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.

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.

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 numerical solution of hyperbolic equation is a well-know hot topic in the field of numerical solution of partial differential equation, among which the discontinuous capturing of hyperbolic equation is always a difficult problem. Inspired by physical-informed neural networks (PINN), this paper presents a PINN-type algorithm to approximately solve discontinuity problem of hyperbolic equations. It takes the data set constructed by coordinate as the input of neural network. The loss function in PINN algorithm is converted to the error between the output value of the training network and the reference solution (entropy compatible format data based on the fine grid) or the exact solution. Then the loss function is minimized by network optimization to obtain the optimal network parameters. Finally, some numerical examples are demonstrated to verify the feasibility of the proposed algorithm. The numerical results show that the proposed algorithm can capture shock waves, and it has high resolution, without nonphysical oscillations.

In order to study the impact of cooperative behaviors between predators on the dynamic behavior of the food chain system, a top-level predator (which only feeds on the predator population) on the basis of the original cooperative hunting model is introduced, and a food chain model with cooperative hunting is established. The local stability of the equilibrium point is discussed by using the linearization method. By establishing an appropriate Lyapunov function, a sufficient condition for the global stability of the system at the equilibrium point is given. In addition, by using the central manifold reduction theorem, the explicit formulas of the branch periodic solution is studied. Numerical simulations are conducted to verify our theoretical analysis. The results show that when there is no cooperative relationship between predators, the positive equilibrium point is stable. With the increase of cooperative predation parameter \alpha, the system will have a stable limit cycle, and the limit cycle will continue to expand following the increase of cooperative predation parameter \alpha. Moreover, if the predator population density is too large, the system will produce continuous periodic oscillation, that is, the three species i.e. diet, mid-level predator, top-level predator, either coexist in the form of periodic oscillation, or the number of species eventually tends to be stable. Therefore, cooperative hunting is more conducive to maintaining ecological balance.

We construct a q-type Lupas-Kantorovich operators based on the q-type integer and q-type calculus, investigate the rate of convergence of q-type Lupas-Kantorovich operators by modulus continuity as well as the properties of statistical convergence and weighted statistical convergence of the operators.

2,5-furandicarboxylic acid (2,5-FDCA) is a monomer of biodegradable polyethylene 2,5-furandicarboxylate (PEF), however, its cost is high. Production of 2,5-FDCA from the cyclodehydration of hexedioic acids (HAs) is one of promising pathways, but facing the problems that it is difficult to detect the side-products and the reaction pathways is unclear. In this work, the side-products of HAs cyclodehydration were qualitative analyzed by high performance liquid chromatography (HPLC), high-resolution mass spectrometry (HRMS), nuclear magnetic resonance (NMR) and Fourier transform infrared spectroscopy (FTIR). The 2-furoic acid and 3-hydroxy-2-oxopyran-6-carboxylic acid (HOCA) were determined as the two main side-products. The reaction pathways for the cyclodehydration of different hexedioic acids are similar when using H₂SO₄ as catalysts: the Galactaric acid is tended to be converted to HOCA, while calcium saccharate is more likely to be converted to 2,5-FDCA. Combined with the works already reported and the results obtained in this work, the possible reaction pathways for the preparation of 2,5-FDCA by cyclodehydration of hexedioic acid are proposed. This work will provide solid foundation for the constructing the catalytic system and industrialization of 2,5-FDCA from cyclodehydration of hexedioic acid.

Accurate and high-quality shape generation of individual teeth from cone-beam computerized tomography (CBCT) is essential for computer-aided dentistry. Existing methods need post-process to extract isosurfaces and the output meshes cannot be directly used as the input for most subsequent applications (such as finite element analysis (FEA). In this paper, we propose the network that directly learns the multi-resolution mesh guided by diffeomorphic deformation. Overall, our solution is a classic two-stage schema widely used in tooth reconstruction. Firstly, we adopt a revised anchor-free detector to locate each individual tooth with high precision. Then, we design the top-to-bottom flows from the multi-level features of each individual, referred to as pyramid flows, to predict diffeomorphic deformation from a sphere to a detailed tooth. Finally, we validate the effectiveness and efficiency of the proposed approach by comparing with the previous segmentation methods and other explicit surface learning-based methods in the experiment.

A class of coupled k-Hessian equations is considered. Firstly, by using the u_{\mathrm{0}}-sublinear theorem, it is proved that the equation has at most one radial k-admissible solution under the super-linear and sub-linear conditions. The uniqueness of radial k-admissible solution is verified by a numerical example. Finally, by incorporate with the monotone iterative technique, the uniform convergence of the solution is also discussed.

As an important form of expressing the relationship among entities, graph networks have been widely used in data analysis, relational reasoning, and information services. For these applications, how to reasonably represent network characteristic information is the primary task of network analysis research. Graph embedding technology solves the problem of how to efficiently and reasonably map massive, heterogeneous, and complex high-dimensional graph data to low-dimensional vector space while still retaining the original data feature information. This paper aims to survey the algorithm and research progress of graph embedding in recent years, analyze the development status of this field, and explore the direction for subsequent research. First, it reviews the principle and basic theory of graph embedding technology, then systematically investigates the current mainstream graph embedding algorithms, including graph embedding approaches based respectively on dimensionality reduction, matrix decomposition,network topology,neural network, generative adversarial network, and hypergraph. Then we show the application scenarios of graph embedding technology and introduce the commonly used test data sets and evaluation criteria. Finally, we highlight the future research trends and directions of graph embedding, such as dynamic graph embedding, graph embedding scalability and interpretability.

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.

Let H be an infinite dimensional complex separable Hilbert space and B(H) be the algebra of all bounded linear operators on H. We call property (W_E) holds for T\in B(H) if \sigma (T)\backslash {\sigma }_{\mathrm{w}}(T)=E(T), where \sigma (T) and {\sigma }_{\mathrm{w}}(T) denote the spectrum and Weyl spectrum of T respectively, and E(T)=\{\lambda \in \mathrm{i}\mathrm{s}\mathrm{o}\text{?}\sigma (T):\text{?}\mathrm{d}\mathrm{i}\mathrm{m}N(T-\lambda I)>\mathrm{0}\}. By using the property of topological uniform descent of operators in this paper, the necessary and sufficient conditions for which the property (W_E) holds for bounded linear operators and its functions are given. Furthermore, we show the applications of the main results, and explore the relationship of property (W_E) between the Drazin invertible operator and its Drazin inverse.

Reliability is the primary topic in the theoretical research of reliability models, especially the premise for discussing other indicators in the δ shock model. In this paper, three methods including multiple integration method, independent convolution method and memoryless method are used to prove the system reliability of Yule-Furry classical δ shock model, and the similarities and differences between the three methods are analyzed. Based on the proof process of the memoryless method, the distribution function of the lifetime T is obtained, and a simple proof of reliability is derived.

In this paper, the asymptotic behavior of solutions for the abstract evolution equations with fading memory and nonlinear damping in the time-dependent space is discussed. As an application of theory of process on time-dependent space, the existence of time-dependent attractors in E_t^{\theta } is proved by using contractive function method and more detailed estimates.

Due to the increasing complexity of data form, multi-view clustering algorithms emerge one after another. The main disadvantages of existing methods include: the computational complexity of these methods is high; the final clustering involves additional processing steps; the similarity graph constructed may not be the optimal graph. In order to solve the above problems, a clustering algorithm based on sparse consensus graph decomposition is proposed. The algorithm is first tested on single-view data, and then extends from single-view data to multi-view data. The algorithm takes into account different contributions of different views to the final result by giving each view appropriate weight, at the same time, makes use of the L_{\mathrm{2,1}} norm to obtain the consensus graph with better performance, learns the non-negative representation matrix on the basis of the consensus graph, and reveals the cluster result directly after alternation iteration. Finally, an update iterative algorithm is proposed and tested on a large number of data sets to verify the effectiveness of the algorithm.

Species inventory is the basis for understanding biodiversity. The classification system of lycophytes and ferns developed by ZHANG Xianchun was adopted to analyze the species diversity of lycophytes and ferns in Zhejiang province. The results showed that (1) there were 27 species of lycophytes in 3 families, 5 genera, and 410 species of ferns in 32 families, 84 genera (including subspecies of non-type species). The top 7 families with more than 15 species were Dryopteridaceae (95 species), Polypodiaceae (51 species), Athyriaceae (51 species), Pteridaceae (49 species), Thelypteridaceae (43 species), Aspleniaceae (27 species) and Dennstaedtiaceae (17 species). The top 6 genera with more than 15 species were Dryopteris (43 species), Asplenium (24 species), Diplazium (21 species), Polystichum (20 species), Pteris (18 species) and Arachniodes (16 species). (2) at genus level, 54 genera of plants distributed in tropic and subtropic regions, 15 genera of plants distributed in temperate zones, and 31 genera of plants distributed in pantropic type, accounting for respectively 60.67%, 16.85%, and 34.83% of the total genera, were recorded. (3) as to the areal types of species, 354 species were not endemic to China, accounting for 81.01% of the total species, and these species were mainly distributed in East Asia and tropical Asia. 83 species were endemic to China, accounting for 18.99% of the total species (except those with world-wide distribution). Among them, East China-Central China and South China-Southwest China (to Northwest China) were two dominant areal types, with 24 species. (4) The ancient plant data and modern species all reflected the ancient origin of the flora. The prolycopod (including 27 species in Lycopodiaceae, Isoetaceae and Selaginellaceae) can be traced back to the devonian period; the ferns in Equisetaceae, Ophioglossaceae, Psilotaceae, Marattiaceae (10 species in total) originated relatively early in comparison to ferns in other families. (5) among lycophytes and ferns in Zhejiang province, 5 species were listed as key-protected wild plants in Zhejiang province; 3 species Isoetes sinensis, Isoetes orientalis, and Isoetes baodongii were in the list of Ⅰ-class national protection of wild plants; 11 species of wild plants were in the list of Ⅱ-class national protection of wild plants, including Huperzia selago var. appressa, Huperzia sutchueniana, Cibotium barometz, etc.

This paper discusses the effect of ex-situ ecological combined remediation (ESECR) system on the purification of phosphorus of different forms in the polluted water of Pulin Creek, a tributary of Jiulong River, and each unit of ESECR treatment system is analyzed on the correlation between different phosphorus forms and environmental factors. Results showed that the average total removal rate of TP, DTP, DP and PP of ESECR treatment system were 84.3%, 84.4%, 90.8% and 78.9% respectively, among them the DP purification effect was the best. In each unit of ESECR treatment system, when the phosphorus content in the raw water was low, the sludge-membrane symbiotic (SSM) high efficiency coagulation water purification system had good TP, DTP and DP purification effect, the average removal rate were 81.4%, 76.0% and 84.8% respectively, the average removal rate of PP was 66.7%; when the content of phosphorus in the raw water was high, the average removal rate of TP, DTP and DP of the SSM high efficiency coagulation water purification system were 37.8%, 44.6% and 45.8%, nevertheless, the purification effect of PP was significant, and the average removal rate was 93.2%. When the processed water of the SSM high efficiency coagulation water purification system with low phosphorus content, the purification effect of ecological pond Ⅱ on TP and DTP was better than that of ecological pond Ⅰ, but the results on DP was opposite. For PP, the purification effect in ecological pond Ⅱ was better than that in ecological pond Ⅰ regardless of the impact of phosphorus content. The purification effect of ecological pond Ⅲ fluctuated, the purification effect on DP is relatively significant, and the average removal rate was 94.1%. In addition to the SSM high efficiency coagulation water purification system, the form of phosphorus in the polluted water of Pulin Creek and purified water by ESECR technology was mainly PP, and the percentage of each form in total phosphorus appeared as PP>DTP>DP. Pearson correlation analysis showed that different phosphorus forms were correlated with pH, water temperature and dissolved oxygen (DO) in ESECR treatment system.

In response to the low computational efficiency in the context of multi-scale structural topology design, an efficient asymptotic homogenization GPU parallel strategy is presented. The strategy leverages the graphics processing unit (GPU) and investigates parallel strategies for level set initialization, large sparse stiffness matrix equations solving and constitutive properties computing. Experimental results demonstrate that the computing efficiency of the asymptotic homogenization can be greatly improved by adopting the parallel strategies, in particular, when refining a three-dimensional unit cell grid to a resolution of 100 000, the GPU parallel strategy achieves a speedup of two orders of magnitude compared to the CPU serial.

Selecting Xi'an urban residents as study objects,behavioral intention as intermediary variable,subjective norm as regulating variable,this paper quantitatively analyzes the relationship between travelers' approval degree to shared bicycles and their actual using behavior in green travel activities.The results show that the approval degree to shared bicycles by travelers can significantly affect their behavioral intention.Generally,in the second level dimension of approval degree,travelers are most concerned about the accessibility of shared bicycles,followed by transit recognition and cost-consuming,operability has the least impact on travelers.The mediating effect test shows that behavior intention plays complete mediating role between travelers' approval degree and the actual behavior of green travel. The moderating effect test shows that subjective norm does not play a regulatory role in the relationship between the approval degree on shared bicycles and the behavioral intention of travelers. Finally,this paper is based on empirical case study,aiming to provide necessary scientific and practical reference for the development of new urban transportation system and the construction of a green urban living space network.