Abstract: The density estimates considered in this paper comprise
a base density and an adjustment component consisting of a linear
combination of orthogonal polynomials. It is shown that, in the
context of density approximation, the coefficients of the linear combination
can be determined either from a moment-matching technique
or a weighted least-squares approach. A kernel representation of
the corresponding density estimates is obtained. Additionally, two
refinements of the Kronmal-Tarter stopping criterion are proposed
for determining the degree of the polynomial adjustment. By way of
illustration, the density estimation methodology advocated herein is
applied to two data sets.
Abstract: In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.
Abstract: We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.
Abstract: The objective of the present research manuscript is to
perform parametric, nonparametric, and decision tree analysis to
evaluate two treatments that are being used for breast cancer patients.
Our study is based on utilizing real data which was initially used in
“Tamoxifen with or without breast irradiation in women of 50 years
of age or older with early breast cancer" [1], and the data is supplied
to us by N.A. Ibrahim “Decision tree for competing risks survival
probability in breast cancer study" [2]. We agree upon certain aspects
of our findings with the published results. However, in this
manuscript, we focus on relapse time of breast cancer patients instead
of survival time and parametric analysis instead of semi-parametric
decision tree analysis is applied to provide more precise
recommendations of effectiveness of the two treatments with respect
to reoccurrence of breast cancer.
Abstract: In the present paper, we present a modification of the
New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari
[J. Math. Anal. Appl. 2006;316:753–763] and use it for solving
systems of nonlinear functional equations. This modification yields
a series with faster convergence. Illustrative examples are presented
to demonstrate the method.
Abstract: A Finite Volume method based on Characteristic Fluxes for compressible fluids is developed. An explicit cell-centered resolution is adopted, where second and third order accuracy is provided by using two different MUSCL schemes with Minmod, Sweby or Superbee limiters for the hyperbolic part. Few different times integrator is used and be describe in this paper. Resolution is performed on a generic unstructured Cartesian grid, where solid boundaries are handled by a Cut-Cell method. Interfaces are explicitely advected in a non-diffusive way, ensuring local mass conservation. An improved cell cutting has been developed to handle boundaries of arbitrary geometrical complexity. Instead of using a polygon clipping algorithm, we use the Voxel traversal algorithm coupled with a local floodfill scanline to intersect 2D or 3D boundary surface meshes with the fixed Cartesian grid. Small cells stability problem near the boundaries is solved using a fully conservative merging method. Inflow and outflow conditions are also implemented in the model. The solver is validated on 2D academic test cases, such as the flow past a cylinder. The latter test cases are performed both in the frame of the body and in a fixed frame where the body is moving across the mesh. Adaptive Cartesian grid is provided by Paramesh without complex geometries for the moment.
Abstract: In this paper, we propose a solution to the motion
control problem of a 2-link revolute manipulator arm. We require the
end-effector of the arm to move safely to its designated target in a
priori known workspace cluttered with fixed circular obstacles of
arbitrary position and sizes. Firstly a unique velocity algorithm is
used to move the end-effector to its target. Secondly, for obstacle
avoidance a turning angle is designed, which when incorporated into
the control laws ensures that the entire robot arm avoids any number
of fixed obstacles along its path enroute the target. The control laws
proposed in this paper also ensure that the equilibrium point of the
system is asymptotically stable. Computer simulations of the
proposed technique are presented.
Abstract: Intuitionistic fuzzy sets as proposed by Atanassov,
have gained much attention from past and latter researchers for
applications in various fields. Similarity measures between
intuitionistic fuzzy sets were developed afterwards. However, it does
not cater the conflicting behavior of each element evaluated. We
therefore made some modification to the similarity measure of IFS
by considering conflicting concept to the model. In this paper, we
concentrate on Zhang and Fu-s similarity measures for IFSs and
some examples are given to validate these similarity measures. A
simple modification to Zhang and Fu-s similarity measures of IFSs
was proposed to find the best result according to the use of degree of
indeterminacy. Finally, we mark up with the application to real
decision making problems.
Abstract: In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations
Abstract: Most real world systems express themselves formally
as a set of nonlinear algebraic equations. As applications grow, the
size and complexity of these equations also increase. In this work, we
highlight the key concepts in using the homotopy analysis method
as a methodology used to construct efficient iteration formulas for
nonlinear equations solving. The proposed method is experimentally
characterized according to a set of determined parameters which
affect the systems. The experimental results show the potential and
limitations of the new method and imply directions for future work.
Abstract: In this paper, a class of predator-prey-chain model with harvesting terms are studied. By using Mawhin-s continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient conditions are established for the existence of eight positive periodic solutions. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.
Abstract: According to conjugate gradient algorithm, a new consensus protocol algorithm of discrete-time multi-agent systems is presented, which can achieve finite-time consensus. Finally, a numerical example is given to illustrate our theoretical result.
Abstract: The notions of intuitionistic fuzzy h-ideal and normal
intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some
of the basic properties of these ideals are investigated. Cartesian
product of intuitionistic fuzzy h-ideals is also defined. Finally a
characterization of intuitionistic fuzzy h-ideals in terms of fuzzy
relations is obtained.
Abstract: A new class of percolation model in complex networks,
in which nodes are characterized by hidden variables reflecting the
properties of nodes and the occupied probability of each link is
determined by the hidden variables of the end nodes, is studied
in this paper. By the mean field theory, the analytical expressions
for the phase of percolation transition is deduced. It is determined
by the distribution of the hidden variables for the nodes and the
occupied probability between pairs of them. Moreover, the analytical
expressions obtained are checked by means of numerical simulations
on a particular model. Besides, the general model can be applied
to describe and control practical diffusion models, such as disease
diffusion model, scientists cooperation networks, and so on.
Abstract: In this paper, a tri–neuron network model with time
delay is investigated. By using the Bendixson-s criterion for high–
dimensional ordinary differential equations and global Hopf bifurcation
theory for functional differential equations, sufficient conditions
for existence of periodic solutions when the time delay is sufficiently
large are established.
Abstract: We propose a novel prioritized limited
processor-sharing (PS) rule and a simulation algorithm for the performance evaluation of this rule. The performance measures of practical interest are evaluated using this algorithm. Suppose that there
are two classes and that an arriving (class-1 or class-2) request encounters n1 class-1 and n2 class-2 requests (including the arriving
one) in a single-server system. According to the proposed rule, class-1
requests individually and simultaneously receive m / (m * n1+ n2) of the service-facility capacity, whereas class-2 requests receive 1 / (m *n1 + n2) of it, if m * n1 + n2 ≤ C. Otherwise (m * n1 + n2 > C), the arriving request will be queued in the corresponding class waiting
room or rejected. Here, m (1) denotes the priority ratio, and C ( ∞), the service-facility capacity. In this rule, when a request arrives at [or
departs from] the system, the extension [shortening] of the remaining
sojourn time of each request receiving service can be calculated using
the number of requests of each class and the priority ratio. Employing
a simulation program to execute these events and calculations enables
us to analyze the performance of the proposed prioritized limited PS
rule, which is realistic in a time-sharing system (TSS) with a
sufficiently small time slot. Moreover, this simulation algorithm is
expanded for the evaluation of the prioritized limited PS system with
N 3 priority classes.
Abstract: In this paper, we present two new one-step iterative
methods based on Thiele-s continued fraction for solving nonlinear
equations. By applying the truncated Thiele-s continued fraction
twice, the iterative methods are obtained respectively. Analysis of
convergence shows that the new methods are fourth-order convergent.
Numerical tests verifying the theory are given and based on the
methods, two new one-step iterations are developed.
Abstract: A number of mass spectrometry applications are already available as web-based and windows-based systems to calculate isotope pattern and to display the mass spectrum based on the specific molecular formula besides providing necessary information. These applications were evaluated and compared with our new alternative application called Theoretical Isotope Generator (TIG) in terms of its functionality and features provided to prove this new application is working better and performing well. TIG provides extra features than others, complete with several functionality such as drawing, normalizing and zooming the generated graph that convey with the molecular information in a number of formats by providing the details of the calculation and molecules. Thus, any chemist, students, lecturers and researchers from anywhere could use TIG to gain related information on molecules and their relative intensity.
Abstract: The paper presents an applied study of a multivariate AR(p) process fitted to daily data from U.S. commodity futures markets with the use of Bayesian statistics. In the first part a detailed description of the methods used is given. In the second part two BVAR models are chosen one with assumption of lognormal, the second with normal distribution of prices conditioned on the parameters. For a comparison two simple benchmark models are chosen that are commonly used in todays Financial Mathematics. The article compares the quality of predictions of all the models, tries to find an adequate rate of forgetting of information and questions the validity of Efficient Market Hypothesis in the semi-strong form.
Abstract: In reality, the process observations are away from the assumption that are normal distributed. The observations could be skew distributions which should use an asymmetric chart rather than symmetric chart. Consequently, this research aim to study the robustness of the asymmetric Tukey’s control chart for skew and non-skew distributions as Lognormal and Laplace distributions. Furthermore, the performances in detecting of a change in parameter of asymmetric and symmetric Tukey’s control charts are compared by Average ARL (AARL). The results found that the asymmetric performs better than symmetric Tukey’s control chart for both cases of skew and non-skew process observation.