Search

In this paper we present a new numerical method for solving fractional differential equations (FDEs) based on Genocchi polynomials operational matrix through collocation method. The operational matrix of fractional integration in Riemann-Liouville sense is derived. The upper bound for the error of the operational matrix of fractional integration is also shown. The properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. Illustrative examples are finally given to show the simplicity, accuracy and applicability of the method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct multiple interpolation functions of (h,q)-Bernoulli numbers and polynomials of higher order. Furthermore, we give alternating sums of powers of consecutive (h,q)-integers. By using p-adic q-Volkenborn integral, we obtain distribution relations of the (h,q)-Bernoulli polynomials of higher order. [ABSTRACT FROM AUTHOR]

This study on the mental solving of systems of linear equations is part of a larger research program, aimed to gain a better understanding of the potential of mental mathematics activities with topics/objects other than numbers. Through outlining the study details and the activities engaged with, the paper reports on the variety of strategies developed for mentally solving systems of linear equations. The analysis pays attention to specificities and particularities of these strategies, focusing on their economical, tailored, and spontaneous nature to solve the tasks. In reflecting on the context of mental mathematics, the paper closes with discussions of the potential and richness of these strategies for exploring systems of linear equations. [ABSTRACT FROM AUTHOR]

The paper describes an extension of the well-known Convective Boundedness Criterion (CBC). It is shown that the newly proposed criterion is a combination of the CBC and the extended convective boundedness criterion (ECBC), as shown in Fig.1. A new scheme (NECBC1) based on the new criterion is designed and tested by two problems: (1) convection of a stepwise profile in an oblique uniform velocity field and (2) convection of an elliptical profile in a stagnation point flow. The numerical tests show the effectiveness of the new criterion and reveal the limitation of the CBC and the ECBC. Moreover, some numerical experiments of some specially-designed schemes and two TVD-Type schemes: the van Albada scheme and Miroslav Cˇada & Manuel Torrilhon’s new third-order scheme, are carried out. Through these numerical experiments, some extra constraints for the new criterion are observed and in the meantime some other possible regions in the normalized diagram (NV) for high-resolution schemes reveal themselves. [ABSTRACT FROM AUTHOR]

This paper presents a new simulated annealing algorithm to solve constrained multi-global optimization problems. To compute all global solutions in a sequential manner, we combine the function stretching technique with the adaptive simulated annealing variant. Constraint-handling is carried out through a nondifferentiable penalty function. To benchmark our penalty stretched simulated annealing algorithm we solve a set of well-known problems. Our preliminary numerical results show that the algorithm is promising. [ABSTRACT FROM AUTHOR]

The notion of stiffness, which originated in several applications of different nature, has dominated the activities related to the numerical treatment of differential problems in the last fifty years. Its definition has been, for a long time, not formally precise. The needs of applications, especially those rising in the construction of robust and general purpose codes, require nowadays a formally precise definition. In this paper, we review the evolution of such notion and we provide also with a precise definition that could be used practically. [ABSTRACT FROM AUTHOR]

To improve the Quality of Service (QoS) ability of TNPOSS (To Next-hop Port Sequence Switch) network, this paper proposes a QoS-enhanced TNPOSS (QTNPOSS) network model by introducing Fractal Leak Bucket (FLB) shaper and Weighted Fair Queuing (WFQ) scheduler. In the proposed model, packets of multimedia traffic are shaped by the FLB shaper and scheduled by the WFQ scheduler. Moreover, the service curve and the Maximum E2E delay of QTNPOSS network are given by using the mathematical tool of the network calculus. Numerical analysis shows that both the long-range dependence (LRD) property of multimedia traffic and the WFQ weight have influences on the maximum E2E delay, and the WFQ weight influences the maximum E2E delay more greatly than the LRD property does. [ABSTRACT FROM AUTHOR]

The purpose of this paper is a discussion of a numerical procedure based on the simplex method for stochastic optimization problems with partially known distribution functions. The convergence of this procedure is proved by the condition on dual problems. [ABSTRACT FROM AUTHOR]

We construct a discrete fundamental solution for the parabolic Dirac operator which factorizes the non-stationary Schrödinger operator. With such fundamental solution we construct a discrete counterpart for the Teodorescu and Cauchy-Bitsadze operators and the Bergman projectors. We finalize this paper with convergence results regarding the operators and a concrete numerical example. [ABSTRACT FROM AUTHOR]

The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are known for a particular family of doubly connected regions and a particular triply connected region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded multiply connected regions with smooth boundaries. The method depends on the values of S (z(t), a), S'(z(t), a) and θ'(t), where θ(t) is the boundary correspondence function of Ahlfors map. A formula is derived for computing S'(z(t), a). An integral equation for θ'(t) is used for finding the zeros of Ahlfors map. The numerical examples presented here demonstrate the method. [ABSTRACT FROM AUTHOR]

In this paper we describe a study involving middle school mathematics teachers who are participating in a large-scale professional development program designed to improve their conceptual understanding of mathematics. The design and implementation of this study were guided by the research question: In what ways do teachers reason through tasks designed to elicit proportional reasoning? Our analysis of the data was conducted through the lens of quantitative reasoning as described by Thompson. We highlight the issues that arose when some teachers performed numerical operations on values that they did not clearly connect to quantities. [ABSTRACT FROM AUTHOR]

To solve PDE problems with different time scales that are localized in space, multirate time integration is examined. This technique enables one to use large time steps for slowly time-varying spatial regions, and small steps for rapidly varying ones. Multirate time stepping is coupled with the local uniform grid refinement and provides a robust and efficient method for the target problem class. We primarily consider implicit time stepping methods, suitable for parabolic problems. Numerical results are presented for a test problem. [ABSTRACT FROM AUTHOR]

This short paper is concerned with a new algorithm for collision and distance calculation between CSG octrees, a generalization of an octree model created from a Constructive Solid Geometry (CSG) object. The data structure uses interval arithmetic and allows us to extend the tests for classifying points in space as inside, on the boundary, or outside a CSG object to entire sections of the space at once. Tree nodes with additional information about relevant parts of the CSG object are introduced in order to reduce the depth of the required subdivision. The new data structure reduces the input complexity and enables us to reconstruct the CSG object. We present an efficient algorithm for computing the distance between CSG objects encoded by the new data structure. The distance algorithm is based on a distance algorithm for classical octrees but, additionally, it utilizes an elaborated sort sequence and differentiated handling of pairs of octree nodes to enhance its efficiency. Experimental results indicate that, in comparison to common octrees, the new representation has advantages in the field of proximity query. [ABSTRACT FROM AUTHOR]

This paper gives a graphical representation of a subclass of complex filiform Leibniz algebras. This class is split into three subclasses called first, second and third class denoted, in dimension n over a field of complex numbersℂ, by FLbn(ℂ), SLbn(ℂ) and TLbn(ℂ), respectively. Here, the combinatorial structures associated with FLbn(ℂ), and SLbn(ℂ), in low dimensions are considered and some structural properties of the combinatorial structures are given. [ABSTRACT FROM AUTHOR]

This article reports on the solutions of the time-fractional diffusion equation. It discusses the numerical analysis of the time-fractional diffusion equation by using the time fractional derivative in the Caputo sense of order. It provides the equation for the Wright function with the series that appears within the solution of the time-fractional diffusion equation.

The fluctuationlessness approximation gives powerful and easily utilizable solutions for a lot of applications of numerical analysis. For example, it helps us to create univariate numerical integration schemes which converge very rapidly. On the other hand, the space extension approaches aim to convert equations into some other structures which can be handled more easily. It is possible to apply this approach to the solutions obtained with fluctuationlessness approximation in order to improve the quality of approximation. [ABSTRACT FROM AUTHOR]

Information about several papers discussed at a symposium on properties preserving numerical schemes for differential equations by the Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa is presented. Topics include the design, analysis, and implementation of numerical methods. Also presented the mathematical epidemiology and the non-standard finite difference method.

The QuadCover algorithm is a well received and flexible algorithm for surface parameterization. For demonstrating QuadCover, we originally used principal curvature lines to guide the parameterization. The current work focuses on fine-tuning the vector fields used in QuadCover to yield state-of-the-art surface parameterizations. We propose new techniques for generating smooth frame fields in non-descriptive regions, branch point movement and frame field scaling with regard to optimal parameterization results. [ABSTRACT FROM AUTHOR]

It is shown that Kundt’s metric for vacuum cannot be constructed when two-dimensional space-like sections of null hypersurfaces are compact, connected manifolds with no boundary unless they are tori or spheres, i.e. higher genus g>=2 is excluded by vacuum Einstein equations. The so-called basic equation (resulting from Einstein equations) is examined. This is a non-linear PDE for unknown covector field and unknown Riemannian structure on the two-dimensional manifold. It implies several important results derived in [3]. It arises not only for Kundt’s class but also for degenerate Killing horizons [2] and vacuum degenerate isolated horizons [1, 7]. [ABSTRACT FROM AUTHOR]

We obtain explicit formulas for ellipsoids bounding reachable sets for linear dynamic systems with geometric bounds on control. We study both locally and globally optimal ellipsoidal estimates with regard to different optimality criteria. In particular, we solve some essentially nonlinear boundary problems related to the search for globally optimal ellipsoids with regard to the volume criterion. It is shown that by using the explicit formulas one can efficiently pass to limits in several asymptotic problems, including passing to the limit when the phase space dimension goes to infinity. [ABSTRACT FROM AUTHOR]

We develop a Galerkin spectral technique for computing localized solutions of equations with higher order dispersion. To this end, the complete orthonormal system of functions in L2(-∞,∞) proposed by Christov [1] is used. As a featuring example, the Sixth-Order Generalized Boussinesq Equation (6GBE) is investigated whose solutions comprise monotone shapes (sech-es) and damped oscillatory shapes (Kawahara solitons). Localized solutions are obtained here numerically for the case of the moving frame which are used as initial conditions for the time dependent problem. [ABSTRACT FROM AUTHOR]

A new type of orbit in the restricted three-body problem is constructed. It is analytically shown that along with the well known chaotic and regular orbits in the three-body problem there also exists a qualitatively different type of orbit which we call “stabilized.” The stabilized orbits are a result of additional orbiting bodies that are placed in the triangular Lagrange points. The results are well confirmed by numerical orbit calculations. [ABSTRACT FROM AUTHOR]

A strategy for developing useful applications on dual-core systems with OpenMP is presented. An application is created by the different two types of methods which are used for achieving a same objective. An application for reconstructing surfaces from 3D scattered point data has been created by using both the Multi-level Partition of Unity implicits (MPU) method and the Delaunay triangulation method. Numerical examples of the application have illustrated that although the CPU time of the application is larger than that of the individual method, the application has both the robustness of the MPU method and the speed performance of the Delaunay triangulation method. [ABSTRACT FROM AUTHOR]

This study examines students' approaches to infinity, before and after instruction, via their engagement with a well-known paradox: the ping-pong ball conundrum. Students' work reveals they perceive infinity as an ongoing process, rather than a completed one, and fail to notice conflicting ideas. We further focus on specific challenging features of this paradox versus other counterintuitive infinity problems. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]

A non-Newtonian, non-isothermal flow analysis including acceleration effects has been developed to simulate the polymer flow in two-dimensional, axisymmetric geometries. The governing mass and momentum equations are solved by a mixed finite element method, in which the velocity components and temperature are interpolated by quadratic functions, and the pressure is interpolated by a linear function. Modeling of the changing feed system geometry is implemented by dynamic meshing. The described analysis is applied to the design and control of a flow regulator. The results describe the behavior of non-steady, viscous flows and are useful for machine design. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]