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The Ramsey number r(G, H) is the smallest positive integer n such that any graph W of order n contains G as a subgraph or its complement contains H as a subgraph. In this paper, we find the exact value for the Ramsey number r(θn, K6); k ≥ 6; n ≥ 6, where θn is a theta graph of order n and K6 is the complete graph of order 6. [ABSTRACT FROM AUTHOR]

We call a Krasner right S‐hypermodule A regular if each cyclic subhypermodule of A is a direct summand of A, and we also call A semiregular if every finitely generated subhypermodule of A lies above a direct summand of A. In this study, some properties of such hypermodules are achieved. This paper consists of concentrating over the radical, as well as their connections with (semi)regularity of hypermodules. Finally, the relationship between f‐supplement submodule and semiregularity is given. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce a new definition of JA‐module Arens regularity, which extends former standard definition. Then a new module structure on the semigroup algebra l1S as l1ES‐module with nontrivial right and left module actions is constructed. Using this construction, it is also proved that l1S is a Jl1S‐module Arens regular if and only if S/≈ is finite. [ABSTRACT FROM AUTHOR]

The problems of operating range and costs are the two most critical bottlenecks restricting the extensive application of electric vehicles (EVs) in China and some other countries. There are also some prominent problems in China's EVs, which lead to poor competitiveness of EVs compared with traditional internal combustion engine vehicles. This paper analyzes the key mathematical factors restricting the development and popularization of EVs in China from the aspects of strategic policy, sales situation, and self-problems. For the best-selling family cars in China, select the representative models with the same body structure, and make statistics on various parameters most concerned by consumers, establish a database through data statistics and analysis software. Through summarizing France's standardization development strategy and relevant issues reflected by the development data of its EVs, this paper puts forward the hypothesis leading the development of EVs through standardization to enhance their competitiveness, gives the specific suggestions, and briefly analyzes the feasibility from the aspects of product situation. The research content of this paper provides a certain basis and ideas for the future research work. [ABSTRACT FROM AUTHOR]

Selecting reasonable blasting parameters of ore and rock is an important measure to achieve good blasting effect. In the mining process, rock fragmentation is an important index to evaluate the blasting effect, which directly affects the technical scheme, equipment selection, economic effect, and other issues of the mine and even seriously threatens the sustainable safety production of the mine. With the rapid development of information technology, the development of computer intelligent image recognition technology is becoming more and more perfect, and its role is becoming more and more important. Based on the neural network method, this paper studies the computer intelligent image recognition technology. In this paper, the GA-BP network image recognition model is established by combining genetic algorithm with BP algorithm and analyzing the principles of intelligent image recognition, image pattern recognition, and BP neural network learning algorithm. On the basis of experimental analysis, the average accuracy of prediction can reach 67.4%. For the efficiency analysis of computer mathematical analysis, it will generally reach 64.3%. In this paper, taking the lump rate and blasting cost as the optimization objective function, the comparison and selection of multiple schemes of production blasting design are carried out, which provides quantitative decision-making basis for the rational selection of production blasting design parameters. [ABSTRACT FROM AUTHOR]

To automatically grade compositions, automatic composition grading primarily employs statistics, mathematical analysis, machine learning, natural language processing, and other technologies. This paper presents a machine learning-based intelligent evaluation model for English composition. As a result, this paper proposes a word vector grouping-based text content representation method and a vector space model-based text content representation method. The Word2Vec model is first trained with words, then used to generate a test model of word vectors, with the statistical information of the corresponding words in each category serving as content text features. The results show that when features based on word vector clustering are added to the content text, the effect of each model improves significantly, especially the maximum entropy model, which improves by 0.048. The XGBoost model has also seen a significant improvement, going from 0.771 to 0.803. The test corpus is made up of 100 articles chosen at random from the corpus, and the test set is checked for errors. The rate of accuracy is 68 percent. The conclusion demonstrates that the model presented in this paper can help promote English teaching reform and quality-oriented higher education while also easing the burden on teachers and students. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the unbalanced data flow integration classification algorithm based on joint nonnegative matrix factorization, in order to solve the problem that the basic clustering results obtained from the original data set have some information loss, thereby reducing the effective information in the integration stage. In this paper, the accuracy of the unbalanced data and the detection time consumption are selected as the research object. Six data sets with imbalanced proportions of minority and majority samples are selected for experiments. Mathematical statistical analysis is first used to observe text classification, disease diagnosis, and network intrusion detection and the classification accuracy of majority class and minority class; the commonly used algorithm for unbalanced data is statistical analysis method. Comparing the univariate method for comprehensive classification of unbalanced data flow based on nonnegative matrix factorization with the unbalanced data algorithm, the observation has accurate rate and detects time-consuming changes. Among them, the comprehensive classification algorithm of unbalanced data flow is based on the classification of data, classifying the data, judging whether two data points belong to the same category, and determining their degree of balance. The research data shows that the unbalanced data flow integrated classification algorithm based on joint nonnegative matrix decomposition can reasonably evaluate the classification performance of the classifier for a few classes, and the detection speed is faster and saves more time. The experimental research shows that the algorithm combines the relationship matrix and information matrix from the original data set into a consensus function, uses NMF technology to obtain the membership matrix, effectively uses potential information, improves the accuracy rate of 69.73%, and shortens 71.65% of the time consumed. [ABSTRACT FROM AUTHOR]

High volume of traffic is loaded on urban highway during peak hours as well as the ramp connecting main road and auxiliary road of highway. Once the demand exceeds the capacity of the ramp, congestion may happen on both main road and the auxiliary road. To deal with this problem, an new urban highway ramp, switchable ramp (SR) that can switch between on and off condition, is proposed in this paper. A macroscopic time-space discrete model is built in this paper to model this process by dividing the studied time period into short time periods and the studied road segment into small sections. The impact of the type of ramp on upstream and downstream traffic flow is analyzed. A segment of urban highway in Chengdu, China, is used as a case study. The traffic flow data in peak hours is collected and used. Mathematical analysis proves that the SR system proposed in this paper can reduce the total travel time (TTT) in the studied area. Results show that the SR system is more useful when the traffic volume is high. [ABSTRACT FROM AUTHOR]

There are many consensus measures that can be computed using Likert data. Although these measures should work with any number n of choices on the Likert scale, the measurements have been most widely studied and demonstrated for n = 5. One measure of consensus introduced by Akiyama et al. for n = 5 and theoretically generalized to all n depends on both the mean and variance and gives results that can differentiate between some group consensus behavior patterns better than other measures that rely on either just the mean or just the variance separately. However, this measure is more complicated and not easy to apply and understand. This paper addresses these two common problems by introducing a new computational method to find the measure of consensus that works for any number of Likert item choices. The novelty of the approach is that it uses computational methods in n-dimensional space. Numerical examples in three-dimensional (for n=6) and four-dimensional (for n=7) spaces are provided in this paper to assure the agreement of the computational and theoretical approach outputs. [ABSTRACT FROM AUTHOR]

Lung cancer is the biggest cause of cancer mortality worldwide and a major impediment to extending life expectancy. In comparison to other cancers, it has a relatively poor survival rate. In this paper, we have developed a mathematical model for lung cancer based on biological phenomena using nonlinear ordinary differential equations and analyzed it both analytically and numerically. According to the findings, CD8+ T cells and dendritic cells have a role in tumor cell variety. Surgery and chemotherapy have been used as treatment options, and we have observed that three doses of chemotherapy after surgery had the greatest results after examining several treatment options. During the treatment period, the cycle of each chemotherapy has been taken every 4 weeks, and the first dose has been taken after 28 days of surgery. Finally, we have evaluated the various starting dates for the best treatment choice and discovered that the patient who begins treatment sooner has a better probability of surviving. [ABSTRACT FROM AUTHOR]

The monitoring and analysis of dynamic changes in land resources can detect the changes of land aimed at a single-band or multiband remote sensing image of multiple phases in a given region or target with image processing methods and can also extract the change information and realize remote sensing monitoring through the comprehensive analysis of multiphase remote sensing images. Synthetic aperture radar (SAR) image change monitoring technology, with the advantages of high resolution, high precision, real-time service, and rapid imaging, can achieve qualitative or quantitative analysis of targets and is gradually widely used in quarterly monitoring, emergency monitoring, postbatch verification, law-enforcement inspection and land inspection, and other remote sensing data acquisitions and analyses. Therefore, on the basis of summarizing the research results of previous research works, this paper expounded the current situation and significance of the researches on the monitoring and analysis of dynamic changes in land resources; elaborated the development background, current situation, and future challenges of SAR sensor data; introduced the methods and principles of band setting, polarization mode, geometric correction, and image filtering; proposed the status target identification of land resources; explored the dynamic information discovery of land resources; conducted the dynamic change monitoring of land resources based on SAR sensor data; analyzed the basis and characteristics of SAR sensor data; performed the generalization and optimization of land resource information; demonstrated the dynamic change analysis of land resources based on SAR sensor data; compared the acceptance ability and accuracy of SAR sensor data; and discussed the discovery and extraction of dynamic information of land resources. The results show that the SAR sensor data can monitor the characteristics of scattering points in land resource observation scenes and can obtain the change information of ground object by distance component and band component, so that the SAR system can make two-dimensional imaging of land resources directly in front of the receiving platform. Thus, the SAR data obtained by multisystem parameters shows great application potential in land resource monitoring, which provides the possibility of decoupling to remove land resources and surface roughness and thus provides possible solutions for land resource analysis in complex environment. The results of this paper provide a reference for the follow-up studies on the monitoring and analysis of dynamic changes in land resources based on SAR sensor data. [ABSTRACT FROM AUTHOR]

Nowadays, skin cancer is a worldwide panic. It is related to ultraviolet radiation. In this paper, we have formulated a SIRS type mathematical model to show the effects of ultraviolet radiation on skin cancer. At first, we have showed the boundedness and positivity of the model solutions to verify the model's existence and uniqueness. The boundedness and positivity gave the solutions of our model bounded and positive, which was very important for real-world situation because in real world, population cannot be negative. Then, we have popped out all the equilibrium points of our model and verified the stability of the equilibrium points. This stability test expressed some physical situation of our model. The disease-free equilibrium point is locally asymptotically stable if R 0 < 1 and if R 0 > 1 , then it is unstable. Again, the endemic equilibrium point is stable, if R 0 > 1 and unstable if R 0 < 1. In order to understand the dynamical behavior of the model's equilibrium points, we examined the phase portrait. We also have observed the sensitivity of the model parameters. After this, we have investigated the different scenarios of bifurcations of the model's parameters. At the set of Hopf bifurcation parameters when infection rate due to UV rays is less than α 1 = 0.01 , proper control may eradicate the existence of disease. From transcritical bifurcation, we can say when recovery rate greater than 1.9, then the disease of skin cancer can be eliminated and when recovery rate less than 1.9 then the disease of skin cancer cannot be eradicated. Finally, numerical analysis is done to justify our analytical findings. [ABSTRACT FROM AUTHOR]

In view of the lack of objective data support for product evaluation methods in the industry, a triangular verification method was proposed; it considered nursing beds as the study object and combined subjective evaluation with eye movement and electroencephalogram. Because the triangular validation method is based on the numerical value between the indicators and the frequency of ranking, this method is worth investigating for analyzing experimental data more scientifically. This paper focuses on the further analysis of the experimental data, especially the use of interval estimation method. After analysis, we obtain that proposal 2 is the optimal solution. This method is more suitable for product evaluation which will collect large amount of experimental data to obtain more accurate results. For industrial product designers, the evaluation of products by users is very important. In the design stage, how to grasp the user's evaluation of the product more accurately is a difficult problem. This paper takes nursing bed as the research object and studies the user participation design in order to make the product more acceptable to most people after it is launched. [ABSTRACT FROM AUTHOR]

Contactors are important components in circuits. To solve the multiobjective optimization problems (MOPs) of contactors, a niching multiobjective particle swarm optimization (NMOPSO) with the entropy weight ideal point theory is proposed in this paper. The new algorithm selecting and archiving the nondominated solutions based on the niching theory to ensure the diversity of the nondominated solutions. To avoid missing the extreme solutions of each objective during the multiobjective optimization process, extra particle swarms used to search the independent optimal solution of each objective are supplemented in this algorithm. In order to determine the best compromise solution, a method to select the compromise solution based on entropy weight ideal point theory is also proposed in this paper. Using the algorithm to optimize the characteristics of a typical direct-acting contactor, the results show that the proposed algorithm can obtain the best compromise solution in MOPs. [ABSTRACT FROM AUTHOR]

Since entering the era of big data, the degree of information sharing is getting higher and higher; the information exchange is becoming more and more convenient, but at the same time, personal information is also easy to be exposed to the network environment, if it is used by criminals to lead to information leakage, and then bring certain risks. Therefore, it is in the information age and do a good job of network information security and confidentiality. At present, the security and secrecy of network information are mainly realized by cryptography. Public key cryptography can encrypt information and ensure the security of information transmission, so it is widely used in the contemporary society. At present, elliptic curve encryption is highly respected in the research field of public key cryptosystem. Elliptic curve encryption is divided into two main points, multiplication and inversion, respectively. Through the comparison of these two algorithms, it can be found that there are several choices if the main research objective is to save time, and the Euclidean extension method is mainly discussed in this paper. In other words, more efficient algorithms are used in the hardware implementation process, and a variety of algorithms can be used instead of a single curve algorithm. In this process, we can find the special features of upper level operation and bottom level finite operation. The upper level operation is KP operation, while the bottom level operation is fast calculation of four kinds of K in finite field operation, and finally realize FPGA algorithm. With the help of Quartus ii developed by predecessors, the upper and lower operations of elliptic curve are carried out using VHDL language. Combined ANXIX9.62 in the elliptic curve of each module to test, so as to ensure the accuracy of the data, reduces the error. According to the test results, the designed chip can efficiently complete the elliptic curve encryption system in the whole process. And the average KP operation time can reach 15.15 ms at 20 MHz frequency. At the same time, the chip can complete the operation on ECC public key with any variable curve in F domain less than 256. Therefore, this chip is a high-speed elliptic curve cryptographic chip with optional system parameters. Based on this, this article on the elliptic curve encryption algorithm based on FPGA hardware implementation of system design, from the view of mathematical study analysis, was carried out on the elliptic curve cryptosystem, according to the above two big difficulty, namely, the polynomial of GF(2), the finite field multiplication, and inversion; there will be a detailed studies of discussion, through software comparison to find the differences between different software, especially the software implementation performance level. In addition, it will also focus on the design of elliptic curve algorithm PGA, so as to explore the solution of the algorithm hardware. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model for the system of prey-predator with immigrant prey has been analyzed to find an approximate solution for immigrant prey population density, local prey population density, and predator population density. Furthermore, we present a novel soft computing technique named LeNN-WOA-NM algorithm for solving the mathematical model of the prey-predator system with immigrant prey. The proposed algorithm uses a function approximating ability of Legendre polynomials based on Legendre neural networks (LeNNs), global search ability of the whale optimization algorithm (WOA), and a local search mechanism of the Nelder–Mead algorithm. The LeNN-WOA-NM algorithm is applied to study the effect of variations on the growth rate, the force of interaction, and the catching rate of local prey and immigrant prey. The statistical data obtained by the proposed technique establish the effectiveness of the proposed algorithm when compared with techniques in the latest literature. The efficiency of solutions obtained by LeNN-WOA-NM is validated through performance measures including absolute errors, MAD, TIC, and ENSE. [ABSTRACT FROM AUTHOR]

In this paper, we study the mathematical analysis of a nonlinear age-dependent predator–prey system with diffusion in a bounded domain with a non-standard functional response. Using the fixed point theorem, we first show a global existence result for the problem with spatial variable. Other results of existence concerning the spatial homogeneous problem and the stationary system are discussed. At last, numerical simulations are performed by using finite difference method to validate the results. [ABSTRACT FROM AUTHOR]

Epilepsy is one of the neurological conditions that are diagnosed in the vast majority of patients. Electroencephalography (EEG) readings are the primary tool that is used in the process of diagnosing and analyzing epilepsy. The epileptic EEG data display the electrical activity of the neurons and provide a significant amount of knowledge on pathology and physiology. As a result of the significant amount of time that this method requires, several automated classification methods have been developed. In this paper, three wavelets such as Haar, dB4, and Sym 8 are employed to extract the features from A–E sets of the Bonn epilepsy dataset. To select the best features of epileptic seizures, a Particle Swarm Optimization (PSO) technique is applied. The extracted features are further classified using seven classifiers like linear regression, nonlinear regression, Gaussian Mixture Modeling (GMM), K-Nearest Neighbor (KNN), Support Vector Machine (SVM-linear), SVM (polynomial), and SVM Radial Basis Function (RBF). Classifier performances are analyzed through the benchmark parameters, such as sensitivity, specificity, accuracy, F1 Score, error rate, and g-means. The SVM classifier with RBF kernel in sym 8 wavelet features with PSO feature selection method attains a higher accuracy rate of 98% with an error rate of 2%. This classifier outperforms all other classifiers. [ABSTRACT FROM AUTHOR]

This paper is concerned with the event-based state and fault estimation problem for a class of linear discrete systems with randomly occurring faults (ROFs) and missing measurements. Different from the static event-based transmission mechanism (SETM) with a constant threshold, a dynamic event-based mechanism (DETM) is exploited here to regulate the threshold parameter, thus further reducing the amount of data transmission. Some mutually independent Bernoulli random variables are used to characterize the phenomena of ROFs and missing measurements. In order to simultaneously estimate the system state and the fault signals, the main attention of this paper is paid to the design of recursive filter; for example, for all DETM, ROFs, and missing measurements, an upper bound for the estimation error covariance is ensured and the relevant filter gain matrix is designed by minimizing the obtained upper bound. Moreover, the rigorous mathematical analysis is carried out for the exponential boundedness of the estimation error. It is clear that the developed algorithms are dependent on the threshold parameters and the upper bound together with the probabilities of missing measurements and ROFs. Finally, a numerical example is provided to indicate the effectiveness of the presented estimation schemes. [ABSTRACT FROM AUTHOR]

This paper proposes effective evidence on the correlation between trend and self-organized criticality (SOC) of the power outage sequence in China. Taking the data series of blackouts from 1981 to 2014 in the China power grid as the research object, the method of V / S is introduced into the analysis of the power system blackout sequence to demonstrate their prominent long-time correlations. It also verifies the probability distribution of load loss about blackout size in the China power grid has a tail feature, which shows that the time series of blackouts in the China power grid is consistent with SOC. Meanwhile, a kind of mathematical statistics analysis is presented to prove that there is a seasonal trend of blackouts, and the blackout frequency and blackout size have not decreased over time but have an upward trend in the China power grid, thereby indicating that blackout risk may be increasing with time. The last 34 years' data samples of power failure accidents in the China power grid are used to test the proposed method, and the numerical results show that the proposed self-organized criticality and trend analysis method can pave the way for further exploration of the mechanism of power failure in the China power grid. [ABSTRACT FROM AUTHOR]

There has been a long history for foundation treatment by quicklime pile, but as for establishing a more precise model formula used by actual construction, further research is needed to be done at present. Therefore, how to quantitate the factors affecting pile spacing is of great reference value for both actual constructions and theoretical studies. Based on the reference formula for handling weak foundation by lime pile and the practical problems in the western region, mathematical model analysis method is used to get a new model for high water content loess foundation treatment after considering the factors such as pile expanding, construction method, piles arrangement, and calcium oxide content. In this model, pile spacing coefficient is created and the model formula for different construction methods and different pile arrangements is also given. As a result, the reference formula used in high water content loess is somewhat conservative. The new model is also verified to be rational by the actual works at the end of the paper. [ABSTRACT FROM AUTHOR]

Physical layer identification is an emerging technique that exploits physical layer features to identify wireless devices. The identification accuracy and the device quantity that can be identified at most are significant for the identification scheme. Existing works primarily focus on the feature correlation analysis for multifeature selection without investigating the least upper bound (supremum) of the performance of a single feature. The supremum indicates the limit of the performance, which is another sight for evaluating the quality of features and improving the performance of the identification scheme. Therefore, this paper first investigates the supremum of the performance of the most commonly used physical layer feature, i.e., carrier frequency offset (CFO). Specifically, we offer a rigorous mathematical analysis and derive the closed-form expression of the supremum of identification accuracy based on the max-min distance analysis (MMDA) criterion. And then, the supremum of the number of distinguishable devices is also analyzed. Finally, we conducted a simulation study to verify the theoretical analysis result. [ABSTRACT FROM AUTHOR]

The cold and high altitude Tibetan area (hereinafter referred to as Tibetan area) is a special geographical area in western China. Whether the local economic development and EE (ecological environment) are coordinated or not directly affects the sustained and healthy economic and social development of the whole Tibetan area. Firstly, this paper discusses the relationship between economic growth and EE on the basis of existing related theoretical research. Then, 15 indicators of economic system and environmental system were selected, and the coupling degree model and coupling coordination degree model were constructed to quantitatively analyze the dynamic model of regional economic and EE coupling and coordinated development in Tibetan areas from 2010 to 2020. The research found that in the past 11 years, the comprehensive index of EE of four regions in Tibetan areas has changed from 0.5 to 0.6, and the comprehensive index of the economy of four regions in Tibetan areas has changed from 0.51 to 0.74. On the whole, the coordination degree and coordinated development degree of green development in Tibetan areas have changed at the same time compared with the years, and since 2016, both of them have had the same trend and both of them are beginning to develop in a good direction. Since 2017, the economic development has been relatively advanced, while the EE has lagged behind, showing a fluctuating state, while the level of coordinated development has been continuously improved. This study has certain reference value for promoting ecological protection and green development in Tibetan areas. [ABSTRACT FROM AUTHOR]

This paper presents a study on capacity policy for an OEM, launching a new short life cycle consumer durable product, and undergoes a demand diffusion process and a production ramp-up process with learning. The demand/supply dynamic system is described by the Bass diffusion demand rate and time constant production rate. The mismatch of demand peak and production plateau creates challenges for balancing the interactive trajectories. Indivisible lumpy capacity increments in the production network exacerbate the difficulty. In conjunction with mathematical and graphical analysis and computation power, we model a discrete optimization model (running on CPLEX) to investigate "how the OEM should determine an optimal capacity size" and "when to market the new product and expand capacity" under various Bass parameters, which describe the behavior intensity of the innovation and imitation of new product consumers. [ABSTRACT FROM AUTHOR]

Ensuring the integrity of remote data is the prerequisite for implementing cloud-edge computing. Traditional data integrity verification schemes make users spend a lot of time regularly checking their data, which is not suitable for large-scale IoT (Internet of Things) data. On the other hand, the introduction of a third-party auditor (TPA) may bring about greater privacy and security issues. We use blockchain to address the problem of TPA. However, implementing dynamic integrity verification with blockchain is a bigger challenge due to the low throughput and poor scalability of blockchain. More importantly, whether there is a security problem with blockchain-based integrity verification is not yet known. In this paper, we propose a scalable blockchain-based integrity verification scheme that implements fully dynamic operations and blockless verification. The scheme builds scalable homomorphic verification tags based on ZSS (Zhang-Safavi-Susilo) short signatures. We exploit smart contract technology to replace TPA for integrity verification tasks, which not only eliminates the risk of privacy leakage but also resists collusion attacks. Furthermore, we formally define a blockchain-based security model and prove that our scheme is secure under the security assumption of cryptographic primitives. Finally, the mathematical analysis of our scheme shows that both the communication complexity and the communication complexity of an audit are O c , in which c is the number of challenge blocks. We compare our scheme with other schemes, and the results show that our scheme has the lowest time consumption to complete an audit. [ABSTRACT FROM AUTHOR]

The second-hand smoke is a phenomenon that needs to be investigated, and its effects on the health of the people are to be examined. To analyze such an issue, the mathematical models are the best tools that help us to study the dynamical behaviors of this phenomenon. For this purpose, in the present paper, we consider a three-compartmental fractal-fractional mathematical model of a specific population of smokers or people that are exposed to second-hand smoke. By assuming some conditions on ϕ - ψ -contractions and compact operators, we prove some theorems in relation to the existence of solutions. The Banach principle for the usual contractions is used for proving the uniqueness of solutions. Next, by some notions of functional analysis, two types of Ulam-Hyers stability for the fractal-fractional second-hand smoker model are established. Moreover, we have a steady-state analysis and obtain equilibrium points and basic reproduction number R 0 . Then, we investigate the sensitivity of the fractal-fractional system with respect to each parameter. For numerical simulation, the Adams-Bashforth (AB) method is used to derive numerical schemes for plotting and simulating the approximate solutions. Finally, the obtained solutions are tested with real data and different values of fractal dimensions and fractional orders. [ABSTRACT FROM AUTHOR]

Deployment of DC Electric Spring (DCES) technology is an innovative demand side management (DSM) program that helps to mitigate voltage interruptions. Conventional control strategy uses proportional-integral controllers to regulate DC spring parameters. As PI controllers have a trade-off between settling time and peak overshoot, they may not be able to achieve the desired dynamic performance under varying DC microgrid (DCMG) conditions. In this regard, this paper proposes an inverted zero compensator for the control of shunt DCES (ShDCES) in DCMG. This controller regulates the ShDCES current and terminal voltage under all operating conditions with reduced settling time and peak overshoot. A power management algorithm is also proposed to optimize the operation of ShDCES under the presence of varying PV generation and critical and noncritical loads. A detailed mathematical analysis of ShDCES and inverted zero compensator design are furthermore incorporated to validate the strategy. The simulation of the proposed method is performed in MATLAB/Simulink environment. The comparison analysis with the conventional controller proves the effectiveness of the new controller. The results are also validated using real-time simulator OP4510RTS. [ABSTRACT FROM AUTHOR]

This paper is devoted to answering some questions using a mathematical model by analyzing India's first and second phases of the COVID-19 pandemic. A new mathematical model is introduced with a nonmonotonic incidence rate to incorporate the psychological effect of COVID-19 in society. The paper also discusses the local stability and global stability of an endemic equilibrium and a disease-free equilibrium. The basic reproduction number is evaluated using the proposed COVID-19 model for disease spread in India based on the actual data sets. The study of nonperiodic solutions at a positive equilibrium point is also analyzed. The model is rigorously studied using MATLAB to alert the decision-making bodies to hinder the emergence of any other pandemic outbreaks or the arrival of subsequent pandemic waves. This paper shows the excellent prediction of the first wave and very commanding for the second wave. The exciting results of the paper are as follows: (i) psychological effect on the human population has an impact on propagation; (ii) lockdown is a suitable technique mathematically to control the COVID spread; (iii) different variants produce different waves; (iv) the peak value always crosses its past value. [ABSTRACT FROM AUTHOR]

Shield tunnelling has become the development direction of tunnel construction due to its safety, economy, and speed. The complex formation has complicated geological changes, including soft rock, hard rock, and soft and hard inhomogeneous formation. It is particularly difficult to select and control the tunnelling parameters in shield tunnelling, while the reasonable selection and control of the tunnelling parameters play an important role in the excavation efficiency, tool wear, and surface settlement. Based on the tunnel project between the Dinggong Road North Station and the People's Park Station online 4 of Nanchang Metro during shield tunnelling construction, this paper collects thrust, torque, and revolution speed of the cutterhead during shield tunnelling in the complex strata with differentiated argillaceous siltstone and gravel and analyzes these parameters by means of mathematical statistics analysis, in order to explore the interrelationship between shield tunnelling parameters under different stratigraphic conditions and put forward optimization suggestions for tunnelling parameters, which can provide a reference for control of tunnelling parameters of earth pressure shield in composite strata. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) and coronavirus (COVID-19) are both infectious diseases that globally continue affecting millions of people every year. They have similar symptoms such as cough, fever, and difficulty breathing but differ in incubation periods. This paper introduces a mathematical model for the transmission dynamics of TB and COVID-19 coinfection using a system of nonlinear ordinary differential equations. The well-posedness of the proposed coinfection model is then analytically studied by showing properties such as the existence, boundedness, and positivity of the solutions. The stability analysis of the equilibrium points of submodels is also discussed separately after computing the basic reproduction numbers. In each case, the disease-free equilibrium points of the submodels are proved to be both locally and globally stable if the reproduction numbers are less than unity. Besides, the coinfection disease-free equilibrium point is proved to be conditionally stable. The sensitivity and bifurcation analysis are also studied. Different simulation cases were performed to supplement the analytical results. [ABSTRACT FROM AUTHOR]

Generally speaking, spoken term detection system will degrade significantly because of mismatch between acoustic model and spontaneous speech. This paper presents an improved spoken term detection strategy, which integrated with a novel phoneme confusion matrix and an improved word-level minimum classification error (MCE) training method. The first technique is presented to improve spoken term detection rate while the second one is adopted to reject false accepts. On mandarin conversational telephone speech (CTS), the proposed methods reduce the equal error rate (EER) by 8.4% in relative. [ABSTRACT FROM AUTHOR]

The integrals evaluated are the products of multivariable Aleph-functions with algebraic functions, Jacobi polynomials, Legendre functions, Bessel-Maitland functions, and general class of polynomials. The main results of our paper are quite general in nature and competent at yielding a very large number of integrals involving polynomials and various special functions occurring in the problem of mathematical analysis and mathematical physics. [ABSTRACT FROM AUTHOR]

The q‐rung orthopair fuzzy set (q‐ROFS) that the sum of the qth power of the membership degree and the qth power of the nonmembership degree is restricted to one is a generalization of fuzzy set (FS). Recently, many researchers have given a series of aggregation operators to fuse q‐rung orthopair fuzzy discrete information. Subsequently, although some scholars have also focused on studying q‐rung orthopair fuzzy continuous information and give its continuity, derivative, differential, and integral, those studies are only considered from the perspective of multivariable fuzzy functions. Thus, the main aim of the paper is to study the q‐rung orthopair fuzzy continuous single variable information. In this paper, we first define the concept of q‐rung orthopair single variable fuzzy function (q‐ROSVFF) to describe the fuzzy continuous information, and give its domain to make sure that this kind of function is meaningful. Afterward, we propose the limits, continuities, and infinitesimal of q‐ROSVFFs, and offer the relationship between the limit of q‐ROSVFF and that of q‐ROSVFF infinitesimal. On the basis of the definition of derivative in mathematical analysis, we define the subtraction and division derivatives and basic operational rules, and offer the simpler proofs for the derivatives of q‐ROSVFFs. What is more, we propose the subtraction and division differential invariances, and give the approximate calculation formulas of q‐ROSVFFs when the value of independent variable is changed small enough. In the real situation, fundamental functions cannot be used to express more complicated functions, thus we define the compound q‐ROSVFFs and give their chain rules of subtraction and division derivatives. Finally, we use numerical examples by simulation to verify the feasibility and veracity of the approximate calculation on q‐ROSVFFs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a delayed differential system to model labor force (occupied labor force and unemployed) evolution. The mathematical analysis of our model focuses on the local behavior of the labor force around a positive equilibrium position; the existence of a branch of periodic solutions bifurcated from the positive equilibrium is then analyzed according to the Hopf bifurcation theorem. Finally, we performed numerical simulations to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

We consider the problem of the optimization of the functioning of a pumped-storage hydroplant. The problem can be mathematically formulated as an optimal control problem, and when the considered hydromodel is of the fixed-head type, an added complication arises: the solution is of the bangsingular-bang type. In this paper, we propose a simple and efficient optimization algorithm to find the solution. [ABSTRACT FROM AUTHOR]

Let L=-div(A∇) be a second-order divergence form elliptic operator, where A is an accretive n×n matrix with bounded measurable complex coefficients in Rn. In this paper, we mainly establish the Lp boundedness for the commutators generated by b∈Iα(BMO) and the square function related to fractional differentiation for second-order elliptic operators. [ABSTRACT FROM AUTHOR]

Roguing and replanting are the most common strategies to control plant diseases and pests. How to build the mathematical models of plant virus transmission and consider the impact of roguing and replanting strategies on plant virus eradication is of great practical significance. In the present paper, we propose the mathematical models for plant virus transmission with continuous and impulsive roguing control. For the model with continuous control strategies, the threshold values for the existences and stabilities of multiple equilibria have been given, and the effect of roguing strategies on the threshold values is also addressed. Furthermore, the model with impulsive roguing control tactics is proposed, and the existence and stability of the plant-only and disease-free periodic solutions of the model are investigated by calculating several threshold values. Moreover, when selecting the design control strategy to minimize the threshold, we systematically analyze the existence of the optimal times of roguing infected plants within a replanting cycle, which is of great significance to the design and optimization of the prevention and control strategy of plant virus transmission. Finally, numerical investigations are given to reveal the main conclusions, and the biological implications of the main results are briefly discussed in the last section. [ABSTRACT FROM AUTHOR]

This paper further investigates the problem of stability for a general linear system with time-varying delays. Firstly an improved type of Lyapunov–Krasovskii functional is introduced with integral and nonintegral terms and time-correlation terms. Referring a few existing papers, some valid inequalities mathematical analysis techniques are used in this paper in order to reduce the conservatism of the system. Finally, two examples are presented to demonstrate the advantages of the proposed tactics in this paper. [ABSTRACT FROM AUTHOR]

In the past decade the humanitarian supply chain (HSC) has attracted the attention of researchers due to the increasing frequency of disasters. The uncertainty in time, location, and severity of disaster during predisaster phase and poor conditions of available infrastructure during postdisaster phase make HSC operations difficult to handle. In order to overcome the difficulties during these phases, we need to assure that HSC operations are designed in an efficient manner to minimize human and economic losses. In the recent times, several mathematical optimization techniques and algorithms have been developed to increase the efficiency of HSC operations. These techniques and algorithms developed for the field of HSC motivate the need of a systematic literature review. Owing to the importance of mathematical modelling techniques, this paper presents the review of the mathematical contributions made in the last decade in the field of HSC. A systematic literature review methodology is used for this paper due to its transparent procedure. There are two objectives of this study: the first one is to conduct an up-to-date survey of mathematical models developed in HSC area and the second one is to highlight the potential research areas which require attention of the researchers. [ABSTRACT FROM AUTHOR]

In the paper, we have considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia coinfection in a human population at different infection stages. Our model revealed that the disease-free equilibrium points of the HIV/AIDS and pneumonia submodels are both locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R H and R P ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R P and R H ) are greater than unity. The full HIV/AIDS-pneumonia coinfection model has both locally and globally asymptotically stable disease-free equilibrium points whenever the basic reproduction number of the coinfection model R H P is less than unity. Using standard values of parameters collected from different kinds of literature, we found that the numerical values of the basic reproduction numbers of the HIV/AIDS-only submodel and pneumonia-only submodel are 17 and 7, respectively, and the basic reproduction number of the HIV/AIDS-pneumonia coinfection model is max 7 , 17 = 17. Applying sensitive analysis, we identified the most influential parameters to change the behavior of the solution of the considered coinfection dynamical system are the HIV/AIDS and pneumonia transmission rates β 1 and β 2 , respectively. The coinfection model was numerically simulated to investigate the stability of the coinfection endemic equilibrium point, the impacts of transmission rates, and treatment strategies for HIV/AIDS-only, pneumonia-only, and HIV/AIDS-pneumonia coinfected individuals. Finally, we observed that numerical simulations indicate that treatment against infection at every stage lowers the rate of infection or disease prevalence. [ABSTRACT FROM AUTHOR]

In this paper, a new topology of multilevel inverter (MLI) is designed with a fewer number of components and low total harmonic distortion (THD) for high-power photovoltaic (PV) systems. The key limitations of conventional MLI topologies are high total harmonic distortion (THD) and the use of a large number of switching components due to which the cost of the overall inverter is high. In conventional MLI, THD can be significantly reduced by the addition of a large value filter element at the input side; however, it will result in increased size and cost. Thus, achieving a pure sinusoidal AC at the output and to maintain a low THD level is a major issue in conventional MLIs. The proposed MLI has the advantage of decreasing the output THD by using a modified form of the cascaded H-Bridge structure and sine pulse width modulation technique. The proposed inverter consists of 6 unidirectional switches and 2 bidirectional switches, and there is no extra requirement for additional voltage balancing capacitors or clinching diodes. The individual switching states and SPWM operation for generating the gate pulses of the proposed MLI are discussed in detail. Relevant waveforms are plotted, equations are derived, and mathematical analysis is carried out. A steady-state analysis of the proposed MLI demonstrates an output voltage with 17 levels while using only four DC sources. Simulation results of the proposed MLI for single-phase and three-phase structures are obtained, and comparison is carried out with existing MLI topologies which shows that the proposed MLI has significantly low THD and better performance. From the results, it is clear that the proposed MLI has a THD of 3.52% in comparison with four conventional MLIs whose THDs are 6.1%, 6.63%, 7.3%, and 9.93%. Moreover, the proposed MLI generates 17 voltage levels by using only 08 switching devices, whereas the conventional MLIs use more than 10 switching devices for the generation of 15 voltage levels. [ABSTRACT FROM AUTHOR]

The FRP-confined concrete-encased steel column is a new form of hybrid column, which integrates advantages of all the constituent materials. Its structural performance, including load carrying capacity, ductility, and corrosion resistance, has been demonstrated to be excellent by limited experimental investigation. Currently, no systematic procedure, particularly for that with reinforced structural steel of arbitrary shapes, has been proposed for the sectional analysis and design for such novel hybrid columns under biaxial loading. The present paper aims at filling this research gap by proposing an approach for the rapid section analysis and providing rationale basis for FRP-confined concrete-encased arbitrarily shaped steel columns. A robust iterative scheme has been used with a traditional so-called fiber element method. The presented numerical examples demonstrated the validity and accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, some new results are obtained for the even order neutral delay difference equation ΔanΔm-1xn+pnxn-kα+qnxn-lβ=0, where m≥2 is an even integer, which ensure that all solutions of the studied equation are oscillatory. Our results extend, include, and correct some of the existing results. Examples are provided to illustrate the importance of the main results. [ABSTRACT FROM AUTHOR]

Bus timetabling is a subproblem of bus network planning, and it determines departure time of each trip of lines to make vehicles from different lines synchronously arrive at transfer stations. Due to the well-designed coordination of bus timetables, passengers can make a smooth transfer without waiting a long time for connecting buses. This paper addresses the planning level of resynchronizing of bus timetable problem allowing modifications to initial timetable. Timetable modifications consist of shifts in the departure times and headways. A single-objective mixed-integer programming model is proposed for this problem to maximize the number of total transferring passengers benefiting from smooth transfers. We analyze the mathematical properties of this model, and then a preprocessing method is designed to reduce the solution space of the proposed model. The numerical results show that the reduced model is effectively solved by branch and bound algorithm, and the preprocessing method has the potential to be applied for large-scale bus networks. [ABSTRACT FROM AUTHOR]