This paper proposes to employ matrix weighted NURBS surfaces to fit and fair quad meshes. For a quadrilateral mesh with given or estimated unit normals at vertices, a matrix weighted NURBS surface can be constructed by choosing the mesh vertices as control points and employing normals at each vertex for computing matrix weights. Compared with traditional NURBS surfaces, matrix weighted NURBS surfaces have quasi-cylindrical accuracy. When the input data is uniformly sampled from a smooth surface, the constructed matrix weighted NURBS surface has good smoothness and fits the mesh model well; if the input grid data contain noise, a fair fitting surface that approximates the original grid well can still be obtained by resampling control vertices on current fitting surfaces and re-calculating vertex normals based on the new quad meshes iteratively.

In order to improve the efficiency and quality of parametric tread pattern retrieval, a novel method is proposed. Firstly, the tread pattern model in B-rep format is converted into an attribute adjacency graph, in which the edge compatibility is used for inexact matching of two attribute adjacency graphs and for the calculation of graph similarity. The geometric features reflected by the design parameters are used to define similarity of tread pattern models. Secondly, to improve query efficiency, various design parameters are used for rough space division and recursive clustering on the tread pattern database. An index structure based on the cluster tree is constructed to speed up model retrieval. Our experimental results show the superiority of the proposed method over the general model retrieval methods, both in search efficiency and quality. This demonstrates the advantage of utilizing design parameters and geometric information of the tread pattern in CAD model retrieval.

Improving the segmentation quality of 3D meshes is always an important problem to computer graphics. To handle this problem, this paper proposes a shape-aware graph attention network. The shape-aware graph attention coefficient is defined to better reflect the similarity between nodes, which not only expands the attention coefficient obtained by network learning with the help of edge features between nodes, but also introduces the attention coefficient related to the local shape information of nodes. On the other hand, the network architecture is adjusted by taking both shape features and labels of 3D mesh model as the input of graph attention network, which enables the participation of labels in network training and verification stages. Residual connection is further employed to make the network output more stable. A large number of experiments show that the proposed algorithm can obtain accurate segmentation boundaries. Compared with the existing classical segmentation algorithms on PSB dataset, the proposed algorithm improves 2% in accuracy, and achieves better Rand index. The reasonableness of the algorithm is proved by ablation experiment.

V-system is a kind of complete orthogonal piecewise polynomial function system on L^{\mathrm{2}}[\mathrm{0,1}], because of the discontinuous nature of its basis functions, it has significant advantages in the expression and analysis of discontinuous signals. However, in the current V-system transformation algorithm, for a signal with a length of N, it not only needs to generate and store an N-order orthogonal matrix in advance, but also its time complexity is as high as \mathrm{{\rm O}}(N^{\mathrm{3}}). Therefore, in order to adapt to the efficient processing needs, this paper designs and implements a fast decomposition and reconstruction algorithm for V-systems from the perspective of multi-resolution analysis of V-systems. This fast algorithm does not need to store additional information, and its time complexity is only \mathrm{{\rm O}}(N^{\mathrm{2}}). The test results show that the fast algorithm proposed in this paper can meet the requirements of high-efficiency processing of large-scale data, which lays the foundation for the application of V-system in more fields.

To address the limitations of current mainstream networks, which rely solely on local neighborhoods for feature aggregation and suffering from insufficient feature extraction capabilities and information loss due to max-pooling, we propose an attention-based point cloud processing network that combines both local and global information. First, we introduce channel attention for local feature aggregation to minimize information loss. Next, we design a dynamic key point learning method to capture the remote dependency information of points and obtain global information. Finally, we develop a spatial attention fusion module to allow each point to learn the global con-textual information. Our proposed method has been benchmarked on several point cloud analysis tasks. It achieved an overall classification accuracy of 94.0% and an average classification accuracy of 91.7% on the ModelNet40 classification task. On the ScanObjectNN classification task, our method reached an overall class fication accuracy of 81.5% and an average classification accuracy of 78.1%. In the ShapeNet segmentation task, we obtained a mean intersection over union of 86.5%. The experimental results show that the proposed network has significantly improved accuracy compared to classical networks such as PointNet, PointNet++, and DGCNN in classification and segmentation tasks, and has also achieved improvement in deferent degree compared to other point cloud processing networks.

A multi-morphology design method based on conformal mapping is proposed to design triply periodic minimal surface (TPMS) microchannels with freeform boundary constraints. This method first maps the boundary of a freeform surface to a plane, allowing for channel topology design in the 2D parametric domain; Then, a Beta growth function algorithm based on loop is proposed to achieve smooth transitions of various TPMS morphological features; Finally, by mapping the designed microchannels to the 3D space constrained by the free surface, the microchannels meet the design requirements. Our results show that the microchannels constructed by this method have good adaptability to complex surface boundaries and can achieve the design goals of internal morphological features.

Overhangs are usually inevitable when fabricating a part of complex shape in 3D printing. Meanwhile, the geometric error on the side surface of an overhang (i.e. the side loss) after fabricating is often significant, which seriously affects the accuracy of the overhang as well as its container (i.e. a part). To solve the above problem, a double-level intelligent improvement approach for overhangs on side loss (i.e. process parameter optimization and geometry pre-compensation) is proposed in this paper. Firstly, a series of experiments with different values concerning the critical design parameter and process parameters are designed based on the Taguchi method. Then, a deliberate measurement method is designed to get the side loss data from the fabricated inverted 'L'-shaped parts. Secondly, two types of side loss prediction networks are respectively constructed for the two sides (that is the overhang side and the non-overhang side) of each inverted 'L'-shaped part. They are mainly designed according to the requirements of support structures on an overhang. Aided with these networks, the geometric error of both sides of an overhang on an inverted 'L'-shaped part (with various values of the critical design parameter) can be predicted accurately. Thirdly, aiming at minimizing the side losses on both sides of an overhang, a single-objective and multiple-variables nonlinear programming problem is formulated. Hereby, the corresponding optimized side losses as well as their counterpart values of key process parameters can be determined. Finally, we compensate the geometries on the two sides of an overhang based on the above-optimized side losses by conducting an inverse modification first and then fabricate the overhang adopting the above-optimized values of key process parameters. Based on fused deposition modeling, experiments were implemented on various inverted 'L'-shaped parts except the ones used in constructing prediction networks, which verified the effectiveness of the proposed approach. Meanwhile, comparative analyses with state-of-the-art works were also carried out. The results show that our method is suitable for overhangs and has great potential to significantly improve their side losses.

Artificial intelligence generated content (AIGC) has received significant attention at present. As the numerous generative models proposed, the emerging diffusion model has attracted extensive attention due to its highly interpretable mathematical properties and the ability to generate high-quality and diverse results. Nowadays, diffusion models have achieved remarkable results in the field of condition-guided image generation. This achievement promotes the development of diffusion models in other conditional tasks and has various applications in areas such as movies, games, paintings, and virtual reality. For instance, the diffusion model can generate high-resolution images in text-guided image generation tasks while ensuring the quality of the generated images. In this paper, we first introduce the definition and background of diffusion models. Then, we present a review of the development history and latest progress of conditional image generation based on diffusion models. Finally, we conclude this survey with discussions on challenges and future research directions of diffusion models.

Land use and ecological environment construction affect each other, and the degree of coordinated development between them is an important standard to measure regional sustainable development. In this paper, the remote sensing ecological index is applied to the research on the coordination of land use degree and ecological environment. Combined with the coupling coordination degree model and spatial autocorrelation analysis, the temporal and spatial characteristics of the coordinated development of land use and ecological environment in 89 districts and counties of Zhejiang province in 2008, 2013 and 2018 are studied. The results show that: (1) on the spatial scale, the degree of land use in Zhejiang province is high in the east and low in the west. The distribution appears as high in the north and low in the south, and the development gap between cities is large. On the time scale, the land use in each region has improved to varying degrees, while the trend of high in the east and low in the west becomes more and more apparent. (2) Due to the advantages of natural and geographical conditions, the quality of ecological environment in Zhejiang Province has generally maintained a high level, and great achievements have been made in the construction of ecological civilization in the past decade. (3) Combined with the evaluation results of land use and eco-environmental quality coordination, the main factor affecting the coordination degree of each district and county is the degree of land use. Based on the comprehensive research results, it is suggested that the districts and counties with high land use degree should drive the development of the surrounding districts and counties, while the districts and counties with ecological environment quality lagging behind the land use degree can learn from the development experience of the districts and counties with high coordination degree, innovate their development mode and realize green development. Districts and counties that have not yet developed in depth can choose development routes suitable for regional characteristics with the help of their own ecological advantages.

The compositions with part of size 1 at the left or the right of positive integers are studied, and the relation between these compositions and the Fibonacci numbers is obtained. And then using the well-known composition identities related to Fibonacci numbers, several new identities are obtained, The combinational bijective proofs are provided.

Algebraic analysis of fuzzy logic is one of the hot issues in the field of fuzzy logic research. In this paper, Fuzzy implication algebras and its ideals problem are further studied by using the method and principle of algebra and lattice theory. Firstly, some new properties of Fuzzy implication algebras are revealed by using pseudo-complement operators. Secondly, the concepts of ideal and generating ideal are introduced in Fuzzy implication algebras, and their properties and equivalent characterizations are investigated. Finally, the lattice theory characteristics of the set consisting of all ideals in a given Fuzzy implication algebra are discussed, it is proved that the set forms a distributive continuous (algebraic) lattice with respect to the set-inclusion order, in particular, it forms a complete Heyting algebra, and then forms a Frame.

The UNet network can be used to predict the dense displacement field in the full-resolution spatial domain, and has achieved great success in the field of medical image registration. However, for three-dimensional images with large deformation, there are still shortcomings such as long running time, inability to effectively maintain the topological structure, and easily leading to the loss of spatial features. A large kernel multi-scale deformable medical image registration network based on cross-attention (LK-CAUNet) is proposed. Based on the classical UNet network, the cross-attention module is introduced to achieve efficient and multi-level semantic feature fusion. The large kernel asymmetric parallel convolution is equipped. It has the ability to learn multi-scale features and complex structures. Besides, an additional square and scaling module is added to let it have the advantages of topological conservation and transform reversibility. Using the brain MRI dataset, it is demonstrated that the proposed method has significantly improved the registration performance compared with the eighteen classical registration methods. Especially compared with the most advanced TransMorph registration method, the Dice score can be improved by 8%, and the parameter quantity is only one fifth of it.

Based on the existing results at home and abroad, this paper uses principal component analysis to combine two subjective sentiment indicators and four objective sentiment indicators into a comprehensive index that can effectively measure investor sentiment. The constructed composite sentiment index can reflect most of the information of the six original indicators, and is significantly correlated with the stock market return rate. When studying the relationship between investment sentiment fluctuation and stock market return fluctuation, vector autoregression (VAR) model is used to explore the relationship between them. Accounting for asymmetry of stock market information, exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model is used in this paper. The results show that the impact of negative and pessimistic sentiment on stock market returns is greater than that of positive and optimistic sentiment. The impact of falling earnings on investor sentiment is far greater than that of rising earnings.

Pollution characteristics and pollution sources of nearshore environment are two key issues for regional Marine environment protection. In this paper, the nearshore area of the Ruian in southern Zhejiang were taken for case study. In May 2020, marine environment investigation and surface water samplings at 16 stations, and analysis of 12 water quality parameters (Salinity, Dissolved Oxygen, Chemical Oxygen Demand, Dissolved Inorganic Nitrogen, Dissolved Inorganic Phosphate, Mercury, Cadmium, Lead, Chromium, Arsenic, Zinc and Copper) for each station were carried out. The pollution evaluation, multivariate statistical methods (using SPSS) and spatial analysis (using ArcGIS) were used to explore the spatial characteristics and pollution sources. The results showed that the sea water quality of the Ruian nearshore area was generally good; however dissolved inorganic nitrogen and dissolved inorganic phosphate in water exceeded the Chinese Standard seriously (worse than the fourth class) in some areas. The evaluation results using the eutrophication index method showed that the eutrophication was the most serious in the near estuarine area of Feiyun River. The evaluation results using the nitrogen phosphorus ratio showed that there was a great risk of red tide around the Beiji islands. According to the results of cluster analysis, the study area can be divided into four parts with different pollution characteristics. According to the results of principal component analysis, the main source of nutrition and chemical oxygen demand are probably due to agriculture, while heavy metal pollution may come from electroplating, parts processing and shipping.

The massive emission of VOCs has caused serious harm to the environment. Catalytic combustion is an efficient way of eliminating VOCs.However,how to prepare catalysts for VOCs elimination with simple and eco-friendly methods is still a big challenge. In our study, supported Cu-based catalysts for catalytic combustion of ethyl acetate (EA) were prepared using the ball-milling method with CeO₂, Al₂O₃, La₂O₃ and ZrO₂ and their corresponding hydroxides as support precursors. The prepared catalysts were characterized by XRD, TEM, XPS and H₂-TPR. The results show that the catalysts with hydroxides as support precursors have better reduction performance, higher content of highly dispersed CuO on the surface, and better catalytic combustion performance of ethyl acetate, except for the catalyst prepared with aluminum hydroxide precursor catalyst. Except for the 10%-Cu-Al(AlH), one of the main reasons that the catalytic activities of the 10%-Cu-YH is that the former forms smaller nanocomposites. In addition, higher ratio of O_ads/O_latt is_{also ascribed to higher catalytic performance of 10%-Cu-CeH than the 10%-Cu-Ce. Among them, 10%-Cu-CeH (T50= 214 ℃, T95= 238 ℃) and 10%-Cu-ZrH (T50= 217 ℃,T95= 239 ℃) prepared with Ce(OH)4 and Zr(OH)4 as support precursors catalyst has the best performance in the catalytic combustion of EA. The above results provide a new idea for the design and preparation of supported non-precious metal catalysts for the catalytic combustion of VOCs.}

Analyzing regional differences and convergence of high-quality development of tourism is an important topic of research. In this paper, we construct an indicator system to estimate high-quality tourism development, and the dimensions include market quality upgrading, supply capacity improvement, efficiency of enterprise resource allocation, development environment enhancement, industry structure optimization, and development achievements sustainability. It adopts entropy weight-TOPSIS method to measure the high-quality development index of China tourism as well as the tourism of 30 provincial regions from 2010 to 2018, applies Dagum Gini coefficient and decomposition to measure the regional differences and resources, and uses coefficient of variation and spatial panel model to reveal the convergence. The results are as follows: (1) the level of China's tourism hight quality development is increasing gradually, but the efficiency of enterprise resource allocation, market quality upgrading and development achievements sustainability are still the main short boards. There are significant regional differences, showing a stepwise decreasing pattern from east to west; (2) the overall difference of China's tourism hight quality development is narrowing gradually, but no significant change in intra-regional differences. Although inter-regional difference shows a decline, it is still the primary source of overall difference; (3) except the central region, the tourism high-quality development exists σ convergence in China as well as in its eastern and western regions. Both absolute β convergence and conditional β convergence are found in all three regions; (4) the levels of economic basis, industrial structure, degree of marketization, and innovation ability have significant effects on the improvement of tourism high-quality development, but there is obvious regional heterogeneity. The countermeasures to narrow the regional differences in tourism high-quality development are proposed accordingly.

Phospholipase D (PLD) derived from Streptomyces has great application potential in food, health products, medicine and other industries, and the commonly used heterologous expression host is E. coli. However, there are problems such as long fermentation time, cumbersome separation and purification steps, and high cultivation cost. Therefore, the effects of intracellular expression, secretory expression and surface display of E. coli on PLD enzyme activity and phosphatidylserine (PS) catalytic synthesis efficiency were comparatively studied. A single factor method was used to derive the optimal induction conditions for PLD expression modes, specifically, the bacterial concentration OD₆₀₀ was 0.7, IPTG concentration was 0.3 mmol·L^-1 and the temperature was 20 ℃. The fermentation time curve under optimal conditions showed that the PLD enzyme activity by the above three methods reached the highest value when the expression was induced for 8 h, which were 0.35, 0.23, and 0.11 U·mL^-1, respectively. Scanning electron microscopy showed that the structure of E. coli cells expressing PLD has been damaged to a certain extent. Among them, the deformation and collapse of the cell structure of the secretory expression strain is the most serious. In the water-ethyl acetate biphase catalyzed phosphatidylcholine (Phosphatidylcholine, PC) system, the PLD surface display strain in the form of a whole cell obtained the highest PS molar conversion rate of 59.1%, compared with the intracellular expression strain and secretion expression strain in the form of sonicated crude enzyme solution, showing that the expression of the E. coli surface display system PLD has great potential for whole-cell catalytic synthesis of PS with reducing production costs.

In this paper, we apply the theory of soft sets to partially ordered semigroup. First, several new notions such as left (right) filter soft partially ordered semigroup, filter soft partially ordered semigroup, whole left (right) filter soft partially ordered semigroup, whole filter soft partially ordered semigroup, prime left (right) ideal soft partially ordered semigroup, prime ideal soft partially ordered semigroup over partially ordered semigroups S are introduced. Further, with prime left (right) ideal soft partially ordered semigroup and prime ideal soft partially ordered semigroup over S, the necessary and sufficient conditions that the non-null soft set over S is a right (left) filter soft partially ordered semigroup and filter soft partially ordered semigroup over S are given separately. Finally, quotient ordered homomorphic images and inverse images under partially ordered homomorphic on left (right) filter soft partially ordered semigroup, filter soft partially ordered semigroup, whole left (right) filter soft partially ordered semigroup and whole filter soft partially ordered semigroup are studied,and some related conclusions are obtained.

Breast cancer is one of the most common malignant tumors in the world. Traditional methods take pathologists a lot of time and effort to diagnose, and the results are greatly affected by individual abilities. Using computer-aided diagnosis methods can improve the accuracy and efficiency of pathological image classification, meet the demands of clinical applications. To this end, a multi-scale feature fusion based on DenseNet and coordinate attention network (MFDC-Net) is proposed. The introduction of coordinate attention mechanism into the dense blocks can locate important feature spatial information precisely. The improved transition layers use average pooling and normal convolutions with different convolution kernels to reduce dimension and expand receptive fields. Finally the improved network employs a multi-scale feature fusion model using dilated convolution, average pooling and normal convolutions to fuse deep image features to improve classification performance. The experimental results show that MFDC-Net model has better classification performance, the accuracy rate of four classifications reaches 97.12%, the easily confused rate decreases to 3.34%. The method can better classify the histopathological images of breast cancer, and can provide an important basis for the diagnosis and treatment of doctors.

The invisibility of watermark and robustness of watermarking algorithms are important issues of concern in the field of image copyright protection, however, most algorithms cannot balance well the relationship between the two. Therefore, a hybrid image watermarking algorithm with high invisibility and robustness based on bi-dimensional empirical mode decomposition (BEMD), discrete cosine transform (DCT) and singular value decomposition (SVD) is proposed in this paper. The watermark image is firstly decomposed by Arnold scrambling and 2D-DCT, and then the host image is decomposed by BEMD to obtain a finite number of different scale intrinsic mode functions and residue. The first intrinsic modal function (IMF1) with low correlation with the host image is selected to perform 2D-DCT, and it is divided into non-overlapping blocks according to the size of the watermark. Then, SVD is performed on the image of each block and the watermarked image after DCT. Finally, the watermark embedding strength is determined and the watermark is repeatedly embedded into each chunk according to the adaptive optimal embedding criterion, which effectively enhances the fault tolerance of the algorithm. Extensive experiments and comparisons with existing algorithms show that the proposed watermarking algorithm not only ensures the robustness of the algorithm against large scale attacks, but also improves the invisibility of the algorithm.