A constrained Bayes estimator is established for the location parameter of an elliptically contoured distribution, when it is suspected that some linear constraints may hold on the parameter space. Under Jeffrey’s prior, the posterior distribution is proposed and the exact form of the constrained empirical Bayes estimator is derived for a general form of balanced loss function. Performance of the estimators

This paper studies an optimal excess-of-loss reinsurance and investment problem with thinning dependent risks. Assume that the insurer’s wealth process is described by a risk model with two dependent classes of insurance business, and the insurer is allowed to purchase excess-of-loss reinsurance from the reinsurer and invest in a risk-free asset and a risky asset whose price follows Heston model. Our

It is well known that periodic orbits with any period can appear in sequential dynamical systems over undirected graphs with a Boolean maxterm or minterm function as global evolution operator. Indeed, fixed points cannot coexist with periodic orbits of greater periods, while periodic orbits with different periods greater than 1 can coexist. Additionally, a fixed point theorem about the uniqueness of

In this paper, we derive a new fractional Halanay-like inequality, which is used to characterize the long-term behavior of time fractional neutral functional differential equations (F-NFDEs) of Hale type with order α∈(0,1). The contractivity and dissipativity of F-NFDEs are established under almost the same assumptions as those for classical integer-order NFDEs. In contrast to the exponential decay

In this paper we derive local L2 error estimates for penalized least-squares approximation on the d-dimensional unit sphere Sd⊆Rd+1, given noisy, scattered, local data representing an underlying function from a Sobolev space of order s>d∕2 defined on a non-empty connected open set Ω⊆Sd with Lipschitz-continuous boundary. The quadratic regularization functional has two terms, one measuring the squared

Recently, several iterative algorithms have been proposed for the solution of multilinear system Axm−1=b in the sense that the tensor A of order m and dimension n is a structured one. In this paper, we continue to address this multilinear system in which the coefficient tensor A is an unstructured one given in tensor-train format, and present a new iterative method for it. The method we propose here

In this paper, we introduce the concept of exceptional family to implicit semidefinite complementarity problems and implicit copositive complementarity problems. Based on the notion of the exceptional family of elements, we prove that the nonexistence of exceptional family of elements is a sufficient condition for the existence theorem of implicit semidefinite complementarity problems and the implicit

As soon as a saddle point is found, people will pay attention to its Morse index. The instability is an important character to a saddle point. For nondegenerate saddle points, the Morse indices can be used to measure their instability and classify them. In this paper, a formula on the Morse index of minimax type saddle point by a Ljusternik–Schnirelman minimax algorithm is established. For nondegenerate

In this paper, a split-step θ method is introduced for solving stochastic Volterra integral equations with general smooth kernels. First, the mean-square boundedness and convergence properties of the numerical solution are analyzed. In particular, when the kernel function in the stochastic integral term satisfies a certain condition, the method can achieve superconvergence. Then, the mean-square stability

Information geometry has been attracting considerable attention in different scientific fields including information theory, neural networks, machine learning, and statistical physics. In reliability and survival analysis, methods of information geometry are employed to discuss the geometry on a reliability model. Most of the existing work of information geometry in reliability analysis focused on

We study the existence and uniqueness of a solution to the stochastic Volterra integral equations (SVIEs) with jumps. Moreover, we apply the Euler–Maruyama approximation for SVIEs with jumps and investigate the boundedness and the convergence of the numerical solution. Furthermore, we show that the numerical solution strongly superconverges with order 1 if the diffusion and jump coefficients satisfy

A time-fractional diffusion equation involving the Dirichlet energy is considered with nonlocal diffusion operator in the space which has dimension d∈{2,3} and the Caputo sense fractional derivative in time. Further, nonlocal term in diffusion operator is of Kirchhoff type. We discretize the space using the Galerkin finite elements and time using the finite difference scheme on a uniform mesh. First

In this paper, we study the convergence of explicit numerical methods in strong sense for stochastic delay differential equations (SDDEs) with super-linear growth coefficients. Under non-globally Lipschitz conditions, a fundamental theorem on convergence has been constructed to elaborate the relationship of convergence rate between the local truncated error and the global error of one-step explicit

This article deals with the dynamic analysis in pad concrete foundation containing Silica nanoparticles (SiO2) subject to seismic load. The foundation is covered by a piezoelectric layer for smart control of the structure. The weight of the building by a column on the foundation is assumed with an external force at the middle of the structure. The foundation is located in soil medium which is modeled

In this work, we numerically consider a thermoelastic problem where the thermal law is modeled using the so-called Moore–Gibson–Thompson equation. This thermomechanical problem is written as a coupled system composed of a hyperbolic partial differential equation for a transformation of the displacement field and a parabolic partial differential equation for a transformation of the temperature. Its

In this paper, we have proposed an improved estimator of the population mean in simple random sampling without replacement by applying Searls (1964) technique on the estimator given by Roy (2003). We have also proposed its extension to stratified random sampling which is a generalization of an estimator given by Grover (2006). We have also used robust regression method to these proposed traditional

This paper is concerned with the delay dependent stability of the stochastic exponential Euler method for stochastic delay differential equations and stochastic delay partial differential equations. By using root locus technique, the necessary and sufficient condition of the numerical delay dependent stability of the method is derived for a class of stochastic delay differential equations and it is

In this paper, some partial penalized immersed finite element methods (PPIFEMs) are proposed and analyzed for solving elasticity interface problems. Through verifying the inverse trace inequality on the interface edges, the optimal convergence in the energy norm is derived. A new test function is constructed to obtain the discrete inf–sup condition of the penalty-free nonsymmetric PPIFEM and is utilized

This paper presents an efficient algorithm for finding all solutions of nonlinear equations using linear programming. This algorithm is based on a simple test (called the LP test) for nonexistence of a solution to a system of nonlinear equations in a given region. In the conventional LP test, a system of nonlinear equations is formulated as a linear programming problem by surrounding component nonlinear

In this paper, the numerical technique with the help of the Lucas wavelets (LWs) and the Legendre–Gauss quadrature rule is presented to study the solution of fractional Fredholm–Volterra integro-differential equations. The modified operational matrices of integration and pseudo-operational of fractional derivative for the proposed wavelet functions are calculated. These matrices in comparison to operational

In order to improve the effectiveness and accuracy of financial status indicators to measure the degree of fiscal tightening, financial market situation and systemic financial risk, the logistic regression method is used to screen the target variables of the indicators. The model improves the objectivity of the selection of target variables. The model chooses 18 alternative indicators such as three-month

This article concerns with the infection dynamics of fractionally extended HIV infection model incorporating antibody and cytotoxic T-Lymphocyte (CTL) immune responses. We study the role of antiretroviral therapy drugs, namely, reverse transcriptase and protease inhibitors in suppressing the HIV infection. The dynamical characteristics of the system are first discussed qualitatively through linear

We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and polynomial lattice rules, which are special classes of QMC methods, have been intensively studied and the so-called component-by-component (CBC) algorithm has been well-established to construct rules which achieve the almost optimal rate of convergence

In this paper, we study the computational applications of the Levi-Civita field whose elements are functions from the additive abelian group of rational numbers to the real numbers field, with left-finite support. After reviewing the algebraic and order structures of the Levi-Civita field, we introduce the Tulliotools library which implements the Levi-Civita field in the C++ programming language. We

Process capability indices are used to measure the performance of a process in the manufacturing industry. This paper derives inferences for the lifetime performance index using k-record values when the lifetime of products has a Weibull distribution. The UMVUE, an exact test and a classical confidence interval are proposed for this index when the shape parameter of Weibull distribution is known. With

Wavelet/frame shrinkage and nonlinear diffusion filtering are two popular methods for signal and image denoising. The relationship between these two methods has been studied recently. This relationship leads to new types of diffusion equations and helps to design the wavelet/frame-inspired diffusivity functions, and on the other hand it helps to design the diffusion-inspired shrinkage functions with

In this paper, we formulate a numerical method to find out the approximate solution for fractional integro-differential equations of variable order (FIDE-VO). The methodology that adopted here is converting the FIDE-VO problem into a system of ordinary differential equations and that has been transformed into a system of algebraic equations in the unknown coefficients. For this purpose, the shifted

In this paper, we are concerned with the weighted plane wave least-squares (PWLS) method for three-dimensional Helmholtz equations, and develop the multi-level adaptive BDDC algorithms for solving the resulting discrete system. In order to form the adaptive coarse components, the local generalized eigenvalue problems for each common face and each common edge are carefully designed. The condition number

New calibrated estimators of quantiles and poverty measures are proposed. These estimators combine the incorporation of auxiliary information provided by auxiliary variables related to the variable of interest by calibration techniques with the selection of optimal calibration points under simple random sampling without replacement. The problem of selecting calibration points that minimize the asymptotic

In this paper, we consider a class of multiscale methods for the solution of nonlinear problem in perforated domains. These problems are of multiscale nature and their discretizations lead to large nonlinear systems. To discretize these problems, we construct a fine grid approximation using the finite element method with implicit time approximation and the Newton’s method. In order to solve these large

In Farin (2006) Farin proposed a method for designing Bézier curves with monotonic curvature and torsion. Such curves are relevant in design due to their aesthetic shape. The method relies on applying a matrix M to the first edge of the control polygon of the curve in order to obtain by iteration the remaining edges. With this method, sufficient conditions on the matrix M are provided, which lead to

This article presents a stable finite difference approach for the numerical approximation of singularly perturbed differential-difference equations (SPDDEs). The proposed scheme is oscillation-free and much accurate than conventional methods on a uniform mesh. Error estimates show that the scheme is linear convergent in space and time variables. By using the Richardson extrapolation technique, the

In this article, we consider a class of singular linear systems of differential equations whose coefficients are constant matrices, and study the response of its stability after a perturbation is applied into the system. We use a linear fractional transformation and through its properties we provide a practical test for robust stability. This test requires only the knowledge of the invariants of the

To construct C1-continuous basis functions for the numerical solutions of two dimensional biharmonic equations on non-convex domains with clamped and/or simply supported boundary conditions, we use B-spline basis functions instead of conventional Hermite finite element basis functions. The C1-continuous B-spline approximation functions constructed on the master patch are moved onto a physical domain

We introduce a new concept of convergence for iterative methods, named restricted global convergence, that consists of locating a solution and obtaining a domain of global convergence. As a consequence, results of semilocal convergence and local convergence are obtained. For this, we use auxiliary points and obtain balls of convergence. The study is illustrated with Chebyshev’s method.

In this paper, we introduce and study a new class of strong mixed vector generalized quasi-variational inequality problems (GQVIP) in fuzzy environment. Then, using the method of the nonlinear scalarization function, the regularized gap functions for GQVIP is established. In addition, error bounds are provided for GQVIP via those regularized gap functions under suitable assumptions. The main results

In this work we consider a new efficient IMplicit Pressure Explicit Saturation (IMPES) scheme for the simulation of incompressible and immiscible two-phase flow in heterogeneous porous media with capillary pressure. Compared with the conventional IMPES schemes, the new IMPES scheme is inherently physics-preserving, namely, the new algorithm is locally mass conservative for both phases and it also enjoys

In this manuscript, we design an efficient sixth-order scheme for solving nonlinear systems of equations, with only two steps in its iterative expression. Moreover, it belongs to a new parametric class of methods whose order of convergence is, at least, four. In this family, the most stable members have been selected by using techniques of real multidimensional dynamics; also, some members with undesirable

For a system of nonlinear fractional differential equations, the problem of reconstructing an unknown external impact is considered. It is complicated by the fact that only a part of system’s parameters is available for measuring. An algorithm for solving this problem is proposed, which is resistant to informational noises and computational errors, and is based on regularization methods and constructions

In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative expression. A deep dynamical study of the family is carried out on polynomial systems by selecting different weight functions and comparing the results obtained in each case. This study shows the applicability of the multidimensional

An initial–boundary value problem with a Riemann–Liouville–Caputo space fractional derivative of order α∈(1,2) is considered, where the boundary conditions are reflecting. A fractional Friedrichs’ inequality is derived and is used to prove that the problem approaches a steady-state solution when the source term is zero. The solution of the general problem is approximated using a finite difference scheme

Nodal point sets, and associated collocation projections, play an important role in a range of high-order methods, including Flux Reconstruction (FR) schemes. Historically, efforts have focused on identifying nodal point sets that aim to minimise the L∞ error of an associated interpolating polynomial. The present work combines a comprehensive review of known approximation theory results, with new results

This paper studies a weak Galerkin finite element method on a domain with curved edges. We consider the two dimensional Poisson’s equation of a fixed curved boundary. Usually, the straight polygon meshes deliver a sub-optimal rate of convergence for the curved domain as approximation order bounded by O(h2) even for high order numerical schemes. In this paper, we shall develop a high order (optimal

Adaptive radial basis function (RBF) methods have been developed recently in Gu and Jung (2020) based on the multiquadric (MQ) RBFs for solving initial value problems (IVPs). The proposed adaptive RBF methods utilize the free parameter in order to adaptively enhance the local convergence of the numerical solution. Methods pertaining to the polynomial interpolation yield only fixed rate of convergence

In this paper, a new numerical scheme which combines the multiscale asymptotic method and the Laplace transformation, is presented for solving the 3-D dual-phase-lagging equation in composite materials. The convergence results of the truncated first-order and second-order multiscale approximate solutions are given rigorously. The numerical experiments are carried out to validate the theoretical results

In this paper, we are interested in solving an elliptic inverse Cauchy problem. As it is well known this problem is one of highly ill posed problem in Hadamard’s sense (Hadamard, 1953). We first establish formally a relationship between the Cauchy problem and an interface problem illustrated in a rectangular structure divided into two domains. This relationship allows us to use classical methods of

We start with a general governing equation for diffusion transport, written in a conserved form, in which the phenomenological flux laws can be constructed in a number of alternative ways. We pay particular attention to flux laws that can account for non-locality through space fractional derivative operators. The available results on the well posedness of the governing equations using such flux laws

Exact solutions of scalar conservation laws have the property that maxima are non-increasing, minima are non-decreasing and no new extrema are created. We present a simple and reliable general condition for numerical schemes to mimic this property. We demonstrate the result by applying it to various schemes, which leads to various CFL-like conditions.

The need to evaluate expressions of the form I(f)≔ trace (WTf(A)W), where the matrix A∈Rn×n is symmetric, W∈Rn×k with 1≤k≪n, and f is a function defined on the convex hull of the spectrum of A, arises in many applications including network analysis and machine learning. When the matrix A is large, the evaluation of I(f) by first computing f(A) may be prohibitively expensive. In this situation it is

Ma and Xu (2016) proposed a Hawkes jump–diffusion model for the firm’s value to describe the unexpectedness of default and default clustering in the framework of Merton’s structural default. However, the authors resorted to Monte-Carlo simulations for the calculation of the default probability and the default correlation, as no other solution method was available in the literature. In this note, we

Based on examining the origin of Clean Development Mechanism (CDM) from a view of ecological conservation, this paper describes CER time series with GED distribution and discovers its heteroskedasticity. The TGARCH and EGARCH models both reflect significant volatility of CER price with GARCH model analysis. In our estimation of Chinese carbon market risk with econometric TGARCH-VaR and EGARCH-VaR models

For computing PageRank problems, a Power-Arnoldi algorithm is presented by periodically knitting the power method together with the thick restarted Arnoldi algorithm. In this paper, by using the power method with the extrapolation process based on trace (PET), a variant of the Power-Arnoldi algorithm is developed for accelerating PageRank computations. The new method is called Arnoldi-PET algorithm

We introduce a new augmented dual-mixed finite element method for the linear convection-diffusion equation with mixed boundary conditions. The approach is based on adding suitable residual type terms to a dual-mixed formulation of the problem. We prove that for appropriate values of the stabilization parameters, that depend on the diffusivity and the magnitude of the convective velocity, the new variational

Two Finite-Difference Time-Domain (FDTD) methods are developed for solving the Schrödinger equation on nonuniform tensor-product grids. The first is an extension of the standard second-order accurate spatial differencing scheme on uniform grids to nonuniform grids, whereas the second utilizes a higher-order accurate spatial scheme using an extended stencil. Based on discrete-time stability theory,

In this paper, Haar wavelet collocation technique is developed for the solution of Volterra and Volterra–Fredholm fractional integro-differential equations. The Haar technique reduces the given equations to a system of linear algebraic equations. The derived system is then solved by Gauss elimination method. Some numerical examples are taken from literature for checking the validation and convergence

This paper studies uniqueness and nonuniqueness for internal potential reconstruction from one boundary measurement in core–shell structure, associated with the steady state Schrödinger equation. A uniqueness theorem of the inverse problem is established. In the meanwhile, a nonuniqueness theorem is also given when different potential and shape are considered. Finally, Tikhonov regularization method

Let J=0In−In0∈R2n×2n. A matrix H∈R2n×2n is called Hamiltonian if (HJ)⊤=HJ. In this paper, the inverse eigenvalue problem for Hamiltonian matrices is considered. The solvability condition for the inverse problem is derived and the representation of the general solution is presented by the generalized singular value decomposition of a matrix pair. Furthermore, the associated optimal approximation problem

This paper deals with a control strategy enforcing consensus in a fractional opinion formation model with leadership, where the interaction rates between followers and the influence rate of the leader are functions of deviations of opinions between agents. The fractional-order derivative determines the impact of the memory during the opinion evolution. The problem of leader-following consensus control

We study the existence of nontrivial solution curves of the coupled Gross–Pitaevskii equations (CGPEs) in some neighborhoods of bifurcation points. The CGPEs are used as a mathematical model for boson–fermion mixtures (BFM). Linear stability analysis is studied numerically. Three multi-parameter continuation algorithms are proposed for computing the ground states of BFM, where the spectral collocation

The performance of gradient methods has been considerably improved by the introduction of delayed parameters. Recently, the revealing of second-order information has given rise to the Cauchy-based methods with alignment, which are generally considered as the state of the art of gradient methods. This paper investigates the spectral properties of minimal gradient and asymptotically optimal steps, and