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Recently, many literatures have proved that prior information and structure in many application fields can be formulated as constraints on regression coefficients. Following these work, we propose a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document}L1 penalized LAD estimation with some linear constraints in this paper. Different from constrained lasso, our estimation performs well when heavy-tailed errors or outliers are found in the response. In theory, we show that the proposed estimation enjoys the Oracle property with adjusted normal variance when the dimension of the estimated coefficients p is fixed. And when p is much greater than the sample size n, the error bound of proposed estimation is sharper than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{k\log (p)/n}$$\end{document}klog(p)/n. It is worth noting the result is true for a wide range of noise distribution, even for the Cauchy distribution. In algorithm, we not only consider an typical linear programming to solve proposed estimation in fixed dimension , but also present an nested alternating direction method of multipliers (ADMM) in high dimension. Simulation and application to real data also confirm that proposed estimation is an effective alternative when constrained lasso is unreliable.

Two lower bounds of Sperb for the first eigenvalue of an elastically attached membrane are proved in an elementary way.

Above method of evaluating the mean value and the root-mean-square deviation of a number of observations with a simultaneous checking of deviations from a normal distribution curve requires a fraction of the time normally required by conventional analytical methods.

This paper is devoted to the study of the qualitative properties of solutions to boundary-value problems for strongly elliptic differential-difference equations. Some results for these equations such as existence and smoothness of generalized solutions in certain subdomains of Q were obtained earlier. Nevertheless, the smoothness of generalized solutions of such problems can be violated near the boundary of these subdomains even for infinitely differentiable right-hand side. The subdomains are defined as connected components of the set that is obtained from the domain Q by throwing out all possible shifts of the boundary Q by vectors of a certain group generated by shifts occurring in the difference operators. For the one dimensional Neumann problem for differential-difference equations there were obtained conditions on the coefficients of difference operators, under which for any continuous right-hand side there is a classical solution of the problem that coincides with the generalized solution. 2 Also there was obtained the smoothness (in Sobolev spaces W k ) of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations in subdomains excluding -neighborhoods of certain points. However, the smoothness (in Ho lder spaces) of generalized solutions of the second boundary-value problem for strongly elliptic differential-difference equations on the boundary of adjacent subdomains was not considered. In this paper, we study this question in Ho lder spaces. We establish necessary and sufficient conditions for the coefficients of difference operators that guarantee smoothness of the generalized solution on the boundary of adjacent subdomains for any right-hand side from the Ho lder space.

WOS:000332084500006 In this short paper, we give a generalization of the classical Korovkin approximation theorem (Korovkin in Linear Operators and Approximation Theory, 1960), Volkov-type theorems (Volkov in Dokl. Akad. Nauk SSSR 115: 17-19, 1957), and a recent result of (Tasdelen and Erencin in J. Math. Anal. Appl. 331(1): 727-735, 2007).

Model averaging has been demonstrated as a powerful tool in statistical prediction over the past decade. However, a majority of related works focus on the parametric model averaging. In this paper, we propose a model averaging estimation under nonparametric varying-coefficient models. Differing from existing works, our proposal concentrates on the development of the B-spline approximation to nonparametric varying coefficient functions for model average estimator, rendering the computational burden more cheaply than the kernel smoothing based estimator. Furthermore, our procedure is asymptotically optimal under mild conditions. The asymptotic optimality established in current paper is in terms of conditional quadratic loss function when the variance of model error is known or unknown, respectively. Three different cases of candidate models are considered. Extensive simulations are carried out to evaluate the finite-sample performance of our estimator. A real data is analyzed for illustration as well.

In this short paper, we will prove the following Theorem: Let \(\mathcal {F}\) be a codimension-one foliation of a complete and connected Riemannian manifold \(M^{n+1}\) with constant sectional curvature \(c {\leq} 0\). Suppose that \(\mathcal {F} \) is transversely orientable, i.e., there exists an unit vector field \(N \epsilon {\mathfrak{X}}(M)\) such that N is normal to the leaves of \(\mathcal {F} \). Suppose that N is geodesic. Then, if the foliation \(\mathcal {F} \) has an umbilical leaf, every leaf of foliation \(\mathcal {F} \) must be umbilical.

The main goal of this paper is to investigate the properties and connections of neatly and semistrictly quasiconvex functions, especially when they appear in constrained and unconstrained optimization problems. The lower global subdifferential, recently introduced in the literature, plays an essential role in this study. We present several optimality conditions for constrained and unconstrained nonsmooth neatly/semistrictly quasiconvex optimization problems in terms of lower global subdifferentials. To this end, for a constrained optimization problem, we present some characterizations for the normal and tangent cones and the cone of feasible directions of the feasible set. Some relationships between the Greenberg-Pierskalla, tangentially and lower global subdifferentials of neatly and semistrictly quasiconvex functions are also given. The mentioned relationships show that the outcomes of this paper generalize some results existing in the literature.

It is shown that one of the results of Schaefer can be obtained in a more elementary way and can be improved. This is an immediate corollary of a paper of the author Duke Math. J.19, 75---91 (1952).

The purpose of this short paper is to give a structure theorem for certain Gorenstein ideals.

The goal of this paper is to investigate a new model, called generalized polynomial complementarity problems over a polyhedral cone and denoted by GPCPs, which is a natural extension of the polynomial complementarity problems and generalized tensor complementarity problems. Firstly, the properties of the set of all $$R^{K}_{{\varvec{0}}}$$ -tensors are investigated. Then, the nonemptiness and compactness of the solution set of GPCPs are proved, when the involved tensor in the leading term of the polynomial is an $$ER^{K}$$ -tensor. Subsequently, under fairly mild assumptions, lower bounds of solution set via an equivalent form are obtained. Finally, a local error bound of the considered problem is derived. The results presented in this paper generalize and improve the corresponding those in the recent literature.

This paper focuses on the global Mittag–Leffler (M–L) synchronization for fractional-order inertial neural networks (FOINNs) including the Caputo derivative and delay. By choosing an appropriate variable transformation, the considered system including the inertial term is transformed into two fractional-order nonlinearly coupled interconnected subsystems. Combining with the delayed-feedback controller, fractional Lyapunov functional approach and inequality analysis technique, multi sets of novel algebraic criteria on the global M–L synchronization between derive-response systems are established. The main prominent highlight of this paper is that the proposed results are characterized by the algebraic inequalities form, which can simplify the calculation and facilitate the test. Two numerical simulation examples validate the theoretical results.

In this paper, we use genus theory to analyze the hardness of the decisional Diffie-Hellman problem for ideal class groups of imaginary quadratic orders acting on sets of elliptic curves through isogenies (DDH-CGA). Such actions are used in the Couveignes-Rostovtsev-Stolbunov protocol and in CSIDH. Concretely, genus theory equips every imaginary quadratic order O with a set of assigned characters chi : cl(O) -> {+/- 1}, and for each such character and every secret ideal class [a] connecting two public elliptic curves E and E' = [a] * E, we show how to compute chi([a]) given only E and E', i.e., without knowledge of [a]. In practice, this breaks DDH-CGA as soon as the class number is even. which is true for a density 1 subset of all imaginary quadratic orders. For instance, our attack works very efficiently for all supersingular elliptic curves over F-p with p 1 mod 4. Our method relies on computing Tate pairings and walking down isogeny volcanoes. We also show that these ideas carry over, at least partly, to abelian varieties of arbitrary dimension. This is an extended version of the paper that was presented at Crypto 2020.

This paper is concerned with the estimation of the regression coefficients for the generalized linear models in the situation where a multicollinear issue exists and when it is suspected that some of the regression coefficients may be restricted to a linear subspace. Accordingly, as a solution to this issue, we propose a new Stein-type shrinkage ridge estimation approach. We provide the analytic expressions for the asymptotic biases and risks of the proposed estimators and investigate their relative performance with respect to the unrestricted ridge regression estimator. Monte-Carlo simulation studies are conducted to appraise the performance of the underlying estimators in terms of their simulated relative efficiencies. It is clear from both the analytical results and the simulation study that the Stein-type shrinkage ridge estimators dominate the usual ridge regression estimator in the entire parameter space. Finally an empirical application is provided where prostate cancer data is analyzed to show the practical usefulness of the suggested approach. Based on the results from the different parts of this paper, we find that the new method developed would be useful for the practitioners in various research areas such as economics, insurance data and medicine.

The Weighted Tree Augmentation problem (WTAP) is a fundamental problem in network design. In this paper, we consider this problem in the online setting. We are given an n-vertex spanning tree T and an additional set L of edges (called links) with costs. Then, terminal pairs arrive one-by-one and our task is to maintain a low-cost subset of links F such that every terminal pair that has arrived so far is 2-edge-connected in T cup F. This online problem was first studied by Gupta, Krishnaswamy and Ravi (SICOMP 2012) who used it as a subroutine for the online survivable network design problem. They gave a deterministic O(log^2 n)-competitive algorithm and showed an Omega(log n) lower bound on the competitive ratio of randomized algorithms. The case when T is a path is also interesting: it is exactly the online interval set cover problem, which also captures as a special case the parking permit problem studied by Meyerson (FOCS 2005). The contribution of this paper is to give tight results for online weighted tree and path augmentation problems. The main result of this work is a deterministic O(log n)-competitive algorithm for online WTAP, which is tight up to constant factors.

Fractional calculus has been widely used to study the flow of viscoelastic fluids recently, and fractional differential equations have attracted a lot of attention. However, the research has shown that the fractional equation with constant order operators has certain limitations in characterizing some physical phenomena. In this paper, the viscoelastic fluid flow of generalized Maxwell fluids in an infinite straight pipe driven by a periodic pressure gradient is investigated systematically. Consider the complexity of the material structure and multi-scale effects in the viscoelastic fluid flow. The modified time fractional Maxwell models and the corresponding governing equations with distributed/variable order time fractional derivatives are proposed. Based on the L1-approximation formula of Caputo fractional derivatives, the implicit finite difference schemes for the distributed/variable order time fractional governing equations are presented, and the numerical solutions are derived. In order to test the correctness and availability of numerical schemes, two numerical examples are established to give the exact solutions. The comparisons between the numerical solutions and the exact solutions have been made, and their high consistency indicates that the present numerical methods are effective. Then, this paper analyzes the velocity distributions of the distributed/variable order fractional Maxwell governing equations under specific conditions, and discusses the effects of the weight coefficient ϖ(α) in distributed order time fractional derivatives, the order α(r, t) in variable fractional order derivatives, the relaxation time λ, and the frequency ω of the periodic pressure gradient on the fluid flow velocity. Finally, the flow rates of the distributed/variable order fractional Maxwell governing equations are also studied.

A consequence of nonlinearities is a multi-harmonic response via a mono-harmonic excitation. A similar phenomenon also exists in random vibration. The power spectral density (PSD) analysis of random vibration for nonlinear systems is studied in this paper. The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function (GFRF). For a class of nonlinear systems, the growing exponential method is used to determine the first 3rd-order GFRFs. The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input. The relationship between the peak of PSD and the parameters of the nonlinear system is discussed. By using the proposed method, the nonlinear characteristics of multi-band output via single-band input can be well predicted. The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD. This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Many papers have been published for finding eigenvalues and eigenvectors of a fuzzy matrix (FM) (i.e. matrix with membership values) as well a fuzzy graph. But, all papers determine such parameters based on conventional arithmetic operators, though the valid operations on FMs are max–min. To the best of our knowledge no papers are published to find eigenvalues and eigenvectors based on max–min operators. In this paper, a novel technique is adapted to find the eigenvalues and eigenvectors of an interval-valued fuzzy graph (IVFG) using max–min operators. The energy of an IVFG is defined and computed using max–min operators. Finally, an application of eigenvalues of an IVFG is discussed for the ecological system. In ecology, the amount of food consumed by a predator from the preys is represented as an interval valued fuzzy membership values which is natural as the consumption of food for a predator from preys is uncertain. So this application is very much appropriate for eigenvalues and eigenvectors as well as energy of an IVFG.

In this paper, the concept of the full Z-linear programming problem (FZLP) is first introduced. It is worth to mention that in these type of problems, all parameters, including the coefficients of variables in the objective functions, the coefficients of the variables in the constraints, the right-hand side of the constraints, as well as the decision variables, are valued as Z-numbers. Clearly, it is critical to provide a method to solve these types of problems, and to find their optimal solutions. Therefore, this paper develops a novel and practical method to find the solution of the problem using the concept of Z-numbers. To prove the applicability of the concept, two illustrative examples are provided to demonstrate the precision and effectiveness of this method. WOS:000718216500001 Q1

The present paper is devoted to identifying the space-dependent source term and initial value simultaneously for a time-fractional diffusion equation. This inverse problem is reformulated on the basis of Fourier method as operator equations of the first kind. The construction of the solution to the inverse problem is derived by using the Landweber iteration method for the solution of the corresponding conjugate operator equation. In this paper, we also present error estimates between the exact solution and the regularized solution by the a priori and the a posteriori parameter choice rules. Numerical verification on the efficiency and accuracy of the proposed algorithm is performed by solving three numerical examples in one-dimensional and two-dimensional cases.

Though there have been many contributions dealing with classical and Bayesian analysis of mixture data under right-censored samples, the Bayesian analysis of left-censored heterogeneous data is lacking in the literature. This paper attempts to bridge up the said gap in the literature by proposing Bayesian methods for estimation of left-censored heterogeneous data. The paper also explored two-component Weibull mixture distribution (2CMWD) as a suitable model for modeling left-censored mixture data. As the explicit derivations for the estimators of the parameters are not possible, MCMC methods and Lindley’s approximation (LA) have been considered for approximate estimation of the model parameters. The sensitivity of the proposed Bayes estimates with respect to change in sample size, mixing parameter, censoring rates, loss function, prior, true parametric value and approximate methods has been discussed. The reliability characteristics for the left-censored 2CMWD have been studied in detail. The proposed estimators performed efficiently to estimate the parameters and reliability characteristics from the left-censored 2CMWD. The proposed estimators were insensitive with respect to change in censoring rates, true parametric values, prior parameters and mixing weights. Three different real datasets have been used to discuss the applicability of the proposed estimators in different real-life studies.

The main purpose of this paper is to analyze nonconforming iterative finite element methods for 2D/3D stationary incompressible magneto-hydrodynamics equations. First, the Crouzeix-Raviart–type finite element is used to approximate the velocity and the conforming piecewise linear element P1 is used for the pressure. Since the finite element method for the velocity field and the pressure is unstable, a simple locally stabilization term is added to satisfy the weak inf-sup condition. Then, the well-posedness and the optimal error estimates of the continuous and discrete problems are analyzed with the nonlinear terms being iteratively updated. Three effective iterative methods are proposed and their stability and convergence analyses are carried out. Finally, the theoretical analysis presented in this paper is verified by numerical experiments.

The purpose of this paper is to provide a nonparametric kernel method to estimate nonlinear structural equation models involving the functional effects between the latent variables. This approach is based on the combination of Principal Component Analysis (PCA) and kernel smoothing technique. The results obtained from different simulations on both nonlinear and linear structural models show the great performance of this method. Furthermore, an application on real data using a recovery satisfaction model is presented in this paper. From where, we show the adequacy of our method in capturing the non linearity between some latent variables.

In this paper, the finite-time stability of a class of fractional-order bidirectional associative memory neural networks(FBAMNNs) with time delay is concerned. Based on the monotonicity of function, a new inequality is proved. For $$0< \alpha < 1$$ and $$1< \alpha < 2$$ , based on the properties of the fractional derivative, the method of step and the fractional Gronwall inequality or the generalized Gronwall inequality, some new criteria on the finite-time stability of FBAMNNs are derived. Finally, three numerical examples are provided to show the effectiveness and superiority of the criteria obtained in this paper.

In recent years, integer-valued time series attract the attention of researchers and find their applications in data analysis. Among various models, the integer-valued autoregressive (INAR) ones are of great popularity and are widely applied in practice. This paper develops some portmanteau test statistics to check the adequacy of the fitted model in a wide group of INAR processes, called generalized INAR. For this purpose, the asymptotic distributions of the test statistics are obtained and, using Monte Carlo simulation studies, their finite sample properties are derived. Besides, the results are applied in analyzing a real data example

This paper proposes the design of transformation based two dimensional (2D) elliptical filters using multi-objective artificial bee colony (MOABC) algorithm. The MOABC algorithm finds the one dimensional (1D) cut-off frequencies and McClellan transformation coefficients by optimizing the contour approximation errors at pass-band and stop-band regions of elliptical filters. This design approach is compared with the state of the art approaches in terms of contour approximation error, pass-band ripple and stop-band attenuation to ensure the efficiency. It is seen that an efficient mapping of 1D filter to 2D filter is possible with minimum contour approximation error using the proposed approach. The second proposal in this paper is the design of low complexity variable bandwidth and variable orientation elliptical filters with direct 2D tunability. This is achieved by mapping the coefficients of different 2D filters into a 2D Farrow structure. The performance of the proposed variable elliptical filter is measured in terms of mean error, mean square error, root mean square error, pass-band ripple, stop-band attenuation and 2D cut-off frequencies. The main feature of the proposed 2D variable filter design lies in the considerable reduction in the number of multipliers when compared to the existing methods, which in turn reduces the resource utilization and power consumption.

In this paper, the author focuses on the joint effects of diffusion and advection on the dynamics of a classical two species Lotka-Volterra competition-diffusion-advection system, where the ratio of diffusion and advection rates are supposed to be a positive constant. For comparison purposes, the two species are assumed to have identical competition abilities throughout this paper. The results explore the condition on the diffusion and advection rates for the stability of former species. Meanwhile, an asymptotic behavior of the stable coexistence steady states is obtained.

The information volume of mass function based on extropy is proposed in this paper. Although the information volume of the probability distribution can be calculated by Shannon entropy, how to calculate the information of the mass function is still being explored. Recently, the concept of extropy was proposed by Lad et al. Based on extropy, the information volume of mass function is proposed in this paper. For a basic probability assignment function (BPA), if the focal elements of the frame of discernment (FOD) are all single elements, the information volume proposed in this paper is equal to the corresponding extropy. Otherwise, the information volume is greater than the corresponding extropy. Besides, when the cardinality of the FOD is identical, both the total uncertainty case and the mass function distribution of the maximum extropy have the same information volume. More precisely, the distribution of the latter can be regarded as the former obtained by decomposing the BPA once. Finally, the experiment proves that the maximum information volume increases with the increase in the cardinality of the FOD, and has the same limit value log $$_2e$$ as the maximum extropy. Some numerical examples are given to prove the nature of the information volume.

The optimization literature is vast in papers dealing with improvements on the global convergence of augmented Lagrangian schemes. Usually, the results are based on weak constraint qualifications, or, more recently, on sequential optimality conditions obtained via penalization techniques. In this paper, we propose a somewhat different approach, in the sense that the algorithm itself is used in order to formulate a new optimality condition satisfied by its feasible limit points. With this tool at hand, we present several new properties and insights on limit points of augmented Lagrangian schemes, in particular, characterizing the strongest possible global convergence result for the safeguarded augmented Lagrangian method.

Linear codes with good parameters have wide applications in secret sharing schemes, authentication codes, association schemes, consumer electronics and communications, etc. During the past four decades, constructions of linear codes with good parameters received much attention and many classes of such codes were presented. In this paper, we obtain a family of linear codes with good parameters over $$\mathbb {F}_p$$ by exploring further properties of constant dimension subspace codes, where p is a prime. The weight distribution of three classes of linear codes presented in this family is determined. Most notably, three classes of linear codes presented in this family are distance-optimal with respect to the Griesmer bound. Also, this paper presents a sufficient and necessary condition for this family of linear codes to have a $$\lambda $$ -dimensional hull. In addition, we show that our linear codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs.

This paper deals with the convergence analysis of a shrinking approximants for the computation of a common solution associated with the fixed point problem of $$\eta $$ -demimetric operator and the generalized split null point problem in Hilbert spaces. The considered sequence of approximants is a variant of the parallel hybrid shrinking projection algorithm that converges strongly to the optimal common solution under suitable set of control conditions. The viability of the approximants with parallel implementation is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature.

The study of the Dirichlet problem with arbitrary measurable data for harmonic functions in the unit disk 𝔻 is due to the dissertation of Luzin. Later on, the known monograph of Vekua was devoted to boundary-value problems only with Holder continuous data for generalized analytic functions, i.e., continuous complex-valued functions f(z) of the complex variable z = x + iy with generalized first partial derivatives by Sobolev satisfying equations of the form $$ {\partial}_{\overline{z}}f+ af+b\overline{f}=c, $$ where the complexvalued functions a; b, and c are assumed to belong to the class Lp with some p > 2 in smooth enough domains D in ℂ. Our last paper [12] contained theorems on the existence of nonclassical solutions of the Hilbert boundaryvalue problem with arbitrary measurable data (with respect to logarithmic capacity) for generalized analytic functions f : D → ℂ such that $$ {\partial}_{\overline{z}}f=g $$ with the real-valued sources. On this basis, the corresponding existence theorems were established for the Poincare problem on directional derivatives and, in particular, for the Neumann problem to the Poisson equations △U = G ∈ Lp; p > 2, with arbitrary measurable boundary data over logarithmic capacity. The present paper is a natural continuation of the article [12] and includes, in particular, theorems on the existence of solutions for the Hilbert boundary-value problem with arbitrary measurable data for the corresponding nonlinear equations of the Vekua type $$ {\partial}_{\overline{z}}f(z)=h(z)q\left(f(z)\right). $$ On this basis, existence theorems were also established for the Poincar´e boundary-value problem and, in particular, for the Neumann problem for the nonlinear Poisson equations of the form △U(z) = H(z)Q(U(z)) with arbitrary measurable boundary data over logarithmic capacity. The Dirichlet problem was investigated by us for the given equations, too. Our approach is based on the interpretation of boundary values in the sense of angular (along nontangential paths) limits that are a conventional tool of the geometric function theory. As consequences, we give applications to some concrete semi-linear equations of mathematical physics arising from modelling various physical processes. Those results can also be applied to semi-linear equations of mathematical physics in anisotropic and inhomogeneous media.

The paper is concerned with the two-machine flow shop, where each job requires an additional resource (referred to as storage space) from the start of its first operation till the end of its second operation. The storage requirement of a job is determined by the processing time of its first operation. At any point in time, the total consumption of this additional resource cannot exceed a given limit (referred to as the storage capacity). The goal is to minimise the makespan, i.e. to minimise the time needed for the completion of all jobs. This problem is NP-hard in the strong sense. The paper analyses how the parameter - a lower bound on the storage capacity specified in terms of the processing times, affects the computational complexity.

In this paper we are interested in the asymptotic enumeration of Cayley graphs. It has previously been shown that almost every Cayley digraph has the smallest possible automorphism group: that is, it is a digraphical regular representation (DRR). In this paper, we approach the corresponding question for undirected Cayley graphs. The situation is complicated by the fact that there are two infinite families of groups that do not admit any graphical regular representation (GRR). The strategy for digraphs involved analysing separately the cases where the regular group $R$ has a nontrivial proper normal subgroup $N$ with the property that the automorphism group of the digraph fixes each $N$-coset setwise, and the cases where it does not. In this paper, we deal with undirected graphs in the case where the regular group has such a nontrivial proper normal subgroup., Comment: 27 pages

Although novel coronavirus pneumonia (COVID-19) was widely spread in mainland China in early 2020, it was soon controlled. To study the impact of government interventions on the spread of disease during epidemics, a differential equation system is established to simulate the process of virus propagation in this paper. We first analyze its basic properties, basic reproduction number $$R_{0}$$ and existence of equilibria. Then we prove that the disease-free equilibrium (DFE) is Globally Asymptotically Stable when $$R_{0}$$ is less than 1. Through the analysis of the daily epidemic data from January 10, 2020 to March 11, 2020, combined with the implementation of the national epidemic policy, we divide the whole process into three stages: the first stage (natural state), the second stage (isolation state), the third stage (isolation, detection and treatment). By using the weighted nonlinear least square method to fit the data of three stages, the parameters are obtained, and three basic reproduction numbers are calculated, which are: $$R_{01} =2.6735$$ , $$R_{02} = 0.85077$$ , $$R_{03} = 0.18249$$ . Sensitivity analysis of threshold parameters and corresponding graphical results were also performed to examine the relative importance of various model parameters to the spread and prevalence of COVID-19. Finally, we simulate the trend of three stages and verify the theory of Global Asymptotic Stability of DFE. The conclusion of this paper proves theoretically that the Chinese government’s epidemic prevention measures are effective in the fight against the spread of COVID-19. This study can not only provide a reference for research methods to simulate COVID-19 transmission in other countries or regions, but also provide recommendations on COVID-19 prevention measures for them.

Infectious diseases have a devastating impact on individual health and social development. Different external environmental factors will affect the scale and the speed of disease outbreaks, such as sanitary conditions and policy interventions. In this paper, we attempt to establish a dual-system susceptible-infectious-quarantine-recovered model with different environmental impacts to explore it. For the deterministic model, we calculate the basic reproduction number, simultaneously, and investigate the local asymptotic stability of the disease-free equilibrium and the endemic equilibrium. Numerical simulations and theoretical analyses verify the conclusion of this paper. It is a surprise that there is a great probability of finding a quarantine inflection point, which can effectively control the scale of infection outbreak when two different systems of infection rate and recovery rate are determined.

In this paper, a new method of ranking fuzzy numbers has been proposed. The method is being developed using the ill-defined quantity value as well as the quantities, left ambiguity and right ambiguity of a fuzzy number. It is seen that there are several methods on ranking fuzzy numbers, but in most of the studies, the ranking methods fail to rank some of the fuzzy numbers. Hence, in this paper, a new ranking method has been introduced to overcome these limitations. The ranking index is formulated by using ill-defined quantity value and by the convex combination of left ambiguity and right ambiguity of a fuzzy number with index of optimism. A quantity $$\theta$$ is also introduced, which decides the inclusion and exclusion of the ambiguity in the ranking index. Further, the rationality validation of the proposed ranking method is also checked, by proving the Wang and Kerre’s reasonable properties. Furthermore, a comparative study is being performed to show the outperformance of the proposed method.

The vast applicability of fractional calculus to model physical phenomena in the form of fractional differential equations and their complexity has created a massive demand for efficient analytic and semi-analytic techniques to solve fractional differential equations. This paper has derived a new operational matrix using the independence polynomial of a complete bipartite graph to solve multi-order fractional differential equations. While deriving the operational matrix, the Caputo sense fractional derivatives have been considered. Series solutions are found by using the collocation matrix method. The main characteristic of this approach is that it reduces a complex fractional differential equation to a system of algebraic equations. The convergence analysis and the time complexity analysis of the proposed scheme are also presented in this paper. Six examples have been considered to illustrate the relevance and applicability of the method described. The results obtained are compared with the exact solutions. We have also compared our results with the ones obtained by other methods available in the literature.

In recent years, tensor data appear more frequently in machine learning. Tucker decomposition is a powerful tool for processing tensor data. However, from the perspective of dimensionality reduction, Tucker decomposition without any regularization is only a tensor version of principal component analysis (PCA) that learning a linear subspace to minimize the distance between the data and their projections on the subspace. However, many high-dimensional tensor data usually reside in low-dimensional submanifolds, rather than low-dimensional linear subspaces. It is necessary to fill the gap between submanifolds and linear subspaces to achieve superior performance. In this paper, we proposed a new dimensionality reduction algorithm of tensor data based on manifold regularized Tucker decomposition (called MRTD for short), in which manifold regularization is in addition to Tucker decomposition. Furthermore, unlike many other similar algorithms that ignore the matrices of Tucker decomposition by absorbing them into a whole matrix, in this paper, we proposed an iterative solution to MRTD that the matrices are calculated based on each other iteratively. Matrices in Tucker decomposition represent different dimensionality reduction operations for each dimension of tensor. Therefore, MRTD is a dimensionality reduction algorithm specially designed for tensor data, not for vector data. The experimental results of MRTD and 5 other related state-of-the-art algorithms on 6 commonly-used real-world datasets are presented, showing the better performance of MRTD.

The main purpose of this paper is to introduce a new formulation of the Tau-collocation method for solving a class of nonlinear weakly singular delay Volterra integro-differential equations based on fractional Muntz Jacobi polynomials. So the paper consists of two main parts: studying the regularity of solution and introducing a simple structure and efficient numerical method. The method generates approximate solution with fractional power terms having the same behavior of the exact solution of the given problem. The convergence analysis of the method is also investigated in $$L^{2}$$ -norm. Some illustrative examples are given to confirm the theoretical results and the accuracy of the approximate solution. The paper is closed by providing real application of the method to some physical problems.

This paper deals with one-way classification analysis when the response variable follows the one-parameter Frechet distribution and the factor effects are random. The stochastic properties of the response variable are studied in detail. Maximum likelihood estimations of the model parameters are also given in explicit expressions. Under the square error loss function, the best predictions for the random-effects are derived. Three procedures for testing the hypothesis of population homogeneity are proposed and misspecification problem is investigated in a special case. Several illustrative examples are also given to assess the performances of the proposed model. Findings of this paper may be used in engineering, survival and, longitudinal studies.

In this paper, we study the long memory property of two processes based on the Ornstein-Uhlenbeck model. Their are extensions of the Ornstein-Uhlenbeck system for which in the classic version we replace the standard Brownian motion (or other L$$\acute{e}$$ e ´ vy process) by long range dependent processes based on $$\alpha -$$ α - stable distribution. One way of characterizing long- and short-range dependence of second order processes is in terms of autocovariance function. However, for systems with infinite variance the classic measure is not defined, therefore there is a need to consider alternative measures on the basis of which the long range dependence can be recognized. In this paper, we study three alternative measures adequate for $$\alpha -$$ α - stable-based processes. We calculate them for examined processes and indicate their asymptotic behavior. We show that one of the analyzed Ornstein-Uhlenbeck process exhibits long memory property while the second does not. Moreover, we show the ratio of two introduced measures is limited which can be a starting point to introduction of a new estimation method of stability index for analyzed Ornstein-Uhlenbeck processes.

Multiplicative calculus (MUC) measures the rate of change of function in terms of ratios, which makes the exponential functions significantly linear in the framework of MUC. Therefore, a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC. Taking this as motivation, this paper lays mathematical foundation of well-known classical Gauss-Newton minimization (CGNM) algorithm in the framework of MUC. This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization (MGNM) method along with its convergence properties. The proposed method is generalized for n number of variables, and all its theoretical concepts are authenticated by simulation results. Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions. From simulation results, it has been observed that proposed MGNM method converges for 12972 points, out of 19600 points considered while optimizing multiplicatively-linear exponential function, whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points, respectively. Furthermore, for a given set of initial value, the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods. A similar pattern is observed for multiplicatively-non-linear exponential function. Therefore, it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.

The periodic behavior of real data can be manifested in the time series or in its characteristics. One of the characteristics that often manifests the periodic behavior is the sample autocovariance function. In this case, the periodically correlated (PC) behavior is considered. One of the main models that exhibits PC property is the periodic autoregressive (PARMA) model that is considered as the generalization of the classical autoregressive moving average (ARMA) process. However, when one considers the real data, practically the observed trajectory corresponds to the “pure” model with the additional noise which is a result of the noise of the measurement device or other external forces. Thus, in this paper we consider the model that is a sum of the periodic autoregressive (PAR) time series and the additive noise with finite-variance distribution. We present the main properties of the considered model indicating its PC property. One of the main goals of this paper is to introduce the new estimation method for the considered model’s parameters. The novel algorithm takes under consideration the additive noise in the model and can be considered as the modification of the classical Yule–Walker algorithm that utilizes the autocovariance function. Here, we propose two versions of the new method, namely the classical and the robust ones. The effectiveness of the proposed methodology is verified by Monte Carlo simulations. The comparison with the classical Yule–Walker method is presented. The approach proposed in this paper is universal and can be applied to any finite-variance models with the additive noise.

The uniqueness problems of meromorphic functions of differential polynomials sharing value have been studied and many results on this topic have been obtained. In this paper, we investigate the uniqueness problems sharing one small function of meromorphic functions concerning differential polynomials. In particular, the results of the paper improve the results due to Zhang and Wu (J Inequal Appl 2019: 1–14, 2019).