By using Goswami’s method, we discussed the mean value problem of the composition of a class of arithmetic functions and the integral part function, and gave an asymptotic formula.

We gave some basic properties of the derivation algebra Der(A), generalized derivation algebra GDer(A), quasiderivation algebra QDer(A), centroid C(A), quasicentroid QC(A) and central derivation algebra ZDer(A) of a multiplicative BiHom-Poisson color algebras A, and proved that GDer(A)=QDer(A)+QC(A).

We considered the characterization problem of weighted right core inverses and weighted right pseudo core inverses over *-rings by 
using algebraic methods. Firstly, the concept of weighted right core inverse was introduced. Secondly,  three equations and right invertible elements were used to give its characterization. Finally, the definition and characterization of weighted right pseudo core inverse were given.

We considered the representation of the Drazin inverses of the sum for two matrices. For n-|th order matrices P and Q, the expression  of the Drazin inverse of the sum for two matrices P+Q was given by using the Cline formula and the properties of Drazin inverse under the conditions such as  P²QP²=0, P³QP=0, PQ³=0, PQ²P=0, P²QPQ=0, etc.

Under some conditions about corresponding principal eigenvalue of  linear operator, we prove the existence of nontrivial solutions and positive solutions of boundary value problem for the semipositive nonlinear Euler-Bernoulli beam equations with simply supported beam boundary condition by using the topological degree method and the fixed point theory.

We considered the effect of starvation-driven diffusion on the coexistence of a Holling-Ⅱ type predator-prey model under homogeneous Neumann boundary conditions. The eigenvalue theory was used to analyze the stability of semi-trivial solution under uniform diffusion and starvation-driven diffusion. By comparing the stability changes of semi-trivial solutions under two kinds of diffusion, we find that starvation-driven diffusion is conducive to the coexistence of species.

We considered  integral boundary value problem of a class of Riemann-Liouville fractional differential equations with multiple fractional derivative terms on infinite intervals. By constructing a new Banach space and using the nonlinear analysis theory, and under the condition that the nonlinear term satisfied the L¹-Carathéodory conditions, some conclusions  for existence and uniqueness of positive solutions to boundary value problems were obtained, and an example was used to illustrate the applicability and universality of the obtained results.

We considered the steady-state solutions of a B-D type predator-prey system with nonlinear cross-diffusion under homogeneous Dirichlet boundary conditions. Firstly, we analyzed the stability of trivial solution and semi-trivial solutions based on the spectral theory of linear operators. Secondly, the sufficient conditions for the existence of coexistence solutions were obtained by using the fixed point index theory in positive cones.

By using the time mapping principle, we prove the existence and multiplicity of positive solutions for the  boundary value problem with one-dimensional Minkowski mean curvature operator in the semipositive case of nonlinear terms and the nonlinear term is generalized from f(0)≥0 to f(0)<0.

Firstly, by using the fractional order concentration-compactness principle, we proved the compactness conditions for a class of nonlinear Kirchhoff equations with electromagnetic fields and critical Hardy-Littlewood-Sobolev term in the whole space to overcome the problem of lack of compactness conditions caused by unbounded regions and critical term in this equation. Secondly, combined with the symmetric mountain path theorem, we proved that the equation satisfied the mountain path structure, and proved the multiplicity of the solution to the equation by using genus theory.

We studied the asymptotic behavior of solutions for a class of  initial-boundary value problems of a semilinear parabolic equation with boundary degeneracy by using the methods of weighted energy estimates and constructing self-similar upper solutions. We obtained the global existence and blowing-up properties of solutions to the problem,  established Fujita type theorem, and characterized the quantitative relationship between the critical Fujita exponent and the degenerate diffusion term and the nonlinear source term.

We considered the convergence problem of the Jamison type weighted sums of extended negatively dependent (END) random variable sequences in a sub-linear expectation space by using the truncation method, and obtained the convergence of the Jamison type weighted sums of END random variable sequences in a sub-linear expectation space. We extended  almost sure  convergence of Jamison type weighted sums of END  random variable sequences  in probability spaces to sub-linear expectation spaces, and the Jamison theorem was generalized.

We  gave necessary and sufficient conditions for bounded linear operators and their operator functions to satisfy the property
 (UW_Π) by using the spectrum sets defined by topological uniform descent property, commonly used spectrum sets and some properties of operators themselves, and discussed  the perturbation problems of property (UW_Π).

Firstly, by using the power function method, we discussed the half-discrete Hilbert-type inverse inequality with non-homogeneous kernel K(n,x)=G(n^λ1x^λ2)(λ₁λ₂>0), gave equivalent conditions for the best half-discrete Hilbert-type inverse inequality and the relationship  between the parameters. Secondly,  as an application, we gave  the equivalent operator expressions and some special cases.

In order to study the effects of human to human diffusion, spatial heterogeneity and different concentrations of Vibrio in static water source environment on cholera transmission, we established  a partially degenerated reaction-diffusion cholera model. Firstly, we defined the basic reproduction number R₀ of the model. Secondly, the global threshold dynamics of the model was determined by the sign of R₀-1. Finally, we discussed  the effects of key model parameters on R₀ through numerical simulation experiments. The results show that moderate urbanization is beneficial to disease control.

The full parabolic attraction-repulsion chemotaxis system defined on Ω was considered. By setting appropriate an auxiliary function and using the differential inequality technique, the differential inequality of the auxiliary function was derived, and the lower bound of the blow-up time was obtained.

Aiming at  the problem of few-shot relation extraction,  we proposed an induction network based on attention mechanism. Firstly, we used  dynamic routing algorithm in induction network to learn the class representation. Secondly, we proposed instance-level attention mechanism to  adjust support set and obtain high-level information between support set and query set samples, thereby obtaining  the support set samples that were more relevant to the query instances. The proposed  model effectively solved  the problem of how to extract relationships when the training data was insufficient. The experiment was conducted  on the few-shot relation extraction FewRel dataset, and the experimental results showed an  accuracy rate of (88.38±0.27)% in the 5-way 5-shot case,  (89.91±0.33)% in the 5-way 10-shot case, (77.92±0.44)% in the  10-way 5-shot case,  (81.21±0.39)% in the  10-way 10-shot case. The  experimental  results show that the model can adapt to tasks and outperforms other comparative  models, achieving better results than comparative  models in few-shot relation extraction.

Aiming at the problem that autoencoder  only extracted features from  the content information contained in a single data, ignoring 
the structure information of data, we proposed a deep graph clustering network based on heterogeneous fusion and discriminant loss. Firstly, the heterogeneous information obtained by two autoencoders was fused, and the problem of information loss was solved when a single autoencoder was used to extract features. Secondly, the discriminant loss function was designed in the clustering training module based on the consistency of distribution within the same cluster, so that the model could be trained end-to-end, and avoiding the mismatch between the feature extraction and the assumptions of the clustering algorithm in the two-stage training methods. Finally, experiments were carried out on six commonly used datasets to verify the effectiveness of the proposed method. The experimental results show that compared with most existing deep graph clustering models, the proposed method  significantly improves the clustering performance on both non-graph and graph datasets.

Aiming at the problem of  the small sample size of high-resolution remote sensing images and  traditional optimized support vector machine (SVM) algorithms easily falling into local optima and slow optimization speed, we  proposed an algorithm based on deep transfer learning and lion swarm optimization SVM (LSO-SVM) to classify remote sensing image scene. Firstly, after enhancing the image through adaptive contrast,  color aggregation vectors were used to extract image color features. Secondly, three kinds of pretrained networks were used to extract the transfer learning depth features of images. Finally, the manually extracted image features and the features obtained using three pretrained networks were fused by using a series of feature fusion methods, and inputted them into LSO-SVM for image scene classification. The results show that the algorithm solves the problems of difficulty in deep learning training in small sample situations and the tendency of traditional optimized SVM algorithms to fall into local optima and slow search speed. Under 80% training conditions, the classification accuracy of UCM Land-Use and RSSCN7 datasets reaches 99.52% and 98.57%, respectively.

We solved the problem of low accuracy in car window recognition of the original YOLOX-S model by introducing deformable convolutional neural networks and Focal loss function (Focal loss) to the YOLOX-S model. Firstly, by introducing deformable convolutional neural networks into the backbone feature extraction network of the YOLOX-S model, offsets were introduced for each sampling point in the convolutional kernel to facilitate the extraction of more representative information from the original image, thereby improving the accuracy of car window recognition. Secondly, using Focal loss instead of binary cross entropy loss function in the original model, Focal loss could alleviate the impact of imbalance between positive and negative samples on training, and it paid  more attention to difficult samples during the training process, thereby improving the  recognition performance of the model for car window targets. Finally, in order to verify the performance of the improved algorithm, 15 627 images were collected and annotated for training and validation in the experiment. The experimental results show that the average target accuracy of the improved car window recognition algorithm increases by 3.88%.

Aiming at the problem of high complexity in mask representation in the field of instance segmentation, we proposed a new mask representation method for instance segmentation, which used three repsesentation units that did not rely on any prior information  to represent and predict mask, and restored the mask in the form of nonlinear decoding. This method could significantly reduce the representation complexity and inference computation of image instance masks.   Based on the representation method, we constructed an efficient single-shot instance segmentation model. The experimental results show that compared to other single-shot instance segmentation models, the model can achieve better performance while ensuring that the  time cost is basically the same. Additionally, we embed the representation method with minimal modifications into the classic model BlendMask to reconstruct attention maps. The improved model has a  faster inference speed compared  to the original model, and the average accuracy of the mask is improved by 1.5%, indicating that the  representation method has good universality.

Aiming at the problem that it was difficult to achieve high-precision and high frame rate tracking under limited computing resources, we proposed a lightweight  siamese network target  tracking algorithm based on ananchor free.   Firstly, the modified lightweight network MobileNetV3 was used as the backbone network to extract features, and reduced parameters and computation of the network  while maintaining deep feature expression capability. Secondly, for traditional cross-correlation operation, we proposed deep cross-correlation module for graph cascading optimization, which highlighted important information of target features through rich feature response graphs. Finally, feature sharing was used  to reduce parameters and computation to improve tracking speed in the anchor classification regression prediction network. Comparative experiments were conducted on two mainstream datasets OTB2015 and VOT2018, the experimental results show that the algorithm has a significant accuracy  advantages compared to  SiamFC tracker, and is more robust in complex tracking scenes. At the same time, the tracking frame rate can reach 175 frames/s.

Aiming at the problem that existing ensemble clustering algorithms usually used K-means algorithm as the base clustering generator, although it could ensure the diversity of clustering members, it ignored that poor base clusterings might cause terrible disturbance to the final clustering result, we proposed a two stage ensemble algorithm based on clustering quality. Considering that K-means algorithm ran efficiently, but the clustering quality was relatively rough, firstly, we proposed to  use K-means algorithm to generate base clustering members in the generation stage, and then  selected clustering members with both high quality and strong diversity through  group aggrement measure to form candidate ensemble. Secondly, the information entropy knowledge was futher applied to construct the weighted-clustering co-association matrix in the ensemble stage. Finally, the final clustering result was obtained by using consensus function. Three indexes were used for comparative experiments on ten real datasets, and the experimantal results show that the algorithm can effectively improve the accuracy of clustering results while maintaining good robustness.

In order to improve the accuracy of short text semantic similarity measurement, we designed a short text semantic similarity measurement algorithm based on a hybrid machine learning model. Firstly, we preprocessed the short text, constructed a word vector model of the short text based on the hybrid machine learning model, and extended the  features of the short text. Secondly, we  combined the various metric features of the short text, implemented dimensional reduction on the various metric features. Finally, we constructed an ensemble learning  model to calculate the semantic similarity results and achieve the  semantic similarity measurement. We tested the performance of the method by using the “Quora Question Pairs” competition dataset, the test results show that the accuracy of the  method is high, the logarithmic loss, and the measurement mean square error are both low, indicating that the similarity measurement accuracy of the method is high.

Aiming at the problem of equipment heterogeneity and the change of Bluetooth beacon nodes in indoor location based on Bluetooth fingerprint, we proposed an indoor location algorithm for heterogeneous devices and environmental changes. Firstly, we used Procrustes analysis method to standardize the received signal strength, and used kernel extreme learning machine (KELM) to model the standardized fingerprint database to reduce the signal strength differences caused by the differences of users’ mobile terminals. Secondly, when the access point (AP) signal changed, the access point signal was recalibrated by Gaussian process regression (GPR), and the fingerprint database was updated to eliminate the positioning error caused by the weak signal, position movement or environmental change of the access point. Test analysis results show that the algorithm can effectively overcome the impact of heterogeneous equipment, and better adapt to the environmental changes.

Aiming at the problem that the control of link load was affected by the search space of the Internet of Things, a small  search space could reduce the load balancing degree， we proposed a load balancing control method of the Internet of Things  link based on  improved genetic algorithm. Firstly, the frequency band transmission model of the Internet of Things link was constructed, and tap interval sampling was used to control the transmission of the Internet of Things link, the frequency band model of the Internet of Things link was established  to obtain the balanced scheduling function, and the frequency band was integrated to complete the load balancing configuration. Secondly, we added  fractional interval equalization to design the link, used the frequency band allocation principle to obtain the frequency band matching probability, adjusted the tap value of the equalizer, and set the inter symbol interference term constraint of the link. Thirdly, we gave the parameter code of genetic algorithm, arranged all requests  in one-dimensional order, and  transformed  linear scale on the fitness function to complete the improvement of genetic algorithm. Finally, we combined  gene evolution chromosomes to expand the search space of the Internet of Things, made the number of iterations less than the maximum coefficient, and realized the balancing control of link transmission load. The experimental results show that the proposed method can effectively  control the load balancing of the Internet of Things link, the link load balancing degree can reach 92%, and can reduce energy consumption.

Aiming at  the problem that marine controlled-source electromagnetic (MCSEM) signals were prone to be interfered by various noises in exploration, which  affected the accuracy of later inversion and data processing, we proposed an attention mechanism-guided convolutional autoencoder marine controlled-source electromagnetic data denoising method. Firstly, based on  the  autoencoder, we constructed a noise suppression network based on convolutional autoencoder for marine controlled-source electromagnetic data. Secondly, we opimized it according to the characteristics of noise in the data, deepened the depth of the network, introduced attention mechanism to make the network pay more attention to the effective signal features in the data, enhanced the feature extraction ability, constructed the network model, and realized the noise suppression of marine controlled-source electromagnetic data. The experimental results show that this method has higher signal-to-noise ratio and lower mean square error than the db8 wavelet noise suppression method and the variational mode decomposition noise suppression method. Meanwhile, it can still retain the signal features and increase the interpretable range of offset distance in the measured data, which proves the effectiveness of this method in the noise suppression of marine controlled\|source electromagnetic data.

For a three-dimensional T chaotic system with logarithmic term, on the basis of fractional-order stability theory, we used  differential 
method to design a more reasonable and concise sliding mode surface. The integer-order and fractional-order T chaotic systems were synchronized under the selected controller, and the MATLAB simulation program was used to verify the correctness of the method.

We studied the robust control problem of three-dimensional Coullet system. Firstly, the complex dynamic behavior of the system was verified by drawing the time domain waveform, chaotic attractor and Lyapunov exponent diagram of the system. Secondly, the sliding mode control method, the sliding mode based high frequency robust control method and the high gain robust control method were used to design the controller and control the system. Finally, the effectiveness of the controller was verified by numerical simulation.

We used SBA-15 hard template replication technology to prepare In₂O₃ series samples with nanowire array structures at different temperatures. The crystal structure, grain size, unit cell parameters, morphology and band gap width of the samples were characterized by X-ray diffractometer, field scanning electron microscope and UV-Vis spectrophotometer, and the gas sensitivity of the samples to ethanol gas was tested and analyzed. The results show that the samples are all three-dimensional nanowire array structures formed by the orderly arrangement and growth of spherical nano In₂O₃ grains. With the increase of sintering temperature, the grain size and nanowire diameter of the samples increase, and the nanowire spacing decreases. The unit cell parameters and the band gap width of the samples show  an increasing and decreasing trend respectively  with the increase of sintering temperature in the range of sintering temperature from 450 ℃ to 650 ℃. When the mass concentration of ethanol gas is 1×10^-4 mg/L and the test temperature is 320 ℃, the sensitivity of the In₂O₃ sample sintered at 450 ℃ is the maximum of 50.59.

 The studies of reactions involving water radical cations and their cluster ion ((H₂O)⁺_n)  can  better understand the mechanisms of certain natural processes,  such as proton transfer in aqueous solutions,  the formation of hydrogen bonds,  the destruction of bio-molecules such as DNA,  and the discovery of novel gas phase reactions and products. In addition,  the potential of water radical cations in  radio-biology have broad application prospects and its use as a primary reactive ion have attracted much attention for efficient selective  chemical ionization as well as improving the analytical sensitivity. At present, there are many studies on the bonding properties and  structure  of protonated water clusters and hydrated electrons, but there are few studies on the isolation and physicochemical properties of (H₂O)⁺_n due to  their ultra-high reaction activity and extremely short lifetime. Since significant progress has been made in the  technology  of mass spectroscopy,  molecular spectrometry  and high-precision  theoretical calculation of quantum chemistry, we review the current knowledge of    (H₂O)⁺_n, including  the formation  methods  and generation mechanisms,  structural theoretical simulation and experimental verification,   chemical property analysis,  and their application research.

Aiming at the problem that the operating pH range of  the conventional Fenton technique was relatively narrow，   increasing  pH  value significantly reduced the removal rate of tetracycline and led to secondary contaminztion,  Fe₃O₄@CF composite electrode was synthesized by loading Fe₃O₄ onto the surface of carbon felt (CF) electrode by using a solvent thermal synthesis method. The materials were characterised by scanning electron microscopy (SEM),  X-ray diffraction (XRD),  X-ray photoelectron spectroscopy (XPS),  Fourier transform infrared absorption spectroscopy (FTIR) and electrochemical impedance (EIS).  We investigated the degradation performance and mechanism of  tetracycline using it as electrode in a non-homogeneous electrically assisted Fenton (EF) system, and conducted cyclic experiments.  The results show that the Fe₃O₄ electrode exhibits the best degradation performance of tetracycline in a non-homogeneous electrically assisted Fenton system.  After 90 min at room temperature,  the initial mass   concentration of tetracycline is 20 mg/L,  an initial pH=3,  a distance between the two electrodes is 2 cm, and an applied current is 50 mA,  the removal rate of tetracycline by Fe₃O₄@CF electrode in the non-homogeneous electro-Fenton system can reach 96.7%. In addition,   the Fe₃O₄@CF electrode has good reusability. In the degradation of tetracycline in the non-homogeneous electro-Fenton system,  ^.OH plays a major role and  ^.O^-₂ plays an auxiliary role.