An entering firm wants to compete for market share of an area by opening some new facilities selected among a finite set of potential locations (discrete space). Customers are spatially separated and there already are other firms operating in that area. In this paper, we use a variant of the well know Huff (proportional) customer choice rule, the so called Pareto-Huff, which have had little attention

Variable metric techniques are a crucial ingredient in many first order optimization algorithms. In practice, they consist in a rule for computing, at each iteration, a suitable symmetric, positive definite scaling matrix to be multiplied to the gradient vector. Besides quasi-Newton BFGS techniques, which represented the state-of-the-art since the 70’s, new approaches have been proposed in the last

In this paper, we consider numerical approximations of the volume-conserved phase-field elastic bending energy model for lipid vesicles where a nonlocal term is added to the model such that the total volume can be conserved precisely. We further develop two linear and unconditionally energy stable schemes by combining the recently developed IEQ and SAV approaches with the stabilization technique, where

Backbone curves are usually obtained by analyzing nonlinear oscillators (e.g., the Duffing equation) whereas the backbones of linear oscillators are incidental by-products of such studies. Nevertheless, we focus on the harmonic oscillator, a linear, homogeneous constant-coefficient second-order ordinary differential equation. The backbone of the sinusoidally forced harmonic oscillator is well known

Broyden’s method is a quasi-Newton method which is used to solve a system of nonlinear equations. Almost all convergence theories in the literature assume existence of a root and bounds on the nonlinear function and its derivative in some neighbourhood of the root. All these conditions cannot be checked in practice. The motivation of this work is to derive a local convergence theory where all assumptions

We present in this paper a new method based on Bernoulli matrix polynomials to approximate the exponential of a matrix. The developed method has given rise to two new algorithms whose efficiency and precision are compared to the most efficient implementations that currently exist. For that, a state-of-the-art test matrix battery, that allows deeply exploring the highlights and downsides of each method

In this paper, a nonlinear singularly perturbed problem with an integral boundary condition is studied. A hybrid finite difference method based on the midpoint difference method and the upwind difference scheme is constructed. An adaptive grid generation algorithm is generated by equidistributing a monitor function. The convergence analysis of the hybrid difference method on the adaptive grid is derived

A novel HIV/AIDS infection model incorporating memory and media coverage effect is formulated. First, we introduce fractional-order derivative to the model. The basic reproduction number R 0 is calculated using the next generation matrix method. Existence, uniqueness, and positivity of the solution of the model are investigated. Existence and local stability analysis of the equilibria of the model

This paper investigates the implementation of Clenshaw-Curtis algorithms on singular and highly oscillatory integrals for efficient evaluation of the finite Fourier-type transform of integrands with endpoint singularities. In these methods, integrands are truncated by orthogonal polynomials and special function series term by term. Then their singularity types are computed using third and fourth-order

indent This paper discusses the analytical solutions of fractional partial differential equations using Integral Transform method.The fractional derivatives are considered with reference to modified Riemann–Liouville derivatives. Fractional Fourier transform (FrFT) is applied to solve fractional heat diffusion, fractional wave, fractional telegraph and fractional kinetic equations. The method proposed

The high-end equipment features with high value, complicated manufacturing process, and high status, and it thus brings a huge challenge to increase reliability, quality, and productivity during the production. In order to tackle this challenge and achieve automation, integration, and intelligence this paper proposes a hybrid metaheuristic for an integrated order scheduling and maintenance planning

In this paper, we study and present a spectral numerical technique for solving a general class of multi-order fractional pantograph equations with varying coefficients and systems of pantograph equations. In this study, the spectral Galerkin approach in combination with the properties of shifted Legendre polynomials is used to reduce such equations to systems of algebraic equations, which are solved

Up to now, the isogeometric boundary element method (IGBEM) has been widely applied in different fields, and the solved problems are basically independent of time. But an excellent numerical method is more than that, so it is necessary to explore a new IGBEM which can solve time-domain problems. Based on this, the isogeometric dual reciprocity boundary element method (IG-DRBEM) is proposed to solve

In this study, Bernstein approximation method has been applied along with Riemann–Liouville fractional integral operator to solve both the second and the first kind of fractional Volterra integral equations (2nd FVIEs and 1st FVIEs respectively). In order to show the applicability and efficiency of the proposed technique, some convergence analysis has been provided. Illustrative numerical experiments

To improve the security of asset securitization and reduce investment risk, the risk reduction methods of asset securitization are investigated. First, the risk and return of investment are measured using multiple methods, and several portfolio methods are introduced. Second, there are problems of fraud risk, underlying assets, and asymmetry risk when assets are being transformed into securitization

A test approach to the model selection problem for multinomial data based on penalized ϕ-divergences is proposed. The test statistic is a sample version of the difference of the distances between the population and each competing model. The null distribution of the test statistic is derived, showing that it depends on whether the competing models intersect or not and whether certain parameter is positive

We address a mathematical model to approximate in a coarse qualitative the interaction between inbreeding-lobbying and interdisciplinarity in academia and perform a one and two-parameter numerical bifurcation analysis to analyse its dynamics. Disciplinary diversity is a necessary condition for the development of interdisciplinarity, which is being recognized today as the key to establish a vibrant

An asymptotic averaging of differential equations with fast oscillating quasi-periodic coefficients so-called “the asymptotic averaging in parametric space” is developed. The system of equations corresponding to structurally heterogeneous thermoelastic media with smoothly varying microstructures is considered. Such materials are usually treated as functionally graded ones. Their description is satisfied

This note states the correction of arguments in the proof of Theorem 3.2 in the original paper.

We propose and analyze a fast two-point gradient (TPG) method for solving non-smooth ill-posed inverse problems where the forward operator is merely directionally but not Gâteaux differentiable. This method is seen as a combination of a derivative-free Landweber iteration and a general case of Nesterov’s acceleration scheme. Since the forward mapping is not Gâteaux differentiable in our case, the standard

The Rosenbrock-Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions arising within each stage of the integrator. This work proposes an extension of Rosenbrock-Krylov methods to address stability questions which arise for methods making use of inexact linear system solution strategies. Two

This paper deals with the problem of efficiency assessment using Data Envelopment Analysis (DEA) when the input and output data are given as fuzzy sets. In particular, a fuzzy extension of the measure of inefficiency proportions, a well-known slacks-based additive inefficiency measure, is considered. The proposed approach also provides fuzzy input and output targets. Computational experiences and comparison

Since the memory-dependent derivative (MDD) was developed in 2011, it has become a new branch of Fractional Calculus which is still in the ascendant nowadays. How to understand MDD and fractional derivative (FD)? What are the advantages and disadvantages for them? How do they behave in Modeling? These questions guide going deep into the illustration of memory effect. Though the FD is defined on an

Almost strictly sign regular matrices are sign regular matrices with a special zero pattern and whose nontrivial minors are nonzero. In this paper we provide several properties of almost strictly sign regular rectangular matrices of maximal rank and analyze their QR factorization.

Notions of orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral representations, orthogonality relations and explicit expressions are established.

Upon the recent development of the quasi-reversibility method for terminal value parabolic problems in Nguyen et al. (2019), it is imperative to investigate the convergence analysis of this regularization method in the stochastic setting. In this paper, we positively unravel this open question by focusing on a coupled system of Dirichlet reaction–diffusion equations with additive white Gaussian noise

With the development of the Internet, Internet finance in new P2P modes will face a great many difficulties and opportunities; so, relevant risk early-warning models need to be researched and analyzed. The early-warning analysis will not only be helpful for P2P, the new mode, but will also be worth learning by the whole Internet financial industries, and there will be a particular demonstration effect

The second-order cone mixed complementarity problems (SOCMCPs) can directly present the KKT conditions of the second-order cone programming, and have broad range of applications. We establish the generalized lower-order penalty algorithm in this article for solving the SOCMCPs. By using the proposed algorithm, the SOCMCP is converted to asymptotic lower-order penalty equations (LOPEs). Under the assumption

We study a spatially semidiscrete approximation of nonlinear stochastic partial differential equations (SPDEs) driven by multiplicative noise under weak assumptions on the coefficients avoiding the standard global Lipschitz assumption in the literature. The discretization in space is done by a piecewise linear finite element method. Under some suitable regularity assumption for the exact solution,

Computed tomography (CT) is a non-invasive scanning technique that allows the visualization of the internal structure of an object from X-ray projections. These projections are frequently affected by different artifacts, including the beam hardening (BH) effect, among others. The BH effect is produced by high X-ray attenuation due to dense elements inside the object of interest. Traditionally, BH artifacts

The Black and Scholes call function is widely used for pricing and hedging. In this paper we present a new global approximating formula for the Black and Scholes call function that can be useful for deriving the risk of options i.e. the implied volatility. Lastly we compare, by numerical tests, our results with some popular methods available in literature (which are generally local) and we show, through

In this paper, a system of time dependent boundary layer originated reaction dominated problems with diffusion parameters of different magnitudes, is considered for numerical analysis. The presence of these parameters lead to the boundary layer phenomena. Here, an optimal order uniformly accurate boundary layer adaptive method moving mesh method is proposed. This method is able to capture the layer

The supply chain finance industry will generate the flow of funds and commodities when providing financing services to small and medium-sized enterprises (SMEs). At this time, banks will face multiple risks such as policy, operation, market and credit. The investigation on supply chain finance under information sharing from the aspect of credit risk assessment will be conducted. The genetic algorithm

In order to realize the financial benefit evaluation of the investment project, the investment project of power transmission and transformation of a power grid enterprise in Sichuan province is taken as an example. First, the overall cost of the investment project is analyzed and introduced, and the sales revenue, running costs, taxes and surcharges in the four years from 2016 to 2019 are calculated

In this paper, an algebraic and robust fractional order differentiator is designed for a class of fractional order linear systems with an arbitrary differentiation order in [0,2]. It is designed to estimate the fractional derivative of the pseudo-state with an arbitrary differentiation order as well as the one of the output. In particular, it can also estimate the pseudo-state. Different from our previous

The classical problem of counting the number of real zeros of a real polynomial was solved a long time ago by Sturm. The analogous problem of counting the number of zeros that a polynomial has on the unit circle is, however, still an open problem. In this paper, we show that the second problem can be reduced to the first one through the use of a suitable pair of Möbius transformations – often called

As widely known, the basic reproduction number plays a key role in weighing birth/infection and death/recovery processes in several models of population dynamics. In this general setting, its characterization as the spectral radius of next generation operators is rather elegant, but simultaneously poses serious obstacles to its practical determination. In this work we address the problem numerically

The moving average (MA) and double moving average (DMA) control charts are a good alternative to the Shewhart chart to detect small to moderate shifts of the process mean more quickly. In this article, we propose the triple moving average (TMA) control chart to improve the detection ability of the MA chart. It is shown that the proposed chart is more effective than the MA and DMA charts in detecting

We investigate the performance of a unified finite element method for the numerical solution of moving fronts in porous media under non-isothermal flow conditions. The governing equations consist of coupling the Darcy equation for the pressure to two convection–diffusion-reaction equations for the temperature and depth of conversion. The aim is to develop a non-oscillatory unified Galerkin-characteristic

In this paper, we propose an efficient and practical implementation of the ensemble Kalman filter (EnKF) via the distribution-free Ledoit and Wolf (LW) covariance matrix estimator. Initially, we develop a tractable implementation of the LW estimator in high-dimensional probability spaces such as those found in the context of operational data assimilation. We employ this well-conditioned, full-rank

We consider the problem of estimating expectations by using Markov chain Monte Carlo methods and improving the accuracy by replacing IID uniform random points with quasi-Monte Carlo (QMC) points. Recently, it has been shown that Markov chain QMC remains consistent when the driving sequences are completely uniformly distributed (CUD). However, the definition of CUD sequences is not constructive, so

In this paper we consider the problem for finding the global minimum value of a continuous function over Rn. We show that, under a growth condition, the objective function which is non-smooth in general has a global minimizer on a closed ball. We pose a nonlinear diffusion equation concerning the optimization problem. A quasi-extremal flow is defined and constructed by the diffusion equation for an

In this paper, we consider a modified Douglas splitting method for a class of differential matrix equations, including differential Lyapunov and differential Riccati equations. The method we consider is based on a natural three-term splitting of the equations. The implementation of the algorithm requires only the solution of a linear algebraic system with multiple right-hand sides in each time step

Experimental design is arguably the most commonly used and effective methodology in scientific investigations and industrial applications. Real-world experiments may have hundreds or even thousands of input variables (factors) and thus a large number of observations (experimental runs) is needed to gain a better understanding of the phenomena under the investigation and estimate the most important

This paper is concerned with a new fractional Jacobi collocation method for solving a system of multi-order fractional differential equations with variable coefficients. The existence, uniqueness, and smoothness results are rigorously studied. From the numerical point of view, first a new interpolation operator based on the orthogonal fractional Jacobi functions as well as its approximation properties

In this article, we establish some sufficient conditions for total controllability of a neutral fractional differential system with impulsive conditions in the finite-dimensional spaces. This type of controllability concerns the controllability problem not only at the final time but also at the impulse time. We use Mittag-Leffler matrix function, nonlinear functional analysis, controllability Grammian

The main motivation of the present work is the numerical study of a system of Partial Differential Equations that governs drug transport, through a target tissue or organ, when enhanced by the simultaneous action of an electric field and a temperature rise. The electric field, while forcing charged drug molecules through the tissue or the organ, thus creating a convection field, also leads to a rise

In this paper, we continue investigating the strong convergence order of the Euler method for Volterra integro-differential equations with fractional Brownian motions. The strong convergence order for a long-memory process is improved by the method with distributions of the centered Gaussian processes. Moreover, for a short-memory process, the optimal strong convergence order of the method with distributions

In this paper we mainly focus on the asymptotic expansion and quadrature rule for a class of singular-oscillatory-Bessel-type transforms. The asymptotic expansion in inverse powers of the frequency ω is obtained after avoiding the singularities. Then, based on the asymptotic expansion, we successfully construct a so-called modified Filon-type quadrature rule. Meanwhile, we also give the corresponding

We present an algorithm for approximating a function defined over a d-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require knowledge about the local geometry of the manifold or its local parameterizations. We do require, however, knowledge regarding the manifold’s intrinsic dimension d. We use the

The original Ait-Sahalia model of the spot interest rate proposed by Ait-Sahalia assumes constant volatility. As supported by several empirical studies, volatility is never constant in most financial markets. From application viewpoint, it is important we generalise the Ait-Sahalia model to incorporate volatility as a function of delay in the spot rate. In this paper, we study analytical properties

In this paper, the n-dimensional stochastic Itô-Volterra integral equation is numerically solved via quintic B-spline collocation method. To reach this aim, the quintic B-spline interpolation, Gauss–Legendre quadrature formula and Itô approximation are presented. By using the quintic B-spline collocation method, n-dimensional stochastic Itô-Volterra integral equation can be reduced to a linear or nonlinear

Many advances in artificial intelligence and machine learning are based on decision making, especially in uncertain settings. Due to its possible applications, decision making is currently a broad field of study in many areas like Computation, Economics and Business Management. The first techniques appeared in scenarios where information was modeled by real numbers. In all cases, one of the key steps

In this paper, an accurate numerical method is presented to solve a class of variable-order fractional diffusion problem. The problem first is discretized by a finite difference method in temporal direction, and then a local discontinuous Galerkin method in space. The stability and L2 convergence of the proposed scheme are derived for all variable-order α(t)∈(0,1). We prove that the scheme is of accuracy-order

In this paper, we develop the numerical theory of decoupled modified characteristic FEMs for the fully evolutionary Navier–Stokes–Darcy model with the Beavers–Joseph interface condition. Based on lagging interface coupling terms, the system is decoupled, which means that the Navier–Stokes equations and the Darcy equation are solved in each time step, respectively. In particular, the Navier–Stokes equations

In this paper, we consider a multiscale hybridizable discontinuous Galerkin (HDG) for heterogeneous linear elasticity problem in a mixed formulation. Within the framework of HDG, the entire problem can be decomposed into a global problem defined in coarse interfaces and several local problems in coarse elements. Our goal here is to propose a multiscale basis space defined in the coarse interface. We

Li et al. (2018) have proposed a regularization of the forward–backward sweep iteration for solving the Pontryagin maximum principle in optimal control problems. The authors prove the global convergence of the iteration in the continuous time case. In this article we show that their proof can be extended to the case of numerical discretization by symplectic Runge–Kutta pairs. We demonstrate the convergence

Lipschitz global optimization is an important research field with numerous applications in engineering, electronics, machine learning, optimal decision making, etc. In many of these applications, even in the univariate case, evaluations of the objective functions and derivatives are often time consuming and the number of function evaluations executed by algorithms is extremely high due to the presence

In this paper, we consider numerical approximations for the anisotropic phase-field crystal model. The model is a sixth-order nonlinear equation with an anisotropic Laplace operator. To develop easy-to-implement and unconditionally energy stable time marching schemes, we combine the scalar auxiliary variable (SAV) approach with the stabilization method, where two extra stabilization terms are added

Large scale systems of algebraic equations are frequently solved by iterative solution methods, such as the conjugate gradient method for symmetric or a generalized conjugate gradient or generalized minimum residual method for nonsymmetric linear systems. In practice, to get an acceptable elapsed computing time when solving large scale problems, one shall use parallel computer platforms. However, such