By using the fixed-point theorem of Krasnoselskii, we give the existence of positive solutions for a class of discrete beam equations with nonlinear boundary conditions, where λ>0 is a parameter, h: ［2,T］_Z→［0,∞) is function, f: (0,∞)→R is continuous, and allows singularity at u=0, grows superlinearly at u=∞.

We considered a predator-prey model with fear effect and spatial heterogeneity. Firstly, we gave the local asymptotic stability of trivial and semi-trivial solutions by using Riesz-Schauder theory. Secondly, we gave the global attractivity of trivial and semi-trivial solutions by using the principle of comparison. Finally, we gave the existence of a positive steady-state solution by using the fixed point theorem. The results show that fear effect and spatial heterogeneity have significant effects on the properties of steady-state solutions of the model.

We considered a class of time delay coupled models with logistic growth. Firstly, by  using the characteristic equation and Lyapunov-LaSalle invariance principle, we proved the global asymptotic stability of the infection free equilibrium when R₀≤1 and the existence of Hopf bifurcation of virus infection equilibrium when R₀>1. Secondly, we obtained the results that the logistic growth and time delay affect the stability of the system. Finally, the correctness of the theoretical results was verified by numerical simulations.

By using  a priori estimates of the solution and the asymptotic compactness of the operator semigroup, we considered the global dynamic behavior  of a fourth-order nonlinear evolution equation describing the dynamic controll of crystal growth process, and  proved the existence of global attractor of the equation in H⁴(0,1) space when  the initial value of the equation  belonged to H¹(0,1).

Let A/S be a Frobenius extension of rings with S coherent and C a semidualizing S-module. Firstly, we prove that G_C-flatness with respect to a semidualizing module is invariant under Frobenius extensions by using the construction method, that is, for an A-module M, M_A is G_CSA-flat module if and only if M_S is G_C-flat. Secondly,  we prove that G_C-flat dimension with respect to a semidualizing module is preserved under Frobenius extensions.

Firstly, we discussed the theory of universal central extensions, the results showed that the composition of two central extensions of δ-Hom-Jordan Lie algebras was no longer a central extension. Secondly, we defined universal α-central extensions by introducing the definition of α-central extensions. Finally, we constructed the universal central extension of δ-Hom-Jordan Lie algebras.

Products commutativity of two oblique projectors on a complex Banach space was studied by using operator matrices block technique. By using {1}-,{1,5}-,{2,5}-inverses and group inverses of some algebraic combinations, such as sum, difference and product of two oblique projectors, equivalent characterizations of product commutability of two oblique projectors were given.

A class of B(n,k) groups were  characterized by using a combinatorial method, and the descriptions  of B(6,22),B(6,23),B(6,24),B(7,29),B(7,30) and B(8,37) groups were obtained.

By introducing  the notion of weakly τ_σ-embedded subgroups, sufficient conditions of σ-solubility and supersolubility of finite groups were given respectively in terms of weakly τ_σ-embedded subgroups, which generalized some existing results of supersolubility.

The concept of local derivations from Lie algebra to adjoint module was extended to any finite dimensional module. The problem of solving the local derivations of the general linear Lie algebra sl(2,C) to any simple module was equivalently transformed into solving the related linear equations. By using the rank of the coefficient matrix was equal to the rank of the augmented matrix, the local derivation spaces from 3-dimensional simple Lie algebra sl(2,C) to two kinds of simple modules V(3) and V(4) were determined.

By using three types of tree coloring algorithms and combinatorial analysis, we completed the neighbor sum distinguishing edge coloring, the neighbor sum distinguishing total coloring and the neighbor full sum distinguishing total coloring of Halin graphs, and proved that the 1-2-3 conjecture and 1-2 conjecture were valid for Halin graphs. The results show that the neighbor full sum distinguishing total chromatic number of Halin graphs is not more than 3.

By using the method of contradiction and the method of constructing concrete coloring, we discussed IE-total coloring and general total coloring of complete bipartite graphs which were vertex-distinguished by multiple sets, gave the optimal coloring scheme,  and determined the chromatic numbers of the corresponding colorings.

Using the power function method, we discussed the inverse Hilbert\|type integral inequality with non-homogeneous kernel K(x,y)=G(x^λ1y^λ2)(λ₁λ₂>0) under the condition that 1/p+1/q=1(0

We considered  the relations between the property (UW_Π) and the hypercyclic property for a bounded linear operator or operator  functions. By defining the new spectral set, we gave a  judgement method for  bounded linear operators or operator  functions satisfying property (UW_Π) and hypercyclic property at the same time, and the obtained results were applied.

We proposed a restricted structure of a filiform Lie superalgebra, and discussed the (restricted) superderivations  algebra of this restricted Lie superalgebra. Firstly, the superderivations algebra was given by using this Z₂×Z-graded structure of this restricted filiform  Lie superalgebra. Secondly, it was proved that the superderivations of the restricted Lie superalgebra were all restricted superderivations.

By using the properties and the moment inequality of coordinatewise asymptotically almost negatively associated (CAANA) sequences in Hilbert space, we considered the problem of the first order moment convergence of CAANA sequences, and obtained the complete moment convergence of CAANA sequences with different distributions in Hilbert space.

Let {X_nn, n≥1} be a strictly stationary negatively associated (NA) sequence of positive random variables with EX₁=μ>0, and
 Var X₁=σ²<∞. Firstly, by using the central strong limit theorems and moment inequalities of weighted sums of NA sequence, 
where N is a standard normal random variable. Secondly, we give a general result of precise asymptotics in complete convergence for products of sums of partial sums of NA sequence for the boundary function and quasi weight function.

Aiming at the problem that computational and storage resources of embedded and mobile devices were limited, and the compact  network optimization was easy to  converge to poor local optimal solutions,  we proposed an  activation map adaptation model for knowledge distillation,  which was composed  of an activation map adapter and an activation map adaptation knowledge distillation strategy. Firstly, the activation map adapter realized activation map size matching, synchronous transformation of teacher-student network features, and adaptive semantic information matching by heterogeneous convolution and stacking of visual feature expression modules. Secondly, the activation map adaptation knowledge distillation strategy embedded the adapter into the teacher network to reconstruct it, and realized adaptively search suitable for the  supervision features of the hidden layer of the student network  during training process,  the front output  of the adapter was used to prompt the front training of the 
student network, so as to realize knowledge transfer from the teacher to the student network, and further optimize it  under the constraint of learning rate. Finally, experimental verification was carried out on the image classification task  dataset cifar-10. The results show  that the classification accuracy of the activation map adaptive knowledge distillation model is improved by 0.6%, the inference loss is reduced by 6.5%, and  the time to converge to 78.2% accuracy is reduced to 5.6% when it is not migrated.

Aiming at  the problems of texture blur and poor image quality in the image processed by single image blind deblurring  algorithm, we  proposed an image blind deblurring network with embedded  attention mechanism. Firstly, the network adopted multi-scale cyclic architecture, which realized multi-scale by cyclic processing of images with different resolutions inside the network, and restored images from coarse to fine. Secondly, a residual channel selection module and jump connection were embedded in the network  to enhance feature extraction, and a multi-scale  structural loss function was designed for training optimization. Finally, it was  compared with the classical  deblurring networks on two widely used datasets GoPro and Kohler, and a visual comparison was made on Lai dataset. The experimental results show that the proposed network achieves a good visual effect of image blind deblurring,  compared with other algorithms, it improves the peak signal-to-noise ratio and structural similarity, and can improve the poor quality of image deblurring.

Aiming at the problem that the current convolutional neural networks usually  obtained multi-scale image features on the conditio
n of reducing receptive fields, and it was difficult to capture the important relationship between channels.  Combined with the features of cycle-generative adversarial networks structure, we proposed a new cycle-generative adversarial networks with multi-scale and self-attention mechanism. Firstly, VGG16 module was used to form U-Net structure in the generator to enhance the extraction of image feature information. At the same time, the down-sampling  and up-sampling  in the network were improved to improve the feature resolution and obtain more detailed information. Secondly, a multi-scale feature fusion block was designed. The multiple parallel dilated convolutions with different sampling rates were used to integrate the spatial information on different scales, and capture image information in multiple proportions while maintaining  a large receptive field of the image. Finally, in or
der to capture the feature dependencies in the spatial dimension and channel dimension, the pixel self-attention module was designed to model the semantic dependencies in the spatial dimension and channel dimension, so as to enhance the representation ability of image features and improve the quality of the generated sketch images.

Aiming at the problem of small number of  samples of apple leaf disease and the lack of sufficient labels, which led to the difficulty of the early detection and classification of apple leaf diseases, we proposed a few-shot learning method for image classification of apple leaf diseases. First, according to the distance of feature vectors  between the images and the density of sample points, we found out the outlier factors in the samples, after the outlier factors were eliminated, the average value of the support set in the embedding space was calculated, and then the classification was performed according to the relationship between the search sample and the value. The experimental results show that the proposed few-shot learning method can significantly improve the classification performance and convergence speed of the model, and has high classification accuracy, its  average classification accuracy is 97.62%, and the classification accuracy of apple rust, scab, mixed diseases and healthy leaves is 98.01%, 97.32%, 96.30%, 98.85%, respectively. It has  strong robustness to data sets such as sample imbalance and uneven background, etc.

Aiming at the problems of low tumor recognition rate and slow convergence speed caused by limited samples of intestinal tumor images, we proposed a feature extraction method of intestinal tumor images based on local binary pattern (LBP) and gray level co-occurrence matrix (GLCM). Firstly, the maximum interclass variance method was used to automatically calculate the image gray threshold and extract the region of interest. Secondly, the LBP+GLCM was used to extract the features of partial intestinal tumor image, and support vector machine was used for recognition. Experimental results of  1 500 intestinal tumor images show that this method can achieve 94.84% recognition accuracy and can effectively assist medical diagnosis and treatment.

Aiming at the problem that the existing sequence recommendation algorithms did not make full use of time information, we proposed  a multi-time embedding mode,  which used  dynamic fusion strategy to alleviate the problem of insufficient long-term preference modeling in existing sequence recommendation algorithms. The multi-time embedding mode could simultaneously model the absolute time information and relative time information of user-item interaction, and fully capture various rules of user-item interaction about time. The dynamic fusion network dynamically integrated the users’ long-term preference and recent preference according to the users’ intentions,  accurately depicted the users’ interest, and improved the diversity of recommendation results.  The proposed time embedding sequence recommendation algorithm based on  long-term memory enhancement was compared with the existing  algorithms on the public datasets MovieLens-1M and Amazon-Beauty. The results show that the proposed algorithm is better than the comparison method in the evaluation indicators HR@N and NDCG@N. Experimental results show that the accuracy of the time embedding sequence recommendation algorithm based on  long-term memory enhancement is higher than that of other  comparison sequence recommendation algorithms.

Aiming at the problems of data sparsity and high dimension, the author proposed a mixed matrix object data clustering method based on k-multiple  value  representation, which effectively  reflected the distribution of cluster centers and matrix objects in clusters. In order to fully mine the hidden information between data, firstly, the algorithm defined the dissimilarity measure between two numerical matrix objects, and gave a heuristic method to update the clustering center. Secondly,  a mixed matrix object data clustering algorithm based on k-multiple value representation was proposed. Finally, the simulation experiments were carried out on real data sets and composite data sets. The experimental results  show that the proposed algorithm can effectively realize data clustering including a large number of records, matrix objects and attributes.

Aiming at the problems of slow convergence speed and large steady-state error of the minimum mean square error algorithm in speech noise reduction, we proposed a variable-step minimum mean square error algorithm based on wavelet threshold. Firstly, the time-frequency analysis of the speech signal was carried out by using the wavelet soft threshold algorithm, the wavelet coefficients of noise were eliminated, and the noise reduction accuracy was improved. Secondly, on the basis of the minimum mean square error algorithm, we proposed  a new variable step size minimum mean square error algorithm to further denoise the transformed speech signal by establishing the nonlinear function relationship between the step size factor and the error signal. 
The experimental results show that compared with other single denoising algorithms, this algorithm has a great  improvement in signal-to-noise ratio and mean square error.

Aiming at the problem of mutual authentication among three participants, we  proposed a (3,3) visual cryptography scheme with mutual authentication capability. According to the different proportions of black and white pixels in the black and white regions of the original image,  the basic matrix was constructed  in this scheme.  The white region of the original image had more white than the black region, so that the black and white region of the restored image could be distinguished. At the same time, the scheme also ensured that the overlapping of shared images could restore the verification images and realize mutual verification among participants. The scheme involved three different verification images and a secret image, in which any two shared images could be superimposed to produce a verification image, and superposition of three shared images could finally  restore the secret image. The experimental results demonstrated the effectiveness of the proposed scheme.

The system adopted the method  of dual positioning of GPS and image recognition, used the PID flight attitude control of unmanned aerial vehicle (UAV), and the open source computer vision library (OpenCV) was used to process the images. The cascade classifier was applied to solve the problem of target accurate detection. The positioning and navigation control system designed by integrating various technologies can quickly complete the transmission and processing of information, and enhance the system function. After GPS rough positioning, the image capture, preprocessing, fitting and discrimination of the target graphics are accurately positioned to ensure the real-time, efficient and accurate navigation  control system of UAV.

Ag-CDs nanoparticles with core-shell structure were obtained by reducing Ag ion with carbon dots (CDs). The results show that the diameter of Ag core is about 30 nm, and the thickness of surface carbon film is about 2.2 nm. Ag-CDs nanoparticles have excellent peroxidase-like activity and surface enhanced Raman scattering (SERS) activity, which can catalyze the oxidation of 3,3′,5,5′-teramethylbenzidine (TMB). Because uric acid can reduce the oxidized TMB, the concentration of uric acid can be detected by colorimetry. Taking Ag-CDs nanoparticles as the SERS substrate, and the concentration of uric acid can be detected by SERS spectrum. The collaborative detection of the two methods can greatly improve the reliability of the detection.

Aiming at the problem of chaotic behavior of permanent magnet synchronous motor, based on Lyapunov stability theory, we proposed a nonlinear feedback controller to realize the stable operation of the chaotic system of a single motor. The effectiveness of the control strategy was verified by theoretical analysis and numerical simulation. By using the motor with feedback controller as the external coupling system, the coordinated coupling function of multiple motors was established to realize the chaos suppression behavior of the whole ring motor networks.

Aiming at the problems that the speed of identifying the lightning signal waveform was slow and inaccurate of the traditional two-dimensional lightning detector, and the data quality was affected by the aging of the components, and the number of components was large, the integration was low, the reliability was poor, and the upgrade space was small. It could only work with linear power supply, and the power supply stability was strictly required. Through the ultra-large field programmable gate array, on-chip programmable system and modern electronic surface mount technology, the anti-interference three-dimensional lightning detector was developed. The detector antenna adopted orthogonal ring structure and was equipped with shielding cover to improve the accuracy of received signal and avoid antenna effect. The front channel board applied large-scale integrated circuits, surface mount components and multilayer board technology to reduce the background noise of the output signals. Based on the embedded soft core, the signal processing board flexibly constructed the central processor to quickly identify the lightning waveform. The power supply module used the switching power supply with strong adaptability and high conversion efficiency to obtain a variety of voltages. The design realized a stable and low-power three-dimensional lightning detector.

The reversible  detection for hydrazine hydrate (N₂H₄·H₂O) and hydrogen peroxide (H₂O₂) in P₂Mo₁₈ solution could be realized by ultraviolet-visible (UV-Vis) spectrum based on the reversible redox and allochroic properties of Dawson type phosphomolybdate (NH₄)₆P₂Mo₁₈O₆₂（P₂Mo₁₈）. After adding the same  amount of N₂H₄·H₂O  to P₂Mo₁₈ solution, the P₂Mo₁₈ was reduced,  and the solution changed from light yellow to blue-green. The absorption peak in the visible region of 400—800 nm gradually increaseed with the increase of N₂H₄·H₂O concentration. After adding the same amount of H₂O₂  to the reduced P₂Mo₁₈ solution, the reduced P₂Mo₁₈ was oxidized again and the solution changed from blue-green to light yellow. The absorption peak in the visible region gradually decreased with the increase of H₂O₂ concentration. The linear equation, linear detection range and detection limit of N₂H₄·H₂O and H₂O₂ were obtained by drawing concentrations of N₂H₄·H₂O and H₂O₂ with the absorbance at 750 nm. The response time, reversibility and anti-interference of the probe were studied by UV-Vis kinetic method  and spectral method. The results show that the detection limits for N₂H₄·H₂O and H₂O₂ are 7.24×10^-5， 2.15×10^-4 mmol/L,  the response time for N₂H₄·H₂O  and H₂O₂ detection are 44.8,23.9 min, respectively.

Silver doped graphene/CdTe quantum dot composites were prepared by using mercaptopropionic acid and mercaptographene as stabilizers in aqueous phase under the protection of nitrogen. The fluorescence emission spectra show that after doping silver ions,  the maximum fluorescence wavelength of the graphene/CdTe quantum dot composites  significantly red-shifts, and increases with the increasing of heating time until equilibrium, which conforms to the law of   the second-order reaction kinetic adsorption model. The maximum fluorescence emission wavelengths can be calculated as 684.93,735.29,746.27 nm by using the second-order kinetic adsorption model  when the initial mass concentrations of silver ions are  18.75,37.50,56.25 mg/mL. Therefore,  the greater the initial mass concentration of silver ions,  the greater the  maximum fluorescence emission wavelength after reaching equilibrium, but the   maximum fluorescence emission intensity  decreases in turn. In order to obtain quantum dots with  large fluorescence emission wavelength and moderate fluorescence emission intensity,  the optimal amount of silver ions  is 37.5 mg/mL.

In order to explore the effect of Maillard reaction precursors on the humus composition of dark-brown soil mixed with basswood chips,  the promoting effects of  three precursors such as  catechol (Cat),  glucose (Glu) and glycine (Gly)  in the process of humification were revealed. The indoor constant temperature culture method was used to extract and analyze the mass ratio of each humus component from the dark-brown soil mixed with basswood chips based on the addition of Cat,  Glu or Gly,  and taking sterile water as the control,   the effects of adding three different precursors on each humus component under the action of microorganisms were investigated. The experimental results show that with the increase of culture time,  the mass ratio of carbon  of water-soluble substance w（C_WSS） and total organic carbon content (TOC) of the dark-brown soil mixed with basswood chips under each treatment show a downward trend. The reduction of  w（C_WSS） in the treatment by adding Maillard reaction precursors is lower than that of CK,  and the addition of Glu can minimize the reduction of w（C_WSS） and TOC.  The mass radio of carbon of humic-extracted acid w（C_HE）of the dark-brown soil is significantly higher than that of CK in the treatment by adding  Maillard reaction precursors during the  culture period,  showing a trend of first decreasing and then increasing. After culture，  w（C_HE） slightly decreases，   and the decreasing range is greater than that of CK.  The reduction  of w（C_HA） of the dark-brown soil with the addition of Maillard reaction precursors is higher than that of CK. The additions of catechol and glycine make the molecular structure of humic acid (HA) more complicated. The Hufu ratio (w（C_HA））/w（C_FA）) of the dark-brown soil with the addition of  Maillard reaction precursors shows a trend of first increasing and then decreasing,  and finally decreases. The decrease of w（C_HA）/w（C_FA））  with Glu is lower than that of CK.  The mass ratio of carbon  of humin w（C_Hu） of the dark-brown soil under each treatment is reduced to varying degrees after the culture,  and the addition of Glu is more conducive to the mineralization and decomposition of w（C_Hu）. The addition of Glu can alleviate the loss of w（C_WSS）,  TOC and w（C_HA） of dark-brown soil，    make w（C_HE） higher than CK during the culture period,  slow down the reduction of w（C_HA）/w（C_FA）,  and be more conducive to the mineralization and decomposition of w（C_Hu） of the dark-brown soil mixed with basswood chips.