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.

With the increasing richness of online fitness resources, autonomous fitness has become a new sporting trend. However, due to the lack of action guidance and correction by professional fitness coaches, autonomous fitness usually cannot guarantee the fitness effect and is easy to cause sports injuries, so real-time monitoring of fitness actions is required. Existing fitness monitoring equipment usually relies on professional hardware such as big screens, stereo camera and other sensors. As a result, they fail to satisfy common needs for virtual fitness due to high cost, complexity of installation and limited application scenario. With gradual maturing of human pose estimation technique, identification of human face and movements of limbs can be realized through easily accessible cell phone camera with high accuracy and speed. Low cost, multi-scenario virtual fitness monitoring on mobile terminal thus it made possible. Based on the background above, this work designs a fitness action evaluation algorithm based on angle thresholds in 3D scenes which relies on cell phone monocular camera and 3D human key point detection technology. The algorithm can detect whether the user's fitness actions are standard in real time and give corresponding responses through voice. The work has implemented a prototype system on an Android phone. This work verifies the usability and real-time performance of the algorithm and the system through a series of user experiments. It also verifies the accuracy of the action evaluation algorithm through comparative experiments with relevant work in recent years. Results shows that the algorithm and functions of the prototype system were greatly recognized by the users with high accuracy, reasonable responding speed for real time usage.

Nowadays,the feature of cyber-security can be extracted intuitively and the cyber-security situation can be perceived in all aspects through cyber-security visualization. However, macro control of the overall analysis process of cyber-security is still a research challenge. In this paper, a set of general cyber-security event analysis model is proposed combined with the cyber-security visualization and the classic SEMMA (sample-explore-modify-model-assess) analytic model in DM. In order to standardize the security event exploration analysis process, it divides the analysis process into several specific steps such as data processing, behavioral feature exploration, anomalous object localization, anomalous event description and behavioral pattern association analysis. Fuzzy C-Means is referenced in the analysis model to quantify host behavior and identify network asset structures in the process of feature exploration. PBNLD (protocol-based node link diagram), a new visual presentation, is presented to construct network communication model, which can enhance the rendering quality of massive scale of nodes. Guided by the security event analysis model, the cyber-security event visual exploration system is built for multi-source security log instance data. Network asset segmentation, network anomaly event extraction and attack event evolution are implemented through multi-views synergy and backtracking way. Experimental results prove the validity of the analytical model.

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.

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.

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 order to solve the problem of large computation and model redundancy when applying deep learning to image watermarking,and to improve the robustness of image watermarking algorithm against noise,rotation,and cropping attacks,this paper adopts the robust image neural architecture search (NAS). Multinomial distribution learning for effective the neural architecture search watermarking network algorithm based on algorithm to find the optimal network structure in the preset search space,and performs efficient embed-ding and robust extraction of image watermarks. Firstly,the linearly connected fully convolutional layers in the sub-network are changed to independent neural unit structure,then we parameterize the connection of nodes in the structural unit,and set the search space for each neuron operation in the structural unit. Secondly,after completing a batch of data set training each time,the probabilities of being selected for the next operation are dynamically updated according to the number of samples and the average loss function value.Finally,the network structure after the search is retrained,which reduces the model parameters by more than 92% comparing with original model as well as the model training time. Since the obtained network structure is more compact,the proposed algorithm can achieve higher performance and better experimental results.Compared to the original network,the newly-developed network relies less on spatial information when hiding images.A larger number of experiments are performed to illustrate the advantages of the proposed algorithm including resisting salt and pepper noise,rotation and flipping,and removing pixel rows (columns) and other attacks on the CIFAR-10 data set; and has significant advantages against attacks of median filtering,Gaussian filtering,JPEG compression,and cropping on ImageNet,especially for the random removal of rows (columns) and salt and pepper noise.

Most of the studies on transit-oriented development TOD in China were focused on planning practice, and to what extent TOD can reduce the urban residents' car kilometers traveled was unclear. Based on the Nanjing household travel survey data, the "T" factor of TOD was defined by whether there was a subway station within the distance of 800 m from the household residence; the "D" factor of TOD was defined by residence density, mix, and walk score. After controlling for socioeconomic and home location factors, a Tobit model was proposed to study the effect of TOD on reducing the urban residents' car kilometers traveled. By classifying four residence types (i.e., TOD, only-T, only-D, and non-TOD) and analyzing the marginal effects, we found that the car kilometers traveled decreases by 19.6% when the "T" factor changes from no subway station to one subway station; and it decreased by 0.7% for every 0.01 increase in the "D" factor; the car kilometers traveled decreased by 43.4% if the effect of both "T" and "D" were combined. Based on the above findings, it was suggested that the planning studies should shift from only-T to TOD and from non-TOD to only-D.

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 convergence of solutions for the Brinkman fluid interfacing with a Darcy fluid in a bounded region in\text{?}{R}^{\mathrm{3}} is studied. We assume that the velocity of fluid is slow and it is governed by the Brinkman equations in {\mathrm{\Omega }}_{\mathrm{1}}, while in {\mathrm{\Omega }}_{\mathrm{2}},the saturated flow satisfies the Darcy equations. With the aid of the maximum of the temperature T and some other a priori bounds, we formulate an energy expression, and the expression satisfies a differential inequality. By integrating, we are able to demonstrate the convergence result for the boundary coefficient.

In recent years, artificial intelligence technologies such as machine learning have been applied to protein engineering, and have shown unique advantages in studies on as protein structure, function prediction, and catalytic activity. In the absence of protein structure, combining protein sequence and functional properties with machine learning is a new research direction. In this papers, based on a new sequence-activity relationship (ISAR) method, the mutant library of gloeobacter violaceus rhodopsin (GR) and the maximum absorption wavelength of the spectrum are modeled by machine learning. It can fit the best model even in the case of a small number of data sets. The proposed method digitizes the protein amino acid sequence, preprocesses it through fast Fourier transform (FFT), and then performs partial least squares regression (PLSR) modeling. Finally, the best model of the amino acid sequence of the rhodopsin mutant protein and the maximum absorption wavelength of the spectrum is obtained. Modeling with the best index LEVM760106, the coefficient of determination is that R² is 0.944, and the minimum mean square error E is 11.64. In contrast, when the wavelet transform was used to preprocess the data, the coefficient of determination is close to 0.944, but the E is greater than 11.64, not as good as the result of FFT preprocessing. It is shown that, this method effectively solves the mathematical model relationship between protein sequence and functional characteristics, and provides support for predicting better mutants in later protein engineering.

The Yangtze River basin plays an important role in Chinese water resources allocation. What proves common knowledge is that it is particularly important to predict the water quality in the Yangtze River basin. Based on the existing research, the recurrent neural network (RNN) model with gate recurrent unit (GRU) and fully connected neural network (FCNN) are combined in this study to improve a multiple water quality parameter prediction (MWQPP) model. It is proposed to predict the four water quality parameters, such as pH, dissolved oxygen (DO), permanganate index (CODMn) and ammonia nitrogen (NH₃-N) in the Yangtze River basin. Based on 7 566 raw data of 23 water quality monitoring points in the Yangtze River basin from 2011 to 2018, the comparative experiments show that the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and coefficient of determination (R²) obtained from the MWQPP model's prediction results are better than traditional models, such as the multiple linear regression model, the random forest model, FCNN model and LSTM model, and the MWQPP model also has better robustness than these traditional water quality prediction models. As we can say, the MWQPP model can provide scientific, reasonable and effective support for water quality assurance and water management in Yangtze River basin.

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.

Based on the generalized autoregressive score (GAS) and heterogeneous autoregressive of realized volatility (HAR-RV) models, introduce investor sentiment factor, this paper constructs HAR-RV GAS and HAR -RV SENT GAS volatility models, aim to predict the superior predictive ability (SPA) test, analyze the ability of in-sample data fitting and out of sample volatility prediction respectively.Through VAR prediction sequence diagram and average quantile loss function, the effect of VaR prediction is analyzed empirically. The results show that HAR-RV-SENT GAS model is the best in volatility and VaR prediction ability, followed by HAR -RV GAS model. This study can provide theoretical reference for financial investors and risk managers.

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.