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This paper is interested in studying the one-phase Stefan problem. For this purpose, we use the nonlinear sentinel method, which relies typically on the approximate controllability and the Fanchel-Rockafellar duality of the minimization problem, to prove the existence and uniqueness of a solution to this problem. In particular, our research focuses on the application of the nonlinear sentinel method to the single-phase Stefan problem. This approach aids in identifying an unspecified boundary section within the domain undergoing a liquid-solid phase transition. We track the evolution of the temperature profile in the liquid-solid material and the corresponding movement of its interface over time. Eventually, the local convergence used for the iterative numerical scheme is demonstrated. [ABSTRACT FROM AUTHOR]

Fuzzy Integral equations is a mathematical tool for modeling the uncertain control system and economic. In this paper, we present numerical solution of nonlinear fuzzy Volterra integral equations (NFVIEs) using successive approximations scheme and block-pulse functions. Additionally, the convergence analysis of the presented approach is investigated involving Lipschitz and several conditions and error bound between the approximate and the exact solution is provided. Finally, to approve the outcomes concerned with the theory a numerical experiment is considered. [ABSTRACT FROM AUTHOR]

Highlights • A finite-buffer vacation queue with batch Markovian arrival process has been analyzed. • The server is subjected to serve under gated-limited service discipline. • Proposed analysis is based on the successive substitution and the supplementary variable method. • The results have been matched with the corresponding infinite-buffer queue. • Numerical results are presented for different service- and vacation-time distributions. Abstract This paper analyzes the finite-buffer single server queue with vacation(s). It is assumed that the arrivals follow a batch Markovian arrival process (BMAP) and the server serves customers according to a non-exhaustive type gated-limited service discipline. It has been also considered that the service and vacation distributions possess rational Laplace-Stieltjes transformation (LST) as these types of distributions may approximate many other distributions appeared in queueing literature. Among several batch acceptance/rejection strategies, the partial batch acceptance strategy is discussed in this paper. The service limit L (1 ≤ L ≤ N) is considered to be fixed, where N is the buffer-capacity excluding the one in service. It is assumed that in each busy period the server continues to serve until either L customers out of those that were waiting at the start of the busy period are served or the queue empties, whichever occurs first. The queue-length distribution at vacation termination/service completion epochs is determined by solving a set of linear simultaneous equations. The successive substitution method is used in the steady-state equations embedded at vacation termination/service completion epochs. The distribution of the queue-length at an arbitrary epoch has been obtained using the supplementary variable technique. The queue-length distributions at pre-arrival and post-departure epoch are also obtained. The results of the corresponding infinite-buffer queueing model have been analyzed briefly and matched with the previous model. Net profit function per unit of time is derived and an optimal service limit and buffer-capacity are obtained from a maximal expected profit. Some numerical results are presented in tabular and graphical forms. [ABSTRACT FROM AUTHOR]

The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many aspects of scientific computing with complex models. The contribution of this paper is twofold. First, we provide novel mathematical analysis of the polynomial quadrature problem that provides a lower bound for the minimal possible number of nodes in a polynomial rule with specified accuracy. We give concrete but simplistic multivariate examples where a minimal quadrature rule can be designed that achieves this lower bound, along with situations that showcase when it is not possible to achieve this lower bound. Our second contribution is the formulation of an algorithm that is able to efficiently generate multivariate quadrature rules with positive weights on non-tensorial domains. Our tests show success of this procedure in up to 20 dimensions. We test our method on applications to dimension reduction and chemical kinetics problems, including comparisons against popular alternatives such as sparse grids, Monte Carlo and quasi Monte Carlo sequences, and Stroud rules. The quadrature rules computed in this paper outperform these alternatives in almost all scenarios. [ABSTRACT FROM AUTHOR]

Interpolation and approximation methods are used across many fields. Standard interpolation and approximation methods rely on "ordering" that actually means tessellation in d-dimensional space in general, like sorting, triangulation, generating of tetrahedral meshes etc. Tessellation algorithms are quite complex in d-dimensional case. On the other hand, interpolation and approximation can be made using meshfree (meshless) techniques using Radial Basis Function (RBF). The RBF interpolation and approximation methods lead generally to a solution of linear system of equations. However, a similar approach can be taken for a reconstruction of a surface of scanned objects, etc. In this case this leads to a linear system of homogeneous equations, when a different approach has to be taken. In this paper we describe novel approaches based on RBFs for data interpolation and approximation generally in d-dimensional space. We will show properties and differences of "global" and "Compactly Supported RBF (CSRBF)", run-time and memory complexities. As the RBF interpolation and approximation naturally offer smoothness, we will analyze such properties as well as approaches how to decrease computational expenses. The proposed meshless interpolation and approximation will be demonstrated on different problems, e.g. in painting removal, restoration of corrupted images with high percentage of corrupted pixels, digital terrain interpolation and approximation for GIS applications and methods for decreasing computational complexity. [ABSTRACT FROM AUTHOR]

As a generalization of cyclic codes, constacyclic codes is an important and interesting class of codes due to their nice algebraic structures and various applications in engineering. This paper is devoted to the study of the q -polynomial approach to constacyclic codes. Fundamental theory of this approach will be developed, and will be employed to construct some families of optimal and almost optimal codes in this paper. [ABSTRACT FROM AUTHOR]

This paper estimates stress intensity factors of rotating solid disks or cylinders with a radial crack subjected to a uniform tension at their outer surface and a uniform temperature change through the body. Material properties of the cylinder are assumed to obey from the power law through the radius of the cylinder. The cracks are assumed to be small and located radially at center, inside or edge of the body. The stress intensity factors are obtained applying an approximate method and using the proper geometric functions for combination of the thermomechanical stresses. The method proposed in this paper is imposed to isotropic FG plates with an edge slanted crack to quantify the difference between present method and numerical methods given in the literature review. Also, the SIFs obtained for the non-homogeneous cylinder are reduced to the homogeneous one and are compared with the corresponding exact solution of isotropic materials. [ABSTRACT FROM AUTHOR]

The complex or non-Hermitian orthogonal polynomials with analytic weights are ubiquitous in several areas such as approximation theory, random matrix models, theoretical physics and in numerical analysis, to mention a few. Due to the freedom in the choice of the integration contour for such polynomials, the location of their zeros is a priori not clear. Nevertheless, numerical experiments, such as those presented in this paper, show that the zeros not simply cluster somewhere on the plane, but persistently choose to align on certain curves, and in a very regular fashion. The problem of the limit zero distribution for the non-Hermitian orthogonal polynomials is one of the central aspects of their theory. Several important results in this direction have been obtained, especially in the last 30 years, and describing them is one of the goals of the first parts of this paper. However, the general theory is far from being complete, and many natural questions remain unanswered or have only a partial explanation. Thus, the second motivation of this paper is to discuss some 'mysterious' configurations of zeros of polynomials, defined by an orthogonality condition with respect to a sum of exponential functions on the plane, that appeared as a results of our numerical experiments. In this apparently simple situation the zeros of these orthogonal polynomials may exhibit different behaviors: for some of them we state the rigorous results, while others are presented as conjectures (apparently, within a reach of modern techniques). Finally, there are cases for which it is not yet clear how to explain our numerical results, and where we cannot go beyond an empirical discussion. [ABSTRACT FROM AUTHOR]

Abstract Field experiments of solute transport through heterogeneous porous and fractured media show that the growth of contaminant plumes may convert between diffusive states. In this paper, we propose a multi-term time–space variable-order fractional advection–diffusion model (MTT-SVO-FADM) to describe the underlying transport dynamics. We consider a numerical approach based on the implicit numerical method for numerical solution of this model. A fully-discrete numerical scheme is developed by using the classical finite difference method. The unconditional stability and convergence of the scheme are discussed and theoretically proved. We use a modified grid approximation method (MGAM) to estimate the model's parameters. The MTT-SVO-FADM is then applied to describe transient dispersion observed at a field tracer test and four numerical experiments. The results show that this model can simulate the experimental data more accurately and can efficiently quantify these transitions. Highlights • A multi-term time–space variable-order fractional advection–diffusion model is proposed. • A fully-discrete numerical scheme is developed. • The unconditional stability and convergence of the scheme are discussed and proved. • A modified grid approximation method is used to estimate the model's parameters. • This model is applied to describe transient dispersion observed at a field tracer test and four numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract In this paper, our main aim is to investigate the stability and strong convergence of an implicit numerical approximations for neutral-type stochastic differential equations with superlinearly growing coefficients. After providing moment boundedness and exponential stability for the exact solutions, we show that the backward Euler–Maruyama numerical method preserves stability and boundedness of moments, and the numerical approximations converge strongly to the true solutions for sufficiently small step size. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we construct wavelet tight frames with n vanishing moments for Dubuc–Deslauriers 2 n -point semi-regular interpolatory subdivision schemes. Our motivation for this construction is its practical use for further regularity analysis of wide classes of semi-regular subdivision. Our constructive tools are local eigenvalue convergence analysis for semi-regular Dubuc–Deslauriers subdivision, the Unitary Extension Principle and the generalization of the Oblique Extension Principle to the irregular setting by Chui, He and Stöckler. This group of authors derives suitable approximation of the inverse Gramian for irregular B-spline subdivision. Our main contribution is the derivation of the appropriate approximation of the inverse Gramian for the semi-regular Dubuc–Deslauriers scaling functions ensuring n vanishing moments of the corresponding framelets. [ABSTRACT FROM AUTHOR]

This paper develops an analogue (or counterpart) to discontinuous Galerkin (DG) methods for approximating a general class of calculus of variations problems. The proposed method, called the discontinuous Ritz (DR) method, constructs a numerical solution by minimizing a discrete energy over DG function spaces. The discrete energy includes standard penalization terms as well as the DG Finite element (DG-FE) numerical derivatives developed recently by Feng, Lewis, and Neilan in [7]. It is proved that the proposed DR method converges and that the DG-FE numerical derivatives exhibit a compactness property which is desirable and crucial for applying the proposed DR method to problems with more complex energy functionals. Numerical tests are provided on the classical p-Laplace problem to gauge the performance of the proposed DR method. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the a priori error analysis for a convection-dominated diffusion 2D problem, when applying the HDG method on a family of anisotropic triangulations. It is known that in this case, boundary or interior layers may appear. Therefore, it is important to resolve these layers in order to recover, if possible, the expected order of approximation. In this work, we extend the use of HDG method on anisotropic meshes. In this context, when the discrete local spaces are polynomials of degree k ≥ 0 , this approach is able to recover an order of convergence k + 1 2 in L 2 for all the variables, under certain assumptions on the stabilization parameter and family of triangulations. Numerical examples confirm our theoretical results. Highlights • We develop an a priori error analysis for a HDG scheme defined on anisotropic meshes that are made of triangles. • We require that the family of triangulations satisfy the maximum angle condition, which is usual in this case. • We include numerical examples that validate our theoretical results. [ABSTRACT FROM AUTHOR]

Highlights • The Sturm sequence number is applied to adaptively determine the number of the lowest modes that need to be calculated. • The complementary part of contribution of the computed modes is approximated by a partial sum of a convergent power series. • The number of items in the partial sum are adaptively determined by the highest excitation frequency only. • The resulting expressions are efficient for the entire range of excitation frequencies of interest. • The proposed method can significantly reduce the computational cost. Abstract This paper presents a numerical method for calculating the frequency response and its sensitivity of an undamped system in a frequency interval. The Sturm sequence number is first used to adaptively determine the number of the lowest modes that need to be calculated. The corresponding modes can be computed by the Lanczos or subspace iteration methods. The complementary portion of contribution of these computed modes is then transformed into the solution to a new system by using the mass orthogonality. The solution of the new system is approximated by the partial sum of the convergent power series of the excitation frequencies, and the number of items therein can be adaptively determined by utilizing only the highest excitation frequency. The sensitivity expression of the frequency response is also established. The resulting expressions of the frequency response and its sensitivity are valid for the entire range of excitation frequencies of interest. By changing only the excitation frequency, we can obtain frequency responses and their sensitivities. This computational methodology is illustrated by its applications to two examples. The results show that the proposed method can remarkably reduce the CPU time required by the direct method. [ABSTRACT FROM AUTHOR]

Light-fidelity (LiFi) is a networked optical wireless communication (OWC) solution for high-speed indoor connectivity for fixed and mobile optical communications. Unlike conventional radio frequency wireless systems, the OWC channel is not isotropic, meaning that the device orientation affects the channel gain significantly, particularly for mobile users. However, due to the lack of a proper model for device orientation, many studies have assumed that the receiver is vertically upward and fixed. In this paper, a novel model for device orientation based on experimental measurements of 40 participants has been proposed. It is shown that the probability density function (PDF) of the polar angle can be modeled either based on a Laplace (for static users) or a Gaussian (for mobile users) distribution. In addition, a closed-form expression is obtained for the PDF of the cosine of the incidence angle based on which the line-of-sight (LOS) channel gain is described in OWC channels. An approximation of this PDF based on the truncated Laplace is proposed and the accuracy of this approximation is confirmed by the Kolmogorov–Smirnov distance. Moreover, the statistics of the LOS channel gain are calculated and the random orientation of a user equipment (UE) is modeled as a random process. The influence of the random orientation on signal-to-noise-ratio performance of OWC systems has been evaluated. Finally, an orientation-based random waypoint (ORWP) mobility model is proposed by considering the random orientation of the UE during the user’s movement. The performance of ORWP is assessed on the handover rate and it is shown that it is important to take the random orientation into account. [ABSTRACT FROM AUTHOR]

The conventional channel resolvability problem refers to the determination of the minimum rate required for an input process so that the output distribution approximates a target distribution in either the total variation distance or the relative entropy. In contrast to previous works, in this paper, we use the (normalized or unnormalized) Rényi divergence (with the Rényi parameter in $[{0,2}]\cup \{\infty \}$) to measure the level of approximation. We also provide asymptotic expressions for normalized Rényi divergence when the Rényi parameter is larger than or equal to 1 as well as (lower and upper) bounds for the case when the same parameter is smaller than 1. We characterize the Rényi resolvability, which is defined as the minimum rate required to ensure that the Rényi divergence vanishes asymptotically. The Rényi resolvabilities are the same for both the normalized and unnormalized divergence cases. In addition, when the Rényi parameter smaller than 1, consistent with the traditional case where the Rényi parameter is equal to 1, the Rényi resolvability equals the minimum mutual information over all input distributions that induce the target output distribution. When the Rényi parameter is larger than 1 the Rényi resolvability is, in general, larger than the mutual information. The optimal Rényi divergence is proven to vanish at least exponentially fast for both of these two cases, as long as the code rate is larger than the Rényi resolvability. The optimal exponential rate of decay for i.i.d. random codes is also characterized exactly. We apply these results to the wiretap channel, and completely characterize the optimal tradeoff between the rates of the secret and non-secret messages when the leakage measure is given by the (unnormalized) Rényi divergence. This tradeoff differs from the conventional setting when the leakage is measured by the traditional mutual information. [ABSTRACT FROM AUTHOR]

Abstract This work proposes a locally stabilized central difference method for time domain analyses, which performs considering the relation between the adopted temporal and spatial discretizations. Here, the standard expressions of the Central Difference Method (CDM) are considered to approximate the time derivatives of the incognita field, and the local (or element) matrices of the spatially discretized model are modified, if the stability criterion of the CDM is not locally fulfilled. Thus, a locally defined time marching methodology is provided, which may be up to fourth order accurate, has guaranteed stability, enhanced precision, and is highly efficient and versatile. The new technique may be stated as a semi-explicit/explicit approach; in this context, just reduced systems of equations have to be dealt with in the analyses and iterative procedures are never required, when nonlinear models are focused. In addition, the new technique is also very simple to implement and entirely automatized, requiring no decision or expertise from the user. Numerical results are presented along the paper, illustrating the performance and effectiveness of the new approach. Highlights • An effective time-marching procedure is proposed for nonlinear dynamics. • It is locally defined, introducing modified elements to guarantee stability. • The method has enhanced accuracy, it is simple and entirely automatized. • It enables reduced solver efforts and it stands as a non-iterative procedure. [ABSTRACT FROM AUTHOR]

Abstract This paper was dealt with buckling and post-buckling behavior of short thin-walled Z-columns made of a carbon-epoxy laminate, subjected to eccentric compressive load. The buckling mode and the buckling load of real structures versus load eccentricity were discussed. The study involved both experimental tests were carried out on real laminated structures and numerical simulations by the finite element method. The buckling load of real structures was determined by approximation methods on the basis of experimental and numerical post-buckling equilibrium paths of the structure. Additionally, in numerical simulations, the bifurcation load value was determined by solving an eigen problem. In all cases, experimental findings and numerical results show high agreement. The study determined the quantitative influence of the direction and value of compressive load eccentricity on the buckling load and rigidity of the structure in the post-buckling state. [ABSTRACT FROM AUTHOR]

The Conway-Maxwell-Poisson distribution is a two-parameter generalization of the Poisson distribution that can be used to model data that are under- or over-dispersed relative to the Poisson distribution. The normalizing constant Z(λ,ν) is given by an infinite series that in general has no closed form, although several papers have derived approximations for this sum. In this work, we start by using probabilistic argument to obtain the leading term in the asymptotic expansion of Z(λ,ν) in the limit λ→∞ that holds for all ν>0. We then use an integral representation to obtain the entire asymptotic series and give explicit formulas for the first eight coefficients. We apply this asymptotic series to obtain approximations for the mean, variance, cumulants, skewness, excess kurtosis and raw moments of CMP random variables. Numerical results confirm that these correction terms yield more accurate estimates than those obtained using just the leading-order term. [ABSTRACT FROM AUTHOR]

Abstract This paper introduces a high-order time stepping scheme, that is based on using Fourier spectral in space and a fourth-order diagonal Padé approximation to the matrix exponential function for solving multi-dimensional space-fractional reaction–diffusion equations. The resulting time stepping scheme is developed based on an exponential time differencing approach such that it alleviates solving a large non-linear system at each time step while maintaining the stability of the scheme. The non-locality of the fractional operator in some other numerical schemes for these equations leads to full and dense matrices. This scheme is able to overcome such computational inefficiency due to the full diagonal representation of the fractional operator. It also attains spectral convergence for multiple spatial dimensions. The stability of the scheme is discussed through the investigation of the amplification symbol and plotting its stability regions, which provides an indication of the stability of the method. The convergence analysis is performed empirically to show that the scheme is fourth-order accurate in time, as expected. Numerical experiments on reaction–diffusion systems with application to pattern formation are discussed to show the effect of the fractional order in space-fractional reaction–diffusion equations and to validate the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

An accurate traveltime approximation has a key role in the success of many seismic data processing, modelling and inversion algorithms. In this paper, we introduce a new explicit six-parameter traveltime approximation as an extension to the known generalized moveout approximation. The parameters of the proposed approximation are estimated at two offsets. Zero-offset two-way time, normal moveout velocity and effective anellipticity are defined at zero offset; the remaining three parameters are defined from traveltime, ray parameter and curvature at a reference offset. Each of these parameters has been previously employed in former traveltime approximations. The proposed method can be used to approximate full offset ray-traced traveltimes by two rays. Potential applications include approximation of migration Green's function and common midpoint forward modelling. It also gives insight for traveltime behaviour in anisotropic media. We provide numerical tests by different sources of non-hyperbolic moveout to show that the proposed method is a general improvement over the original generalized moveout approximation. It improves the accuracy and makes the parameter selection more symmetrical, while adding a minimum computational burden. [ABSTRACT FROM AUTHOR]

Mean Value Analysis (MVA) has long been a standard approach for performance analysis of computer systems. While the exact load-dependent MVA algorithm is an efficient technique for computer system performance modeling, it fails to address multi-core computer systems with Dynamic Frequency Scaling (DFS). In addition, the load-dependent MVA algorithm suffers from numerical difficulties under heavy load conditions. The goal of our paper is to find an efficient and robust method which is easy to use in practice and is also accurate for performance prediction for multi-core platforms. The proposed method, called Approximate Performance Evaluation for Multi-core computers (APEM), uses a flow-equivalent performance model designed specifically to address multi-core computer systems and identify the influence on the CPU demand of the effect of DFS. We adopt an approximation technique to estimate resource demands to parametrize MVA algorithms. To validate the application of our method, we investigate three case studies with extended TPC-W benchmark kits, showing that our method achieves better accuracy compared with other commonly used MVA algorithms. We compare the three different performance models, and we also extend our approach to multi-class models. [ABSTRACT FROM AUTHOR]

We present a novel distributed Gauss–Newton method for the non-linear state estimation (SE) model based on a probabilistic inference method called belief propagation (BP). The main novelty of our work comes from applying BP sequentially over a sequence of linear approximations of the SE model, akin to what is done by the Gauss–Newton method. The resulting iterative Gauss–Newton belief propagation (GN-BP) algorithm can be interpreted as a distributed Gauss–Newton method with the same accuracy as the centralized SE, however, introducing a number of advantages of the BP framework. The paper provides extensive numerical study of the GN-BP algorithm, provides details on its convergence behavior, and gives a number of useful insights for its implementation. [ABSTRACT FROM AUTHOR]

Coprime arrays can achieve an increased number of degrees of freedom by deriving the equivalent signals of a virtual array. However, most existing methods fail to utilize all information received by the coprime array due to the non-uniformity of the derived virtual array, resulting in an inevitable estimation performance loss. To address this issue, we propose a novel virtual array interpolation-based algorithm for coprime array direction-of-arrival (DOA) estimation in this paper. The idea of array interpolation is employed to construct a virtual uniform linear array such that all virtual sensors in the non-uniform virtual array can be utilized, based on which the atomic norm of the second-order virtual array signals is defined. By investigating the properties of virtual domain atomic norm, it is proved that the covariance matrix of the interpolated virtual array is related to the virtual measurements under the Hermitian positive semi-definite Toeplitz condition. Accordingly, an atomic norm minimization problem with respect to the equivalent virtual measurement vector is formulated to reconstruct the interpolated virtual array covariance matrix in a gridless manner, where the reconstructed covariance matrix enables off-grid DOA estimation. Simulation results demonstrate the performance advantages of the proposed DOA estimation algorithm for coprime arrays. [ABSTRACT FROM AUTHOR]

This paper aims to investigate an efficient numerical scheme for the optimal control of fractional-order dynamic systems. By using the Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations, the fractional optimal control problem under consideration is converted into a linear programming problem. Then, the internal model principle is employed in order to extend the new scheme for the fractional dynamic systems affected by the external persistent disturbances. Numerical examples and comparative results verify the validity and applicability of the new technique. [ABSTRACT FROM AUTHOR]

In this paper, a numerical scheme based on hybrid Chelyshkov functions (HCFs) is presented to solve a class of fractional optimal control problems (FOCPs). To this end, by using the orthogonal Chelyshkov polynomials, the HCFs are constructed and a general formulation for their operational matrix of the fractional integration, in the Riemann–Liouville sense, is derived. This operational matrix together with HCFs are used to reduce the FOCP to a system of algebraic equations, which can be solved by any standard iterative algorithm. Moreover, the application of presented method to the problems with a nonanalytic dynamic system is investigated. Numerical results confirm that the proposed HCFs method can achieve spectral accuracy to approximate the solution of FOCPs. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new technique for the asymmetric approximation of discrete functions arising in seasonal customer demand extrapolation. We adapt the technique for two different settings, the so-called pull and push models. Our main goal here is to find effectively extrapolations minimizing the loss. For bothmodels, we discuss several features related to sampling, approximation, and extrapolation. [ABSTRACT FROM AUTHOR]

The efficient solution of coupled PDEs/ODEs problems arising in cardiac electrophysiology is of key importance whenever interested to study the electrical behavior of the tissue for several instances of relevant physical and/or geometrical parameters. This poses significant challenges to reduced order modeling (ROM) techniques –such as the reduced basis method –traditionally employed when dealing with the repeated solution of parameter dependent differential equations. Indeed, the nonlinear nature of the problem, the presence of moving fronts in the solution, and the high sensitivity of this latter to parameter variations, make the application of standard ROM techniques very problematic. In this paper we propose a local ROM built through a k -means clustering in the state space of the snapshots for both the solution and the nonlinear term. Several comparisons among alternative local ROMs on a benchmark test case show the effectivity of the proposed approach. Finally, the application to a parametrized problem set on an idealized left-ventricle geometry shows the capability of the proposed ROM to face complex problems. [ABSTRACT FROM AUTHOR]

Abstract We study the interpolation Macdonald functions, remarkable inhomogeneous generalizations of Macdonald functions, and a sequence A 1 , A 2 , ... of commuting operators whose common eigenfunctions are the interpolation Macdonald functions. Such a sequence of operators arises in the projective limit of finite families of commuting q-difference operators studied by Okounkov, Knop and Sahi. The main theorem is an explicit formula for the operators A k. Our formula involves the family of Hall–Littlewood functions and a new family of inhomogeneous Hall–Littlewood functions, for which we give an explicit construction and identify as a degeneration of the interpolation Macdonald functions when q → 0. This article is inspired by the recent papers of Nazarov–Sklyanin on Macdonald and Sekiguchi–Debiard operators, and our main theorem is an extension of their results. [ABSTRACT FROM AUTHOR]

A. Horn's problem concerns finding two self adjoint matrices, so that A , B , and A + B have prescribed spectrum. In this paper, we show how it connects to an interpolation problem for two variable real zero polynomials and a tracial moment problem. In addition, we outline an algorithm to construct a pair ( A , B ) . [ABSTRACT FROM AUTHOR]

In this paper we propose an iterative numerical method for approximating solutions of fractional integral equations of the second kind, based on Picard iteration and a suitable quadrature formula. Under certain conditions, we prove the existence and uniqueness of the solution and give error estimates of the approximations. Numerical examples are given, which illustrate the good approximations. [ABSTRACT FROM AUTHOR]

A typical interpolation strategy for line segments consists of a transition scheme, a Look-ahead ACC/DEC scheduling, and an interpolation algorithm. In these three parts, the main computation occurs in the first and second part. Some research work has been carried out to decrease the computation in the previous literatures, but these methods occupy a lot of computing resources for the optimization process during the calculation of transition curve parameters and feed rates. Consequently, the computational efficiency of interpolation strategy is greatly reduced. To deal with the issue, a real-time interpolation strategy is proposed in this paper. In the transition scheme, a Bézier curve is utilized to smooth the line segments. Based on the relationship among the approximation error, the approximation radius, and the transition curve, the curve can be directly generated when the approximation error is given. In the ACC/DEC scheduling, a 3-segment feed rate profile with jerk continuity is constructed. Meanwhile, a Look-ahead planning based on Backward Scanning and Forward Revision (BSFR) algorithm is utilized to eliminate redundant computation. Compared with Zhao’s and Shi’s strategy, the proposed strategy has the merits of C2 and G2 continuity for the tool path, jerk continuity for the tool movement, and distinguished real-time performance for interpolation. The experiments of 3D pentagram and 2D butterfly are carried out with different strategies and their results demonstrate that the interpolation efficiency can be greatly improved with the proposed strategy. [ABSTRACT FROM AUTHOR]

Sparse spectral clustering (SSC) has become one of the most popular clustering approaches in recent years. However, its high computational complexity prevents its application to large-scale datasets such as hyperspectral images (HSIs). In this paper, we propose two efficient approximate sparse spectral clustering methods for HSIs clustering in which clustering performance is improved by utilizing local information among the data. Firstly, we construct a smaller representative dataset on which sparse spectral clustering is performed. Then the labels of ground object are extending to whole dataset based on the local information according to two extending strategies. The first one is that the local interpolation is utilized to improve the extension of the clustering result. The other one is that the label extension is turned to a problem of subspace embedding, and is fulfilled by locally linear embedding (LLE). Several experiments on HSIs demonstrated that the proposed algorithms are effective for HSIs clustering. [ABSTRACT FROM AUTHOR]

High efficiency video coding (HEVC) fractional interpolation algorithm has very high computational complexity. In this paper, two approximate HEVC fractional interpolation filters are proposed. They significantly reduce computational complexity of HEVC fractional interpolation with a negligible PSNR loss and bit rate increase. In addition, two approximate HEVC fractional interpolation hardware are proposed. They, in the worst case, can process 45 quad full HD (${3840\times 2160}$) fps. They consume up to 67.1% less energy than original HEVC fractional interpolation hardware. Therefore, they can be used in consumer electronics products that require a low energy HEVC encoder. [ABSTRACT FROM AUTHOR]

This paper is devoted to construct approximations of the probability density function of the non-autonomous first-order homogeneous linear random differential equation, where the initial condition and the diffusion coefficient are assumed to be a random variable and a stochastic process, respectively. We combine Random Variable Transformation technique and Karhunen–Loève expansion to construct reliable approximations under general conditions. Several numerical examples illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]

This paper is on numerical treatment of problems that describe high contrast composite materials with complex geometry. In particular, a heterogeneous domain decomposition method for a class of diffusion problems with rapidly oscillating coefficients that also have large variation of values within the domain is proposed. The method combines a FEM discretization in one subdomain with an asymptotic representation of the Dirichlet to Neumann map for the other subdomain. Numerical results that demonstrate the feasibility of the proposed approach are also provided. [ABSTRACT FROM AUTHOR]

The volume under a surface (VUS) is an effective measure for evaluating the discriminating power of a diagnostic test with three ordinal diagnostic groups. In this paper, we investigate the difference of two correlated VUS’s to compare two treatments for discrimination of three-class classification data. A jackknife empirical likelihood (JEL) procedure is employed to avoid the variance estimation in the existing methods. We prove that the limiting distribution of the empirical log-likelihood ratio statistic follows a χ2 distribution. Extensive numerical studies show that the JEL confidence intervals outperform those based on the normal approximation method. The proposed method is also applied to the Alzheimer’s disease data. [ABSTRACT FROM AUTHOR]

In this paper, a numerical procedure called multistage optimal homotopy asymptotic method (MOHAM) is introduced to solve multipantograph equations with time delay. It was shown that the MOHAM algorithm rapidly provides accurate convergent approximate solutions of the exact solution using only one term. A comparative study between the proposed method, the homotopy perturbation method (HPM) and the Taylor matrix method are presented. The obtained results revealed that the method is of higher accuracy, effective and easy to use. [ABSTRACT FROM AUTHOR]

A tensor T , in a given tensor space, is said to be h -identifiable if it admits a unique decomposition as a sum of h rank one tensors. A criterion for h -identifiability is called effective if it is satisfied in a dense, open subset of the set of rank h tensors. In this paper we give effective h -identifiability criteria for a large class of tensors. We then improve these criteria for some symmetric tensors. For instance, this allows us to give a complete set of effective identifiability criteria for ternary quintic polynomials. Finally, we implement our identifiability algorithms in Macaulay2. [ABSTRACT FROM AUTHOR]

The aim of this paper is a construction of parametric polynomial interpolants of a circular arc possessing maximal geometric smoothness. Two boundary points of a circular arc are interpolated together with higher order geometric data. Construction of interpolants is done via a complex factorization of the implicit unit circle equation. The problem is reduced to solving only one nonlinear equation determined by a monotone function and the existence of the solution is proven for any degree of the interpolating polynomial. Precise starting points for the Newton–Raphson type iteration methods are provided and the best solutions are then given in a closed form. Interpolation by parametric polynomials of degree up to six is discussed in detail and numerical examples confirming theoretical results are included. [ABSTRACT FROM AUTHOR]

This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which is applied when searching for the smoothing parameters of radial basis functions, is revisited. The main contribution of this paper is a smoothing algorithm that relies on a bootstrap-based radial basis function. The proposed method incorporates a k-nearest neighbour search and then projects the point set to the approximated thin-plate spline surface. Therefore, the denoising process is achieved, and the features are well preserved. A comparison of the proposed method with other smoothing methods is also carried out in this study. [ABSTRACT FROM AUTHOR]

Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. For generic domains, the generation of a sphere pack may be complex and time-consuming, especially if the pack must comply with a prescribed sphere size distribution and the stability requirements of the simulation. The primary goal of this paper is to present an efficient algorithm that is capable of producing packs with millions of spheres following a statistical sphere size distribution inside complex arbitrary domains. This algorithm uses a new strategy to ensure that the sphere size distribution is preserved even when large particles are rejected in the growing process. The paper also presents numerical results that enable an evaluation of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Various studies have emphasized the interesting advantages related to the use of new transition curves for improving the geometric design of highway horizontal alignments. In a previous paper, one of the writers proposed a polynomial curve, called a polynomial parametric curve (PPC), proving its efficiency in solving several design problems characterized by a very complex geometry (egg-shaped transition, transition between reversing circular curves, semidirect and inner-loop connections, and so on). The PPC also showed considerable advantages from a dynamic perspective, as evidenced by the analysis of the main dynamic variables related to motion (as well as rate of change of radial acceleration, steering speed, roll speed, and so on). In this paper, an optimization procedure using genetic algorithms (GAs) for selecting the different parameters of the PPC has been proposed. In particular, a specific algorithm defines the parameter values in order to minimize an appropriate fitness function. Besides, the final PPC can be examined from a dynamic point of view for evaluating the compliance with the comfort and safety conditions. Moreover, to simplify the geometric representation and the calculation of the dynamic variables of the PPC, using computer software, a specific and innovative routine has been specifically developed by the writers. [ABSTRACT FROM AUTHOR]

The paper presents a numerical procedure for solving a class of optimal control problems for heterogeneous systems. The latter are described by parameterized systems of ordinary differential equations, coupled by integrals along the parameter space. Such problems arise in economics, demography, epidemiology, management of biological resources, etc. The numerical procedure includes discretization and a gradient projection method for solving the resulting discrete problem. A main point of the paper is the performed error analysis, which is based on the property of metric regularity of the system of necessary optimality conditions associated with the considered problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose an a posteriori error estimator for the numerical approximation of a stochastic magnetostatic problem, whose solution depends on the spatial variable but also on a stochastic one. The spatial discretization is performed with finite elements and the stochastic one with a polynomial chaos expansion. As a consequence, the numerical error results from these two levels of discretization. In this paper, we propose an error estimator that takes into account these two sources of error, and which is evaluated from the residuals. [ABSTRACT FROM AUTHOR]

This paper reports a multiscale asymptotic analysis and computation for predicting heat transfer performance of periodic porous materials with radiation boundary condition. In these porous materials thermal radiation effect at micro-scale have an important impact on the macroscopic temperature field, which is our particular interest in this study. The multiscale asymptotic expansions for computing temperature field of the problem are constructed, and associated explicit convergence rates are obtained on some regularity hypothesis. Finally, the corresponding finite element algorithms based on the multiscale method are brought forward and some numerical results are given in details. The numerical tests indicate that the developed method is feasible and valid for predicting the heat transfer performance of periodic porous materials, and support the approximate convergence results proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the Natural transform decomposition method (NTDM) which has been constructed by combining Natural transform method (NTM) and Adomian decomposition method (ADM) has been proposed. This algorithm has been applied to obtain the approximate solutions for the modified Camassa-Holm equation (mCHE) and modified Degasperis-Procesi equation (mDPE). Then, two and three dimensional surfaces have been drawn by using Wolfram Mathematica 9. A table including numerical results between approximate solutions which are obtained by using NTDM in this paper and approximate solutions which have already founded by the help of using VIM by Jafari H. et al. with the same values of parameters has been formed for mCHE and mDPE. [ABSTRACT FROM AUTHOR]

The main approach for a Wi-Fi indoor positioning system is based on the received signal strength (RSS) measurements, and the fingerprinting method is utilized to determine the user position by matching the RSS values with the pre-surveyed RSS database. To build a RSS fingerprint database is essential for an RSS based indoor positioning system, and building such a RSS fingerprint database requires lots of time and effort. As the range of the indoor environment becomes larger, labor is increased. To provide better indoor positioning services and to reduce the labor required for the establishment of the positioning system at the same time, an indoor positioning system with an appropriate spatial interpolation method is needed. In addition, the advantage of the RSS approach is that the signal strength decays as the transmission distance increases, and this signal propagation characteristic is applied to an interpolated database with the Kriging algorithm in this paper. Using the distribution of reference points (RPs) at measured points, the signal propagation model of the Wi-Fi access point (AP) in the building can be built and expressed as a function. The function, as the spatial structure of the environment, can create the RSS database quickly in different indoor environments. Thus, in this paper, a Wi-Fi indoor positioning system based on the Kriging fingerprinting method is developed. As shown in the experiment results, with a 72.2% probability, the error of the extended RSS database with Kriging is less than 3 dBm compared to the surveyed RSS database. Importantly, the positioning error of the developed Wi-Fi indoor positioning system with Kriging is reduced by 17.9% in average than that without Kriging. [ABSTRACT FROM AUTHOR]