Mathematical Theory and Modeling
http://www.iiste.org/Journals/index.php/MTM
<p><span id="internal-source-marker_0.04939836589619517"><span id="internal-source-marker_0.04939836589619517">Mathematical Theory and Modeling </span>is a peer reviewed journal published by IISTE. The journal publishes original papers at the forefront of mathematical theories, modelings, and applications. The journal is published in both printed and online versions. The online version is free access and download.</span></p><p><span>IISTE is member of <a href="http://www.crossref.org/01company/17crossref_members.html">CrossRef</a>.<br /></span></p>en-USMathematical Theory and Modeling2224-5804New Approach on Identification of Circular Cone
http://www.iiste.org/Journals/index.php/MTM/article/view/38447
<p>The objective of this paper is to provide elementary approach for identiﬁcation of circular cone by using known results. In this paper, the author identiﬁed oblique circular cone by considering two diﬀerent slant heights of a cone, the axis of a cone and larger angle of a triangle which is obtained from the lateral surface of a circular cone. The author found that there are four diﬀerent types of circular cones namely right circular cone, acute oblique circular cone, right oblique circular cone and obtuse (critical) oblique circular cone by using very elementary ways.</p> <p class="AA">Keywords: circle, circular cones, oblique circular cones, triangles.</p>Getachew Abiye Salilew7Generalised Ratio Estimators Using Conventional Location Parameters in Survey Sampling
http://www.iiste.org/Journals/index.php/MTM/article/view/38448
<p>The present paper concentrates on estimating the finite population mean by proposing the new generalised ratio type estimators in simple random sampling without replacement using linear combination of coefficient of variation and population deciles of auxiliary variable. The expressions for mean square error and bias were calculated and compared with the classical and existing estimators. Theoretical results are supported by numerical illustration.</p> <p><strong>Keywords: C</strong>oefficient of variation; deciles; ratio-type estimators; mean square error; bias; efficiency.</p>Mir Subzar7Closed Ideal with Respect a Binary Operation * On BCK-Algebra
http://www.iiste.org/Journals/index.php/MTM/article/view/38449
<p>In this paper, we define a new ideal of BCK-algebra, we call it a closed ideal with respect a binary operation ∗, and denoted by (∗ -closed ideal). We stated and proved some properties on closed ideal and give some examples on it.</p> <p><strong>Indexing Terms/Keywords: </strong>BCK-algebra, Closed Ideal, A Binary Operation ∗ on BCK-Algebra.</p>Azal Taha Abdul WahabRusul Hassan NaserZahraa M. Ali7Using An Accelerating Method With The Trapezoidal And Mid-Point Rules To Evaluate The Double Integrals With Continuous Integrands Numerically
http://www.iiste.org/Journals/index.php/MTM/article/view/38450
<p>In this research we have used a compound method which is composed of Trapezoidal and Mid-Point Rules to evaluate the approximate values of the double Integrals with Continuous Integrands because of the resultant approximate values are fast when approximating from the true values of integrals if compared with other Newton -Cotes formulas. [ S.S. Sastry, 2008". The symbol of this rule is <em>TM</em>, in this method 2n is, the number of subintervals [a,b], equivalent to 2m ( the number of subintervals of [c,d] and (h=ћ), we accelerate the resultant approximate to the true values of integrals through applying Aitken's accelerate on the compound rule <em>TM</em> to procure a new method we called it <em>A(TM)</em> where the symbol A indicates to the Aitken’s acceleration method and the symbol <em>TM</em> ( <em>y</em> indicates to the Trapezoidal rule on the external and <em>x</em> indicates to the Mid-point rule on the internal dimensions).</p> <p><strong>Keywords: </strong>double integrals, Trapezoidal and Mid-Point Rules and Newton-Cotes</p>Azal Taha Abdul WahabRusul Hassan Naser7Robust Nonparametric and Semiparametric Model Calibration Estimators by Penalty Function Method
http://www.iiste.org/Journals/index.php/MTM/article/view/38486
<p>Use of nonparametric model calibration estimators for population total and mean has been considered by several authors. In model calibration, a distance measure defined on some design weights thought to be close to the inclusion probabilities, is minimized subject to some calibration constraints imposed on the fitted values of the study variable. The minimization is usually by way of introducing langrage equation whose solution gives the optimal design weights to be used in estimation of population total. Sometimes a solution to the langrage constants does not exist. Numerical approaches are some of the alternatives to the langrage approach. In this paper, we have derived nonparametric and semiparametric model calibration estimators by treating the calibration problem as a nonlinear constrained minimization problem, which we transform to an unconstrained optimization problem using penalty functions. We show that the resulting nonparametric and semiparametric estimators are robust in the sense that they are quite efficient when the model is correctly specified for the data and that the estimators do not fail even when the model is misspecified for the data. When the penalty constant approaches zero, the estimators reduce to the Horvitz Thompson design estimator.</p> <p><strong>Keywords: </strong>model<strong> </strong>calibration, nonparametric model, semiparametric model, penalty function</p>Pius Nderitu Kihara7