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A recent paper (Zhang R, Yu X. Traveling waves for a four‐compartment lattice epidemic system with exposed class and standard incidence. Math Meth Appl Sci. 2022; 45: 113‐136) presented a four‐compartment lattice epidemic system with exposed class and standard incidence. The authors studied the existence and non‐existence of traveling wave solutions of this system. However, the limit behavior of R$$ R $$‐component of traveling wave solutions is still open. In this paper, we solve this open problem and establish the boundedness of traveling wave solutions by analysis technique. Meanwhile, we study the non‐existence of traveling wave solutions with non‐positive wave velocity. [ABSTRACT FROM AUTHOR]

Variance swaps is a kind of financial instrument that plays an important role in volatility risk management. In this paper, we study the pricing problem of log‐return variance swaps under the double mean reversion DMR (Heston‐CIR) model. Compared with Kim's work, we introduce the square‐root process into the diffusion term of the long‐term mean and present a stochastic approach that greatly simplify the solution of the problem without solving PDEs. An analytical solution and approximate solution are obtained. Some numerical examples show that the exact solution and MC simulation fit well. It is worth mentioning that the difference between the approximate solution and the exact solution is small when the parameters are selected appropriately. By the mean time, the parameter of the long‐term mean has an important impact on the solution, which implies that the introduction of a multi‐factor model is necessary. [ABSTRACT FROM AUTHOR]

The aim of a ranking aggregation problem is to combine several rankings into a single one that best represents them. A common method for solving this problem is due to Kemeny and selects as the aggregated ranking the one that minimizes the sum of the Kendall distances to the rankings to be aggregated. Unfortunately, the identification of the said ranking—called the Kemeny ranking—is known to be a computationally expensive task. In this paper, we study different ways of computing the Kemeny ranking with quantum optimization algorithms, and in particular, we provide some alternative formulations for the search for the Kemeny ranking as an optimization problem. To the best of our knowledge, this is the first time that this problem is addressed with quantum techniques. We propose four different ways of formulating the problem, one novel to this work. Two different quantum optimization algorithms—Quantum Approximate Optimization Algorithm and Quantum Adiabatic Computing—are used to evaluate each of the different formulations. The experimental results show that the choice of the formulation plays a big role on the performance of the quantum optimization algorithms. [ABSTRACT FROM AUTHOR]

We consider the incremental subgradient algorithm employing dynamic step sizes for minimizing the sum of a large number of component convex functions. The dynamic step size rule was firstly introduced by Goffin and Kiwiel [Math. Program., 1999, 85(1): 207‐211] for the subgradient algorithm, soon later, for the incremental subgradient algorithm by Nedic and Bertsekas in [SIAM J. Optim., 2001, 12(1): 109‐138]. It was observed experimentally that the incremental approach has been very successful in solving large separable optimizations and that the dynamic step sizes generally have better computational performance than others in the literature. In the present paper, we propose two modified dynamic step size rules for the incremental subgradient algorithm and analyse the convergence and complexity properties of them. At last, the assignment problem is considered and the incremental subgradient algorithms employing different kinds of dynamic step sizes are applied to solve the problem. The computational experiments show that the two modified ones converges dramatically faster and more stable than the corresponding one in [SIAM J. Optim., 2001, 12(1): 109‐138]. Particularly, for solving large separable convex optimizations, we strongly recommend the second one (see Algorithm 3.3 in the paper) since it has interesting computational performance and is the simplest one. [ABSTRACT FROM AUTHOR]

The generalized time‐fractional Fisher's equation is a substantial model for illustrating the system's dynamics. Studying effective numerical methods for this equation has considerable scientific importance and application value. In that direction, this paper presents designing and analyzing a high‐order numerical scheme for the generalized time‐fractional Fisher's equation. The time‐fractional derivative is taken in the Caputo sense and approximated using Euler backward discretization. The quasilinearization technique is used to linearize the problem, and then a compact finite difference scheme is considered for discretizing the equation in space direction. Our numerical method is convergent of Ok2−α+h4$$ O\left({k}^{2-\alpha }+{h}^4\right) $$, where h$$ h $$ and k$$ k $$ are step sizes in spatial and temporal directions, respectively. Three problems are tested numerically by implementing the proposed technique, and the acquired results reveal that the proposed method is suitable for solving this problem. [ABSTRACT FROM AUTHOR]

The function approximation technique (FAT) is a powerful mathematical tool recently utilized to design model‐free controllers for robots. However, some FAT‐based controllers depend on joint velocities, which may not be available in many real‐world applications. This problem is solved in this paper by proposing an output feedback tracking control for cooperative robotic arms using the Bernstein–Chlodowsky polynomial as an uncertainty approximator. In other words, the Bernstein–Chlodowsky approach is adopted to approximate the lumped uncertainties consisting of disturbances and unmodeled dynamics. An adaptive rule is then suggested to update the approximator's coefficients matrix. Moreover, it is assured that controlled system error signals are uniformly ultimately bounded (UUB) utilizing the Lyapunov lemma. Finally, the designed Bernstein–Chlodowsky controller is applied to a cooperative system with two arms handling a load. Besides, the results of applying the designed technique are compared with the outcomes of the Chebyshev neural network (CNN) as a state‐of‐the‐art approximation method. The simulation outcomes indicate the capability of the designed method. [ABSTRACT FROM AUTHOR]

Our goal of this paper is to solve the problem of common fixed point of a quite large family of demiclosed cutters on Hilbert spaces. We introduce two new extrapolated simultaneous block‐iterative methods. The first method converges weakly to a common fixed point of the family and the second one is a specific combination of the first and the steepest descent method and converges in norm. Its strong convergence is proved without additional conditions on the cutters such as the approximately shrinking property of each cutter and bounded regular assumption on their fixed point sets, assumed recently in the literature. Some particular cases of the last method, applications and computational experiments to a convex optimization over the intersection of level sets are given for illustration and comparison. [ABSTRACT FROM AUTHOR]

This paper introduces a fractional version of reaction‐diffusion equations with non‐local boundary conditions via a non‐singular fractional derivative defined by Atangana and Baleanu. The orthonormal discrete Legendre polynomials are introduced as suitable family of basis functions to find the solution of these equations. An operational matrix is derived for fractional derivative of these polynomials. A collocation method based on the expressed polynomials and their operational matrices is developed for solving such problems. The established method transforms solving the original problem under consideration into solving a system of algebraic equations. Some numerical examples are used to investigate the validity of the presented method. [ABSTRACT FROM AUTHOR]

This paper is devoted to solve the backward problem for radially symmetric time‐fractional diffusion‐wave equation under Robin boundary condition. This problem is ill‐posed and we apply an iterative regularization method to solve it. The error estimates are obtained under the a priori and a posteriori parameter choice rules. Numerical results show that the proposed method is efficient and stable. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a derivative‐free iterative method for finding the solutions of convex constrained nonlinear equations (CCNE) using the projection strategy. The new approach is free from gradient evaluations at each iteration. Also, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Compared with traditional methods for solving CCNE that assumes Lipschitz continuity and monotonicity to establish the global convergence result, an advantage of our proposed method is that the global convergence result does not require the assumption of Lipschitz continuity. Moreover, the underlying operator is assumed to be pseudomonotone, which is a milder condition than monotonicity. As an applications, we solve the LASSO problem in compressed sensing. Numerical experiments illustrate the performances of our proposed algorithm and provide a comparison with related algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a well‐balanced and positive‐preserving nonstaggered central scheme, which has second‐order accuracy on both time and spatial scales, for open‐channel flows with the variable channel width and the nonflat bottom. We perform piecewise linear reconstructions of the conserved variables and energy as well as discretize the source term using the property that the energy remains constant, so that the complex source term and the flux can be precisely balanced so as to maintain the steady state. The scheme also ensures that the cross‐sectional wet area is positive by introducing a draining time‐step technique. Numerical experiments demonstrate that the scheme is capable of accurately maintaining both the still steady‐state solutions and the moving steady‐state solutions, simultaneously. Moreover, the scheme has the ability to accurately capture small perturbations of the moving steady‐state solution and avoids generating spurious oscillations. It is also capable of showing that the scheme is positive‐preserving and robust in solving the dam‐break problem. [ABSTRACT FROM AUTHOR]

In studying the stability of Bénard problem, we usually have to solve a variational problem to determine the critical Rayleigh number for linear or nonlinear stability. To solve the variational problem, one usually transforms it to an eigenvalue problem which is called Euler–Lagrange equations. An operator related to the Euler–Lagrange equations is usually referred to as Euler–Lagrange operator whose spectrum is investigated in this paper. We have shown that the operator possesses only the point spectrum consisting of real number, which forms a countable set. Moreover, it is found that the spectrum of the Euler–Lagrange operator depends on the thickness of the fluid layer. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an inverse problem of recovering the zeroth‐order coefficient and fractional order simultaneously in a time‐fractional reaction‐diffusion‐wave equation by using boundary measurement data from both of uniqueness and numerical method. We prove the uniqueness of the considered inverse problem and the Lipschitz continuity of the forward operator. Then the inverse problem is formulated into a variational problem by the Tikhonov‐type regularization. Based on the continuity of the forward operator, we prove that the minimizer of the Tikhonov‐type functional exists and converges to the exact solution under an a priori choice of regularization parameter. The steepest descent method combined with Nesterov acceleration is adopted to solve the variational problem. Three numerical examples are presented to support the efficiency and rationality of our proposed method. [ABSTRACT FROM AUTHOR]

In this paper, some results about the controllability of spectral centrality in a complex network are presented. In particular, the inverse problem of designing an unweigthed graph with a prescribed centrality is considered. We show that for every possible ranking, eventually with ties, an unweighted directed/undirected complex network can be found whose PageRank or eigenvector centrality gives the ranking considered. Different families of networks are presented in order to analytically solve this problem either for directed and undirected graphs with and without loops. [ABSTRACT FROM AUTHOR]

This paper is concerned with the large particle limit for the consensus‐based optimization (CBO), which was postulated in the pioneering works by Carrillo, Pinnau, Totzeck and many others. In order to solve this open problem, we adapt a compactness argument by first proving the tightness of the empirical measures {μN}N≥2$$ {\left\{{\mu}^N\right\}}_{N\ge 2} $$ associated to the particle system and then verifying that the time marginal of the limit measure μ$$ \mu $$ is the unique weak solution to the mean‐field CBO equation. Such results are further extended to the model of particle swarm optimization (PSO). [ABSTRACT FROM AUTHOR]

In the settings of real Hilbert spaces, this paper proposes modified forward– backward scheme with inertial extrapolation step for solving inverse problems. In our proposed method, it is possible for the inertial factor to be chosen as 1 unlike many previous inertial forward–backward splitting methods available in the literature. Weak and strong convergence of our proposed method are obtained under some standard conditions. In order to show the numerical advantage gained when the inertial factor is chosen as 1, a number of numerical implementations are performed on two different inverse problems: LASSO and SCAD penalty problems. [ABSTRACT FROM AUTHOR]

In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are generated. An operational matrix concerning fractional integration of these wavelets is extracted. A numerical scheme is established based on these wavelets and their fractional integral matrix together with the collocation technique to solve fractional pantograph equations. The presented method reduces solving the problem under study into solving a system of algebraic equations. Several examples are provided to show the accuracy of the method. [ABSTRACT FROM AUTHOR]

This paper studies the inhomogeneous nonlinear Schrödinger equations, which may model the propagation of laser beams in nonlinear optics. Using the cross‐constrained variational method, a sharp condition for global existence is derived. Then, by solving a variational problem, the strong instability of solitary waves of this equation is proved. [ABSTRACT FROM AUTHOR]

In this paper, the inverse problem of initial value identification for homogeneous anomalous diffusion equation with Riemann‐Liouville fractional derivative in time is studied. We prove that this kind of problem is ill‐posed. We analyze the optimal error bound of the problem under the source condition and apply the quasi‐boundary regularization method, fractional Landweber iterative regularization method, and Landweber iterative regularization method to solve this inverse problem. Based on the results of conditional stability, the error estimates between the exact solution and the regular solution are given under the priori and posteriori regularization parameter selection rules. Finally, three examples are given to illustrate the effectiveness and feasibility of these methods. [ABSTRACT FROM AUTHOR]

In this paper, we show the existence of solutions of the convex minimization problems and common fixed problems in CAT(1) spaces under some mild conditions. For this, we propose the new modified the proximal point algorithm. Further, we give some applications for the convex minimization problem and the fixed point problem in CAT(κ) spaces with the bounded positive real number κ. Our results improve and generalize many recent important results in the literature. [ABSTRACT FROM AUTHOR]