus. The experimental results show that the model can be effective for nonword error correction.

Aiming at the problem of slow mining efficiency and low accuracy in traditional clustering algorithm, we proposed a multilevel k-means clustering algorithm based on minimum spanning tree, and applied to data mining. Firstly, we analyzed the 
data types of the clustering samples and designed the clustering criterion function according to the analysis results. Secondly, we divided the sample data by the minimum spanning tree, and selected the initial clustering center. The data space of the sample was divided into rectangular unit,  the sample object data was calculated, descended and selected in the rectangular unit, the effective initial clustering center was obtained to reduce the time spent in data mining. The experimental results show that, compared with the traditional algorithm, the proposed method can quickly and accurately excavate the data, and the efficiency of mining is increased by about 50%.

Using the maximum algebra method frequently\|used in discrete event dynamic systems, we considered the dynamic behavior of the network process data on a mutifunction vehicle bus (MVB). A mathematical model based on the process data communication on MVB  was constructed, the nonblock condition of MVB network process data communication was analyzed and verified by mathematical calculation and simulation experiment under the condition of introducing
 periodic input control, and the possible blocking problem in process data communication was solved. The experimental results show whether process data transmission system is blocked depends on the value of the time matrix of process date and the time interval of bus manager reading main frame on the communication memory, the value of the latter is greater than or equal to the maximum value of the former, the whole network will enter the periodic steady state with a period of 1, 
which effectively improves the reliability of process data communication of the MVB network.

Firstly, based on the theory of the computational geometry and graph coloring, the author analyzed and solved the problem of selforganizing network coverage and channel allocation by establishing the optimization model of selforganizing network (Ad Hoc) under the assumption of different constraints in the region, and using the MATLAB software for programming and system simulation. Secondly, combined with the idea of the probability theory and mathematical statistics, the problem of the invulnerability of network topology was quantitatively analyzed. The simulation and experimental results proved the validity of the model and the feasibility of the control method.

Aiming at the problem of long timeconsuming and poor realtime of large data images classification, using the advantages of cloud computing technology to obtain the ideal classification results of large data images, we proposed a large data image classification mechanism based on Hadoop platform. Firstly, a large number of images were collected, the image database was constructed, and the effective features of the image classification were extracted. Secondly, based on the Hadoop platform, the Map function was used to subdivide the large data image classification problems, and subproblems were classified and solved by multiple nodes parallel and distributed, and the corresponding image classification results were obtained. Finally, the Reduce function was used to combine image classification results of subproblems, and the simulation test of large data image classification was realized  by using VC++60 programming. Test results show that the proposed classification mechanism can overcome the drawbacks of current image classification mechanism,  greatly shorten  the time of image classification, and the classification speed can adapt to online requirements of large data image classification, and the overall effect of image classification is obviously superior to the other image classification mechanisms.

Aiming at the problem of the image segmentation of farmland green crop plants under outdoor, we proposed an image segmentation method for farmland green crop plants which based on G-R color feature of green crop plants, combined with the Otsu method for the maximum variance between clusters and area threshold segmentation. The algorithm solved the difficult problem of segmentation of farmland green crop plants and background in the farmland images under the conditions of uneven illumination and complicated soil of outdoor. The experimental results show that the method is not only insensitive to crop, soil and light changes, but also can eliminate the effects of the shadow part of image, compared with the color indexing method EXGOtsu and RGB algorithm (G>R and G>B), the segmentation effect of the method is better.

We combined the saving algorithm with the genetic algorithm to solve the optimization problem of communication network planning. The algorithm integrated the fast convergence characteristics of the saving algorithm, and the various design cost and practical communication restrictions of the communication network can be fully considered through the genetic algorithm. The experimental results show that, compared with the traditional greedy algorithms or minimum spanning tree methods, the algorithm has higher computing speed and better feasible solutions.

The quantum entangled degrees of entangled states decreased  with the transmission distance increasing or external interference. The entangled degree was reduced or no longer entangled under the decoherence effect of interaction between light and environment. We designed a set of  one\|dimensional photonic crystals when the entangled light  of two-photon or three-photon passed through photonic crystal, and the superimposed parameter was 003—098, the entangled degree E was 0.8—1, so that the quantum  entangled  state could be transported for a  long distance to achieve quantum communication better.

We gave the mathematical expression of analytical solution of Doppler spectra of laser backscattering from rotating Lambertian cones, and compared the analytical solution with the numerical solution. The results show that with the increase of the calculation accuracy of numerical solution, the difference between the numerical solution and the analytical solution becomes smaller,  the analytical solutions and the numerical solutions can be mutually validated.

Using the B3LYP method of density functional theory, we optimized the geometric configuration of Ala molecules under implicit solvent, under the same theoretical method, we calculated the orbital wave function and charge decomposition analysis (CDA) of the Ala system fragments under the implicit water and methanol solvent. The results show that the calculated results of the extended charge decomposition analysis (ECDA) of CH₃ fragements are 0.001 3, and the results of the ECDA calculation of the NH₂ fragements are 0.000 8 under implicit methanol solvent and implicit water solvent, 
the quantitative results are basically consistent. Comparison of r_i of the CDA calculation results of CH₃ and NH₂ fragments, the qualitative results are basically consistent.

Based on the Becke method and the Hirshfeld method, we calculated the atomic contribution of the valine molecular orbits. 
The  results show that the qualitative results of the analysis of high occupied orbit by the Becke method and the Hirshfeld method are basically consistent,  and the quantitative results are  slightly different.  The qualitative results of analysis of virtual orbit are  not completely consistent, and the quantitative results are obviously different.

The gold nanoparticles with diameter of 50—60 nm were prepared by the optimized Turkevich method. The  trace amounts of salbutamol molecules with  concentrations of 10^-3—10^-5 mol/L were detected by surface-enhanced Raman scattering spectra. The results show that the minimum  detection limit is 5×10^-5 mol/L. In the range of 100—750 μmol/L, the Raman intensity and  concentration have a good  linear relationship, and  the correlation  coefficient R²=0.996 57, but  the Raman intensity and the concentration does not satisfy the linear relationship in a wider  concentration range. 
The trace amounts of salbutamol molecules can be detected by surface-enhanced Raman scattering method based on gold nanoparticles in real time and rapidly.

Using MP2/6-311++G(2-df,pd-)//B3LYP/6-31+G(d,p) double theory and SMD model method for self consistent reaction field (SCRF) theory, we studied the optical isomerism process of two stable conformation lysine molecules based on amino nitrogen as hydrogen transport bridge in water liquid phase environment. The calculation of potential energy surface shows when the two and three water clusters are used as hydrogen transport medium, the ratedetermining step Gibbs free energy barriers of conformation 1 optical isomer are 11602,11271 kJ/mol, respectively. The ratedetermining step Gibbs free energy barriers of conformation 2 optical isomer are 11027,11429 kJ/mol, respectively. When hydroxyl radical and water molecule chain are used as hydrogen transport medium, the Gibbs free energy barriers of conformation 1 and 2 damage induced by hydroxyl radical pumping hydrogen are -5306,-5605 kJ/mol, indicating no barrier reaction. The results show that under the water liquid phase environment, lysine molecules can be slowly optical isomers, and hydroxyl radicals can quickly cause lysine damage.

Using bagasse as biological template, the hierarchical porous structure ZnO was prepared by morphgenetic transformation method. The ZnO samples were phaseanalyzed by Xray diffraction (XRD), scanning electron microscopy (SEM) and specific surface area test method, and the gassensing experiment was carried out. The results show that the samples obtained after calcination is pure wurtzite hexagonal ZnO with bagasse template completely removed. The surface of ZnO samples show honeycomblike structure, which is formed by the interconnection of porous channels. The response of hierarchical porous ZnO reaches a maximum of 24.5 at 340 ℃ for 100 cm3/m3 acetone, about 2.23 times higher than that of
 conventional templatefree ZnO. Response time and recovery time are 6 s and 1 s, respectively, shorter  than that of the conventional templatefree ZnO, and it has good gas selectivity.

A series of cobalt based oxide thermoelectric materials Ca₃Co₂O₆ and Ca_2.85M_0.15Co_2-yCu_yO₆ (M=A
g,Er; y=0,0.1,0.2) were prepared by solgel method and atmospheric sintering technology. The phase composition and morphology of the samples were studied by Xray diffraction (XRD) and scanning electron microscopy (SEM). The electrical conductivity and Seebeck coefficient of the samples were measured in the range of 300—1 000 K. The effects of different doping elements on the thermoelectric properties of the composite were investigated. The results show that all the materials prepared are single phase with compact structure, and the different codoping elements can enhance the thermoelectric p
roperties of the materials, when the doping amount of Ag⁺ and Cu^2+ is 015 and 02, respectively, the best thermoelectric properties can be obtained. The power factor of  Ca_2.85Ag_0.15Co_1.8Cu_0.2O₆ is 71 μW/(K2·m) at 965 K.

A self-emulsifying epoxy resin film\|forming agent was prepared by using epoxy resin as hydrophobic group and polyethylene glycol as hydrophilic group under the action of boron trifluoride ethyl ether. The film-forming agent was analyzed by infrared spectrum, scanning electron microscope and laser particle size analyzer. The results show that film-forming agent contains hydrophilic hydroxyl and long chain epoxy groups. And the particle size of emulsion after self-emulsifying is 70—150 nm. The self-emulsifying film-forming agent has good stability, and its storage stability can be more than 30 d. The emulsion can remain stable after centrifugation for 3 h.

We prepared reduced graphene oxide/thionin composite materials, and modified them onto the surface of the glassy carbon electrodes. There were two active sites in bovine serum albumin molecule, and the characteristics of the chiral enantiomers were different from their active points. We immersed the modified electrode in bovine serum albumin, and used for the selective recognition of tryptophan (Trp) enantiomers (D/L-Trp). The preparation and reactive process of the electrode were characterized by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). The results show that under the same experimental conditions, the chiral surface shows different electrochemical signals for D/L-Trp, the reaction between the chiral surface and D/L-Trp has stereoselectivity, and is more effective with L-Trp.