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.

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.

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.

The identification of minerals in petrographic thin sections is essentially required in petrological research, and is a prerequisite for further understanding of rock classification, petrogenesis, material flow and evolution history. Traditional methods rely on manual identification with optical microscope, which is costly, time-consuming, and subject to expert judgment and personal experience. Following the development of deep learning technology, it is possible for computer to automatically extract more accurate semantic information from images of petrographic thin sections. This paper proposes a deep learning-based method on petrographic thin section images for automatic mineral identification, which not only utilizes the deep convolutional neural network to extract different mineral features in the images for semantic segmentation and recognition, but also takes into account the plane polarized light images and cross polarized light images for comprehensive automatic identification. Our paper used the photomicrograph dataset of rocks for petrology teaching at Nanjing University for mineral identification and achieved the overall accuracy of 86.7% and Kappa coefficient of 0.818 demonstrating the advantage of the proposed approach compared with those of the traditional image classification methods.

The equation of rotating surface is one of the key contents in the teaching of vector algebra and spatial analytic geometry in higher mathematics. The existing higher mathematics textbooks mostly concern the solution methods of the surface equation formed by the rotation of the coplanar curve on the coordinate plane around the coordinate axis. Based on the equation of the such rotating surfaces, this paper deduces the equation of the general rotating surface formed by rotating a space curve around a fixed space line by using the formula of direction angle and rotation axis. It determines the rotation axis by looking for attitude and its relative position between the two coordinate systems. The method for solving the general equation of rotating surface proposed in this paper not only is a useful supplement to the current teaching content, but also provides a practical reference for constructing the surface rotation.

Based on the land use data in Zhejiang province of 8 periods from 1980 to 2020, this study analyzed the water system spatiotemporal pattern, water surface ratio, transformation trend, landscape pattern and other characteristics in different periods of Zhejiang province, trying to reveal the driving factors of these changes. The results show that: (1) the total water area of Zhejiang province tends to rise, the area of rivers and beaches tend to decrease, while the area of lakes, reservoirs, ponds and tidal flats tend to increase. The transfer of water system was concentrated in rivers, lakes and coastal side. (2) The water landscape pattern index of Zhejiang province increase by MPS, NP, LST, FRA, CCONTAG, and decrease by PD, ED, LPI, COHESION and AI, reflecting the fragmentation, dispersion and complexity of water landscape. (3) The area of water system shows different pattern in different cities, in particular, the area of rivers, reservoirs ponds in Hangzhou is the largest, the area of lakes in Jiaxing and Huzhou is the largest, the area of tidal flats in Ningbo is the largest, the area of beaches in Shaoxing is the largest. The water system of each basin mainly consists of reservoirs and ponds, and their area were increased during these periods, while the area of other land types changed little. (4) The water area system of Zhejiang province was closely related to human activities (GDP, total output value of agriculture, forestry, animal husbandry and fishery, population density), while the influence of natural factors on water area was relatively stable with the influence of annual precipitation greater than that of annual temperature.

Kalamaili area in the northeastern margin of Junggar Basin is an important gold deposit distribution area in China. The fault systems in the area are complex and play a significant ore-controlling role. At present, no scholars have studied the relationship between the fractal characteristics of faults and the distribution of gold deposits in this area. The spatial distribution law, development complexity degree and the control law of faults in different directions and scales in this area need be further studied. In this paper, the fractal dimension of the fault system in the study area is calculated at different scales and in different directions. The fractal dimension of all faults is 1.421, and the fractal dimension of faults is 1.382 in NW direction, 1.223 in NWW direction, 0.998 in EW direction and 0.960 in NE direction. The fractal dimension values of all faults and NW faults in this area are greater than the critical value of fractal dimension (1.22-1.38) that reflects the connectivity of geological bodies. The results show that the geological bodies in Kalamaili area of East Junggar have high connectivity, which provides a favorable migration channel and convergence place for gold mineralization hydrothermal fluid. The NW trending fault structure is the most complex, which is the dominant ore-guiding structure in the study area and plays a controlling role in the formation of gold deposits.This is consistent with the distribution characteristics of NW to NWW trending faults derived from Kalamaili deep fault and Qingshui-Sujiquan fault in most gold deposits (points) in the study area.

The quaternion analytic signal is a generalization of analytic signal in the quaternion sense. It is constructed by an original signal and its quaternion partial and total Hilbert transforms. The signal feature representation can be provided by the polar form of the quaternion analytic signal, such as the local amplitude and local phase angle, the latter includes the structural information of the original signal. The aim of this work is to study the quaternion analytic signal associate with right-sided quaternion Fourier transform and it applications. Firstly, quaternion analytic signal associate with right-sided quaternion Fourier transform is defined. By using Possion operator, the quaternion analytic signal is extended to the quaternion scale function. The quaternion scale function provides the signal features representation. At last, three novel types of phase and amplitude-based edge detectors are proposed. Comparisons with competing methods on real-world images consistently show the superiority of the proposed methods.

Pythagorean fuzzy set (PFS) is an extension of traditional intuitionistic fuzzy set (IFS). It can deal with decision-making problems with multi-attribute information in a wider area. In this paper, we first point out errors in the ranking criterion of Pythagorean fuzzy number (PFN) proposed in a paper, and analyze the reasons that cause these errors through the derivation of reliable information (accuracy function). Then, we propose a new score function through the curved trapezoidal area (CTA) corresponding to the reliable information, which provides a ranking criterion of PFN.The basic properties of the score function are discussed. Finally, we show an example indicating the effectiveness and advantage of the new ranking method.

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.

Photobiological hydrogen production by green algae exhibits a bright application prospect in solar energy utilization and hydrogen energy production due to the advantages of high energy conversion efficiency, environmental friendliness as well as abundant raw materials. This paper analyzes the potential factors limiting photobiological hydrogen production by green algae based on the mechanism, and summarizes various methods to improve the efficiency of photobiological hydrogen production by green algae. The main problems and development trends in the commercial application of photobiological hydrogen production by green algae are briefly reviewed, which are referable for the large-scale application of photobiological hydrogen production by green algae in the future.

Contradictory equations often appear in the predictions of housing price, the number of shared bike rentals, air pollution and other problems. It is of important theoretical significance and practical application value to conduct research on the related numerical method. When the number of contradictory equations is huge, it is too difficult to use the traditional least square method to solve the problem due to the accumulation of errors. In view of this, this paper adopts the least square support vector machine (LS-SVM) algorithm, which is suitable for machine learning of big data process, to solve the huge contradictory equations, and applies the algorithm to problems with practical application background. Experimental results show that the linear, nonlinear, univariate and multivariable contradictory equations can be solved numerically, the change of data type and data volume does not affect the results much, and the appropriate model can be built to obtain high accuracy results as long as the appropriate parameters are selected.

In this paper, we study the regularity theory of very weak solutions for a class of elliptic equations which inhomogeneous terms are p-Laplace operators. Combining Hodge decomposition and the regularity theory of partial differential equations, the relation between the very weak solution of p-Laplacian elliptic equations and the weak solution in the classical sense is established.

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.

The bifurcation mode and firing behavior of the four-dimensional Hindmarsh-Rose (HR) neuron model under electric field are analyzed in detail. Several groups of bifurcation diagrams of the neural system with two parameters are derived by numerical simulation, which correspond to the maximum Lyapunov exponent diagram and the ISI bifurcation diagram. It is found that the system has period-doubling bifurcation, period-adding bifurcation and chaotic structure with "jaggedness" on the biparametric plane. Since parameter identification of neuron model is an important part of neuron dynamics analysis, by constructing a suitable objective function, we propose an adaptive hybrid particle swarm genetic algorithm to convert the parameter identification problem of neuron model into an optimization problem. Numerical simulation results show that the proposed algorithm is effective and feasible in the parameter identification of neuron model.

In order to take prompt and effective response to environmental emergencies caused by benzene leakage, the method of generating emergency plan based on case-based reasoning and emergency response effect is studied. Firstly, based on the random forest algorithm and expert knowledge, a method of calculating weight is constructed to retrieve all the historical similar cases. The similar case set is then obtained. Secondly we develop a system to evaluate the emergency response effect of each similar case. Thirdly we introduce an adaptive group consensus adjustment algorithm to get the group evaluation opinions. The comprehensive evaluation value of each response plan is obtained by jointly accounting for the case similarity and disposal effect, based on which the optimal scheme can be generated. An example is used to illustrate the feasibility and effectiveness of the proposed method.