This thesis discusses a derivative free three-step iterative method to solve a nonlinear equation. The proposed method is derived by estimating the first de-rivative of the method proposed by Sharma and Arora [Appl. Math. Comput., 273 (2016), 924-933] using a divided difference by one parameter. Analytically it is shows that the method has an eighth order convergence and requires four function…
This thesis discusses alternative definitions of triangular fuzzy numbers to be positive and negative based on the area comparison, and given alternative arithmetic for triangular fuzzy numbers. Next, these definitions are applied to solve the fully fuzzy linear system using the decomposition method. Keywords: Triangular fuzzy numbers, alternative arithmetic, fully fuzzy linear system, decom…
This thesis discusses the modification of three step iteration method to solve nonlinear equations f(x) = 0. The new iteration method is formed from a combination of Newton, Halley, and Chebyshev methods. To reduce the number of evaluation functions, several derivatives on this method will be estimated with Taylor polynomials. The convergence analysis shows that the new method in the order…
This thesis discusses the pencil of ellipse. It can be used to solve some problems of ellipse. If there are Q1 and Q2, then Q1 + kQ2 = 0 with k as parameter of real numbers to form pencil of ellipse. An equation of ellipse contain the parameter that not only produce an ellipse, but it forms lines, circle, parabola and hyperbola as well. There are some special conditions from pencils of elli…
This thesis discusses multi-input intervention analysis to investigate the effect of interventions which may come from internal and/or external factors in time series data. The purpose of this study is to give a theoretical and empirical studies on the multi-input intervention analysis, particularly to develop and construct a model procedure of the multi-input intervention cused by pulse an…
Miquel’s theorem usually is applicable for a triangle. Miquel’s theorem states that if from any triangle is choose a point on each of its side, and then constructed circle passing through each vertex of the triangle and through the points on the two adjacent sides, all three of those circle meet at a point. This point is called a Miquel’s point. In this thesis, the authors make genera…
Tribonacci sequences are generalization of Fibonacci sequences having a unique shape and easily recognizable, where each subsequence term obtained by summing of the previous three terms that begins with 0, 0, and 1. Pascal’s triangle shape is obtained from the coefficients of the powers of summation of the two numbers, i.e. (x+y)^n. All numbers in every row of the Pascal’s triangle …
This thesis discusses Miquel point in any quadrilateral that is the Miquel point inside the convex quadrilateral and the Miquel point in the nonconvex quadrilateral by constructing a triangle inward so that the four circumcircles of each triangle intersect at one point. Provided proofs use the cyclic quadrilateral and the circle. Then the convex quadrilateral formed fr…
Special lines, such as angle bisectors, altitudes, medians, and perpendicular bisector can be constructed in a triangle. These special lines are concurrent with their corresponding concurrent points, and called incenter and excenter, orthocenter, centroid, and circumcenter. This thesis discusses how to construct the multiple Kosnita using circumcenter and orthocenter passing through excente…
This thesis discusses the pencil of parabola. Given two parabolas l1 and l2 and we have l1 + kl2 = 0 with real-valued k and k 6= −1 performing a pencil of parabola through the points of intersection of two parabolas. This thesis also discusses the existence of a parabola and a special cases such as the pencil of parabola passing through a point, pencil of parabola touching the axis of sy…
B-algebra constructed from a noncommutative group. So that, we find the concept of B-algebra by the properties of the group. If there is a subgroup in the group, hence there is B-subalgebra in the B-algebra. In this thesis, we constructed the concept of prime ideals in B-algebras.This thesis using method of construct prime ideals in BC I and BC K -algebras by Borzooei and Zahiri. The resul…
This thesis discusses aboud fully fuzzy linear equation modifications of trapezoidal fuzzy beginning by modifacation algebra such as multiplication of fuzzy number, division of fuzzy number and invers of fuzzy number. Then given a definition when Trapezoidal fuzzy number is said to be positive or negative by using broad rules on the positive x-axis area and negative x-axis area. Finally, th…
This thesis presents an aircraft landing scheduling problem at single run-way. The focus of this discussion is to minimize the additional costs due to non-compliance of the aircraft landing target at a given time. A mix integer programming approach is used to solve this problem. At the end of this study a simulation is given to see the result of applying the method in this issue. The result cos…
This thesis discusses the optimization of portfolio stock selection using the weighted meta goal programming (WMGP) model. The optimization problem of stock portfolio selection with the WMGP model is solved by combining the weight of trust in each type of WMGP and comparing it with the weighted goal programming (WGP) portfolio. The final result is in the form of the selection of five stocks whi…
This thesis discusses two two-step methods for finding multiple roots of nonlinear equations. Both methods use Newton’s method for multiple roots in the first step. For the second step the first and second methods are respectively using the Osada method and the linear combination of the Newton-Halley and Newton-Osada methods. Analytically, the two methods have a six-order convergenc…
The positiveness of a triangular fuzzy number will be introduced using the area concept. Then an alternative arithmetic for triangular fuzzy number will be constructed, especially for inverse of triangular fuzzy number and inverse of fuzzy matrix. The inverse of fuzzy matrix can be applied to solving fully fuzzy linear system directly. Keywords: Arithmetic fuzzy number, triangular fuzzy numb…
This thesis gives some consequences of Dao’s Theorem on six circumcenters associated with a cyclic hexagon. Furthermore, it is also given the development of the Dao’s theorem in forming two pairs of orthologic triangles whose orthologic centerpoint is equal to the center point of the initial circle, with proof using a simple concepts that the high school student can understand, they are…
This thesis discusses some of the r characteristic that satisfy the equation 11x ≡ r (mod 100) and 111x ≡ r (mod 1000), where r € Ɲ and positive integer x ≥ 0. In general the r value obtained is x as tens and the units is 1. In the equation 11x ≡ r (mod 100) and 111x ≡ r (mod 1000), for x = 10m the value r = 1 and for the value x = 10m + 1 obtained value r = 11. The value obta…
Kosnita’s theorem is usually constructed using circumcenter-circumcenter. In this thesis, Kosnita’s theorem is developed by using incenter-circumcenter, incenter-incenter, incenter-centroid and centroid-centroid through excenter triangle. The proof of this theorem uses the simple geometry concept such as bisector, centroid, orthocenter and congruency. In this thesis it can be proved th…
This thesis discusses an application of non-preemptive goal programming based on the model of traveling salesman problem. This study involves seven cities which can be connected by road network in West Sumatera. In this study, we consider two cases with the assumption that the tourist started to self-drive from dierent city. The results show that the goal programming gives a route with mi…