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We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of [ABSTRACT FROM AUTHOR]

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]

The problem of biasness and availability of auxiliary variable for the estimating population mean is a big concern, both can be handled by proposing unbiased estimators in the absence of auxiliary variable. So in this paper unbiased exponential type estimators of population mean have been proposed. The estimators are proposed in the absence of the instrumental variable called the auxiliary variable by taking the advantage of the population and the sample median of the study variable. To about the first order approximation, the theoretical formulations of the bias and mean square error (MSE) are obtained. The circumstances in which the suggested estimators have the lowest mean squared error values when compared to the existing estimators were also deduced. In comparison to the currently used estimators, it was discovered that the suggested estimators of population mean had the lowest MSE, hence highest efficiency. Also least influence from the data's influential observations when it came to accurately calculating the population mean for skewed data. The theoretical findings of the paper are validated by the numerical study. [ABSTRACT FROM AUTHOR]

In this paper, a highly accurate method is introduced to achieve the numerical solution of the advection diffusion equation (ADE). This approach contains collocation technique based on nonic B-spline functions in the spatial-domain discretization and Adams Moulton scheme in the temporal-domain discretization. Two test problems are studied to validate effectiveness of the new presented method and efficiency of the approximate results are tested by calculating rate of temporal-convergence and error norm L8 for the suggested method. The obtained numerical results are compared in the tables by the other available studies in literature and it is observed that a better approximate solution is provided than the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, some properties of linear functionals are studied, which are used in functional analysis, optimization theory, numerical analysis, approximation theory, various applications, etc. [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]

The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H2O and N2. As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found to exist between the correlation energy contributions from various excitation levels of the configuration-interaction approach, considered as functions of the size of the correlating orbital space. The method for extrapolating a sequence of smaller configuration-interaction calculations to the full configuration-interaction energy and for constructing compact accurate configuration-interaction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as many-body perturbation theory, coupled-cluster theory, as well as with variational calculations wherever possible. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

From the eigenvalue problem theory, we see that the convergence rate of the biharmonic eigenvalues obtained by the mixed method in I. Bab u ˇ ska and J. Osborn, [Eigenvalue Problems, Handbook of Numerical Analysis, Vol. II, North-Holland, Amsterdam, 1991.] is h 2 k − 2 for k ≥ 2. In this paper, we give a presentation of the lowest-order virtual element method for the approximation of Kirchhoff plate vibration problem. This discrete scheme is based on a conforming H 1 (Ω) × H 1 (Ω) formulation, following the variational formulation of Ciarlet–Raviart method, which allows us to make use of simpler and lower-regularity virtual element space. By using the classical spectral approximation theory in functional analysis, we prove the spectral approximation and optimal convergence order h 2 for the eigenvalues. Finally, some numerical experiments are presented, which show that the proposed numerical scheme can achieve the optimal convergence order. [ABSTRACT FROM AUTHOR]

This paper is the first application of the tensor-train (TT) cross approximation procedure for potential energy surface fitting. In order to reduce the complexity, we combine the TT-approach with another technique recently introduced in the field of numerical analysis: an affine transformation of Cartesian coordinates into the active subspaces where the PES function has the most variability. The numerical experiments for the water molecule and for the nitrous acid molecule confirm the efficiency of this approach. [ABSTRACT FROM AUTHOR]

This paper is devoted to particle transport in a tube formed by alternating wide and narrow sections, in the presence of an external biasing force. The focus is on the effective transport coefficients--mobility and diffusivity, as functions of the biasing force and the geometric parameters of the tube. Dependences of the effective mobility and diffusivity on the tube geometric parameters are known in the limiting cases of no bias and strong bias. The approximations used to obtain these results are inapplicable at intermediate values of the biasing force. To bridge the two limits Brownian dynamics simulations were run to determine the transport coefficients at intermediate values of the force. The simulations were performed for a representative set of tube geometries over a wide range of the biasing force. They revealed that there is a range of the narrow section length, where the force dependence of the mobility has a maximum. In contrast, the diffusivity is a monotonically increasing function of the force. A simple formula is proposed, which reduces to the known dependences of the diffusivity on the tube geometric parameters in both limits of zero and strong bias. At intermediate values of the biasing force, the formula catches the diffusivity dependence on the narrow section length, if the radius of these sections is not too small. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of the calendering mechanism. The calendered material is represented using the Carreau-Yasuda fluid model. The governing flow equations in the calendering process are made first dimensionless then the lubrication approximation theory (LAT) is used to simplify them. The simplified flow equations are transformed into stream function and then are numerically solved. A numerical method is constructed with Matlab's built-in-bvp4c routine to find the stream function and pressure gradient. We use the Runge-Kutta algorithm to calculate the pressure and mechanical quantities related to the calendering process. In this analysis the pressure distribution increases with increasing Weissenberg number, however the pressure domain length decreases as the Weissenberg number increases. The pressure inside the nip region decreases from its Newtonian value when the power law index is less than one (shear thinning), and the pressure profile increases from its Newtonian pressure when the power law index is greater than one(shear thickening). How the Carreau-Yasuda fluid model parameters influence the velocity and related calendering process quantities are also discussed via graphs. [ABSTRACT FROM AUTHOR]

In this paper, univariate Padé approximation is applied to fractional power series solutions of fractional quadratic Riccati differential equation.. As it is seen from the tables, univariate Padé approximation gives reliable solutions and numerical results. [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]

Stochastic variational inequalities (SVI) provide a unified framework for the study of a general class of nonlinear optimization and Nash-type equilibrium problems with uncertain model data. Often the true solution to an SVI cannot be found directly and must be approximated. This paper considers the use of a sample average approximation (SAA), and proposes a new method to compute confidence intervals for individual components of the true SVI solution based on the asymptotic distribution of SAA solutions. We estimate the asymptotic distribution based on one SAA solution instead of generating multiple SAA solutions, and can handle inequality constraints without requiring the strict complementarity condition in the standard nonlinear programming setting. The method in this paper uses the confidence regions to guide the selection of a single piece of a piecewise linear function that governs the asymptotic distribution of SAA solutions, and does not rely on convergence rates of the SAA solutions in probability. It also provides options to control the computation procedure and investigate effects of certain key estimates on the intervals. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the numerical solution of certain matrix-valued PDEs. Such PDEs arise, for example, when constructing a Riemannian contraction metric for a dynamical system given by an autonomous ODE. We develop and analyze a new meshfree discretization scheme using kernel-based approximation spaces. However, since these approximation spaces have now to be matrix-valued, the kernels we need to use are fourth-order tensors. We will review and extend recent results on even more general reproducing kernel Hilbert spaces. We will then apply this general theory to solve a matrix-valued PDE and derive error estimates for the approximate solution. The paper ends with applications to typical examples from dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper we consider the two-dimensional nonlocal phase-field and hyperbolic nonlocal phase-field models to obtain their numerical solutions. For this purpose, we propose a localized method based on radial basis functions (RBFs), namely localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for spatial discretization. The basic idea of the LRBF-PSM is to construct a set of orthogonal functions by RBFs on each overlapping sub-domain from which the global solution can be obtained by extending the approximation on each sub-domain to the entire domain. This approach does not require meshing in spatial domain and hence inherits the meshless and spectral convergence properties of the global radial basis functions collocation method (GRBFCM). Some numerical results indicate that the obtained simulations via the LRBF-PSM is effective and stable for approximating the solution of nonlocal models investigated in the current paper. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach to integrate optimal control of perimeter intersections (i.e. to minimize local delay) into the perimeter control scheme (i.e. to optimize traffic performance at the network level). This is a complex control problem rarely explored in the literature. In particular, modeling the interaction between the network level control and the local level control has not been fully considered. Utilizing the Macroscopic Fundamental Diagram (MFD) as the traffic performance indicator, we formulate a dynamic system model, and design a Model Predictive Control (MPC) based controller coupling two competing control objectives and optimizing the performance at the local and the network level as a whole. To solve this highly non-linear optimization problem, we employ an approximation framework, enabling the optimal solution of this large-scale problem to be feasible and efficient. Numerical analysis shows that by applying the proposed controller, the protected network can operate around the desired state as expressed by the MFD, while the total delay at the perimeter is minimized as well. Moreover, the paper sheds light on the robustness of the proposed controller. This multi-scale hybrid controller is further extended to a stochastic MPC scheme, where connected vehicles (CV) serve as the only data source. Hence, low penetration rates of CVs lead to strong noises in the controller. This is a first attempt to develop a network-level traffic control methodology by using the emerging CV technology. We consider the stochasticity in traffic state estimation and the shape of the MFD. Simulation analysis demonstrates the robustness of the proposed stochastic controller, showing that efficient controllers can indeed be designed with this newly-spread vehicle technology even in the absence of other data collection schemes (e.g. loop detectors). [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]

This paper deals with variational inclusions of the form 0∈K−f(x) where f:Rn→Rm is a semismooth function and K is a nonempty closed convex cone in Rm. We show that the previous problem can be solved by a Newton-type method using the Clarke generalized Jacobian of f. The results obtained in this paper extend those obtained by Robinson in the famous paper (Robinson in Numer. Math. 19:341-347, 1972). We provide a semilocal method with a superlinear convergence that is new in the context of semismooth functions. Finally, numerical results are also given to illustrate the convergence. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new modelling approach for the dynamic granular matter formation process in the form of a system of difference equations, directly tailored to the physical nature of the process at hand. Respectively, the dynamic 1D and 2D discrete models, proposed in this paper, are not constructed as numerical schemes approximating some partial differential equations (PDEs).We propose here to look for the functions describing the standing and the rolling layers of the granular matter as the limits of discrete solutions to the aforementioned model equations as the size of the mesh tends to zero. In particular, this approach allows us to differentiate between the influx of the rolling layer coming down from different directions to the corner points of the standing layer. Such points are difficult to adequately describe by means of PDEs and their straightforward numerical approximations, typically 'ignoring' the system's behaviour on the sets of zero measure. However, these points are critical for understanding the dynamics of formation process when the standing layer is created by the moving front of the rolling matter or when the latter is filling a cavity and/or stops rolling. The existence of distributed (infinite-dimensional) limit solutions to our discrete models as the size of the mesh tends to zero is also discussed. We illustrate our findings by numerical examples which use our models as the direct algorithm. [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]

The frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining 'on the fly' quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman-Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to 'on the fly' computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable 'on the fly'; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential. [ABSTRACT FROM AUTHOR]

Trotter's theorem forms the theoretical basis of most modern molecular dynamics. In essence this theorem states that a time displacement operator (a Lie operator) constructed by exponentiating a sum of noncommuting operators can be approximated by a product of single operators provided the time interval is 'very small.' In theory 'very small' implies infinitesimally small (at which point the approximate product becomes exact), while in practical analysis a finite time interval is divided into several small subintervals or steps. It follows, therefore, that the larger the number of steps the better the approximation to the exact time displacement operator. The question therefore arises: How many steps are sufficient? For bounded operators, standard theorems are available to provide the answer. In this paper we show that a very simple combinatorial formula can be derived which allows the computation of the global differences (as a function of the number of steps) between the Taylor coefficients of the exact time displacement operator and an approximate one constructed by using a finite number of steps. The formula holds for both bounded and nonbounded operators and shows, quantitatively, what is qualitatively expected-that the error decreases with increasing number of steps. Furthermore, the formula applies irrespective of the complexity of the system, boundary conditions, or the thermodynamic ensemble employed for averaging the initial conditions. The analysis yields explicit expressions for the Taylor coefficients which are then used to compute the errors. In the case of the algorithmically based practical numerical simulations in which fixed, albeit small, steps are repeatedly applied, the rise in the number of steps does not reduce the size of the steps but increases the total time of interest. The combinatorial formula shows that, here, the errors diverge. Furthermore, this work can be used to supplement other efforts such as the use of shadow Hamiltonians where the truncation of the series expansion of the latter will produce errors in the higher order propagator moments. [ABSTRACT FROM AUTHOR]

The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes 'significantly' during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical examples to demonstrate the effectiveness of our new method. [ABSTRACT FROM AUTHOR]

Tau leaping methods enable efficient simulation of discrete stochastic chemical systems. Stiff stochastic systems are particularly challenging since implicit methods, which are good for stiffness, result in noninteger states. The occurrence of negative states is also a common problem in tau leaping. In this paper, we introduce the implicit Minkowski-Weyl tau (IMW-τ) methods. Two updating schemes of the IMW-τ methods are presented: implicit Minkowski-Weyl sequential (IMW-S) and implicit Minkowski-Weyl parallel (IMW-P). The main desirable feature of these methods is that they are designed for stiff stochastic systems with molecular copy numbers ranging from small to large and that they produce integer states without rounding. This is accomplished by the use of a split step where the first part is implicit and computes the mean update while the second part is explicit and generates a random update with the mean computed in the first part. We illustrate the IMW-S and IMW-P methods by some numerical examples, and compare them with existing tau methods. For most cases, the IMW-S and IMW-P methods perform favorably. [ABSTRACT FROM AUTHOR]

An analytical energy gradient formula for the density-matrix-based linear-scaling divide-and-conquer (DC) self-consistent field (SCF) method was proposed in a previous paper by Yang and Lee (YL) [J. Chem. Phys. 103, 5674 (1995)]. Since the formula by YL does not correspond to the exact gradient of the DC-SCF energy, we derive the exact formula by direct differentiation, which requires solving the coupled-perturbed equations while including the inter-subsystem coupling terms. Next, we present an alternative formula for approximately evaluating the DC-SCF energy gradient, assuming the variational condition for the subsystem density matrices. Numerical assessments confirmed that the DC-SCF energy gradient values obtained by the present formula are in reasonable agreement with the conventional SCF values when adopting a reliable buffer region. Furthermore, the performance of the present method was found to be better than that of the YL method. [ABSTRACT FROM AUTHOR]

A method for constructing diabatic potential-energy matrices from ab initio quantum chemistry data is described and tested for use in exact quantum reactive scattering. The method is a refinement of that presented in a previous paper, in that it accounts for the presence of the nonremovable derivative coupling. The accuracy of quantum dynamics on this type of diabatic potential is tested by comparison with an analytic model and for an ab initio description of the two lowest-energy states of H3. [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 fractional version of the logistic equation will be studied in this paper. Motivated by unsuccessful previous papers, we showed how to obtain the correct solution. The algorithm is very simple. Its numerical implementation will be studied and exemplified using a Padé approximation. [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]

In this paper, we introduce and study a new viscosity approximation method based on the conjugate gradient method and an averaged mapping approach for finding a common element of the set of solutions of a constrained convex minimization problem and the set of solutions of a split variational inclusion problem. Under suitable conditions, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of the split variational inclusion problem and the set of solutions of the constrained convex minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area. Finally, preliminary numerical results indicate the feasibility and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to prove that the implicit numerical approximation can converge to the true solution to highly nonlinear hybrid stochastic pantograph differential equation. After providing the boundedness of the exact solution, the paper proves that the backward Euler–Maruyama numerical method can preserve boundedness of moments, and the numerical approximation converges strongly to the true solution. Finally, the exponential stability criterion on the backward Euler–Maruyama scheme is given, and a high order example is provided to illustrate the main result. [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]

In this paper, we investigate several modified exponential finite-difference methods to approximate the solution of the one-dimensional viscous Burgers' equation. Burgers' equation admits solutions that are positive and bounded under appropriate conditions. Motivated by these facts, we propose nonsingular exponential methods that are capable of preserving some structural properties of the solutions of Burgers' equation. The fact that some of the techniques preserve structural properties of the solutions is thoroughly established in this work. Rigorous analyses of consistency, stability and numerical convergence of these schemes are presented for the first time in the literature, together with estimates of the numerical solutions. The methods are computationally improved for efficiency using the Padé approximation technique. As a result, the computational cost is substantially reduced in this way. Comparisons of the numerical approximations against the exact solutions of some initial-boundary-value problems for different Reynolds numbers show a good agreement between them. [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]

In this paper, we consider the problem of estimating the scale parameter of the inverse Rayleigh distribution based on general progressively Type-II censored samples and progressively Type-II censored samples. The pivotal quantity method is used to derive the estimator of the scale parameter. Besides, considering that the maximum likelihood estimator is tough to obtain for this distribution, we derive an explicit estimator of the scale parameter by approximating the likelihood equation with Taylor expansion. The interval estimation is also studied based on pivotal inference. Then we conduct Monte Carlo simulations and compare the performance of different estimators. We demonstrate that the pivotal inference is simpler and more effective. The further application of the pivotal quantity method is also discussed theoretically. Finally, two real data sets are analyzed using our methods. [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]

In this paper we study the uniform approximation of functions by a generalization of the Picard and Gauss-Weierstrass operators of max-product type in exponential weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity. We extend and improve previous results. [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]

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]

In this paper, through appropriate rational approximation, we prove that a function f in , with particular interest in the index range can be decomposed into a sum in the sense of , where is a half strip domain in the complex plane, g and h are the non-tangential limits of functions in and , respectively. For the case we show that a rational function in can be decomposed into a sum of rational functions in and . [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]

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]

Abstract Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge dimension. Little is known, however, about the asymptotic behavior of ensemble methods. In this paper, we prove convergence in L p of ensemble Kalman smoother to the Kalman smoother in the large-ensemble limit, as well as the convergence of EnKS-4DVAR, which is a Levenberg–Marquardt-like algorithm with EnKS as the linear solver, to the classical Levenberg–Marquardt algorithm in which the linearized problem is solved exactly. [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 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]

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]