-
On the Log-Concavity of the Root of the Catalan-Larcombe-French Numbers
Issue:
Volume 2, Issue 4, November 2017
Pages:
95-98
Received:
29 October 2016
Accepted:
31 March 2017
Published:
17 April 2017
DOI:
10.11648/j.ajmcm.20170204.11
Downloads:
Views:
Abstract: Recently, some combinatorial properties for the the Catalan-Larcombe-French numbers have been proved by Sun and Wu, and Zhao. Recently, Z. W. Sun conjectured that the root of the Catalan-Larcombe-French numbers is log-concave. In this paper, we confirm Sun's conjecture by establishing the lower and upper bound for the ratios of the Catalan-Larcombe-French numbers.
Abstract: Recently, some combinatorial properties for the the Catalan-Larcombe-French numbers have been proved by Sun and Wu, and Zhao. Recently, Z. W. Sun conjectured that the root of the Catalan-Larcombe-French numbers is log-concave. In this paper, we confirm Sun's conjecture by establishing the lower and upper bound for the ratios of the Catalan-Larcombe...
Show More
-
On a Construction of the Optimal Trajectories by Applying the Equilibrium Mechanisms in the Discrete Dynamical Models
Issue:
Volume 2, Issue 4, November 2017
Pages:
99-102
Received:
14 March 2017
Accepted:
6 May 2017
Published:
13 July 2017
DOI:
10.11648/j.ajmcm.20170204.12
Downloads:
Views:
Abstract: The model of economic dynamics, consisting of two units that produce, respectively, means of production and objects of commodities. It is assumed that the trajectory of еру model with a fixed budget admits characteristics and has an equilibrium state. These conditions allow us to construct effective trajectories of the model with the help of the equilibrium mechanisms. The determination of the equilibrium prices serves to determine the utility function. Formulas for determining the equilibrium coefficients are given. The conditions for constructing the efficiency of the trajectory are determined.
Abstract: The model of economic dynamics, consisting of two units that produce, respectively, means of production and objects of commodities. It is assumed that the trajectory of еру model with a fixed budget admits characteristics and has an equilibrium state. These conditions allow us to construct effective trajectories of the model with the help of the eq...
Show More
-
Numerical Approach for Solving Stiff Differential Equations Through the Extended Trapezoidal Rule Formulae
Yohanna Sani Awari,
Micah Geoffrey Kumleng
Issue:
Volume 2, Issue 4, November 2017
Pages:
103-116
Received:
18 September 2017
Accepted:
9 October 2017
Published:
8 November 2017
DOI:
10.11648/j.ajmcm.20170204.13
Downloads:
Views:
Abstract: The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backward differentiation formulae (BDF). In this paper, we focus on the derivation of the fourth, sixth and eighth order extended trapezoidal rule of first kind (ETRs) formulae through Hermite polynomial as basis function which we named FETR, SETR and EETR respectively. We then interpolate and collocate at some points of interest to generate the desire method. The stability analysis on our methods suggests that they are not only convergent but possess regions suitable for the solution of stiff ordinary differential equations (ODEs). The methods were very efficient when implemented in block form, they tend to perform better over existing methods.
Abstract: The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backward differentiation formulae (BDF). In this paper, we focus on the derivation of the fourth, sixth and eighth order extended trapezoidal rule of first kind (ETRs) formulae through Hermite polynomial as basis function which we n...
Show More
-
Newton’s Method for Solving Non-Linear System of Algebraic Equations (NLSAEs) with MATLAB/Simulink® and MAPLE®
Aliyu Bhar Kisabo,
Nwojiji Cornelius Uchenna,
Funmilayo Aliyu Adebimpe
Issue:
Volume 2, Issue 4, November 2017
Pages:
117-131
Received:
25 November 2017
Accepted:
7 December 2017
Published:
3 January 2018
DOI:
10.11648/j.ajmcm.20170204.14
Downloads:
Views:
Abstract: Interest in Science, Technology, Engineering and Mathematics (STEM)-based courses at tertiary institution is on a steady decline. To curd this trend, among others, teaching and learning of STEM subjects must be made less mental tasking. This can be achieved by the aid of technical computing software. In this study, a novel approach to explaining and implementing Newton’s method as a numerical approach for solving Nonlinear System of Algebraic Equations (NLSAEs) was presented using MATLAB® and MAPLE® in a complementary manner. Firstly, the analytical based computational software MAPLE® was used to substitute the initial condition values into the NLSAEs and then evaluate them to get a constant value column vector. Secondly, MAPLE® was used to obtain partial derivative of the NLSAEs hence, a Jacobean matrix. Substituting initial condition into the Jacobean matrix and evaluating resulted in a constant value square matrix. Both vector and matrix represent a Linear System of Algebraic Equations (LSAEs) for the related initial condition. This LSAEs was then solved using Gaussian Elimination method in the numerical-based computational software of MATLAB/Simulink®. This process was repeated until the solution to the NLSAEs converged. To explain the concept of quadratic convergence of the Newton’s method, power function of degree 2 (quad) relates the errors and successive errors in each iteration. This was achieved with the aid of Curve Fitting Toolbox of MATLAB®. Finally, a script file and a function file in MATLAB® were written that implements the complete solution process to the NLSAEs.
Abstract: Interest in Science, Technology, Engineering and Mathematics (STEM)-based courses at tertiary institution is on a steady decline. To curd this trend, among others, teaching and learning of STEM subjects must be made less mental tasking. This can be achieved by the aid of technical computing software. In this study, a novel approach to explaining an...
Show More
