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…
This thesis discusses the area of the outer Napoleon and the outer semi Napoleon in triangle and special quadrilateral. The area of the outer Napoleon in a triangle constructed from an arbitrary triangle and the area of the outer Napoleon in a quadrilateral are constructed from rectangles that have two parallel sides including rhombus and parallelogram, while the area of the outer semi Napoleon…
Morley’s theorem is applied using inner angles on triangles and squares, in this paper will be developed Morley’s Theorem Using the outer angle on triangles and squares (rhombus, isosceles trapezoid and kite). In any triangle, the Morlay theorem using an outer angle produces an equilateral triangle, the rhombus produces an the rectangle, the isosceles trapezoid pro duces an the kite an…
Derivative of function is one of the topics in the mathematics book in Se- nior High School (SMA). In some textbooks used by students, there is no general form of the nth derivative of the function h(x)/f (x) or h(x)/√f (x). This thesis discusses how to obtain the general form of thenth derivative func- tion 1/(ax + b), (ax + b)/(cx + d), 1/√ax + b, and (ax + b)/√cx …
Fibonacci sequence is defined by Fn = Fn−1 + Fn−2 for n ≥ 2 with F0 = 0 and F1 = 1. Lucas sequence is defined by Ln = Ln−1 + Ln−2 for n ≥ 2 with L0 = 2 and L1 = 1. While Fibonacci-Like sequence is a generalized of Fibonacci and Lucas sequence that defined by Sn = Sn−1 + Sn−2 for n ≥ 2 with S0 = 2 and S1 = 2. The Fibonacci-Like sequence forms the sequence numbers 2, 2…
This study presents the n/2th derivative of sine function f (x) = sin px and cosine function f (x) = cos px where p is a positive integer and x is a variable. The n/2th derivative is a fractional derivative of an arbitary order. The fractional derivative can be obtained by using Riemann-Lioville integral fractional definition that is closely related to gamma functi…
This article discusses an iterative method to solve a nonlinear equation, which is free from derivatives, obtained by approximating a derivative in the method proposed by Rhee et al. [Int. J. Comput. Math., 95 (2018), 2174-2211] by the method of divided difference. We show analytically that the method is of order eighth and for each iteration it requires four evaluation functions. Numeric…
Wind speed is the airspeed moving horizontally at a height of two meters above the ground. This study aims to obtain the best wind speed model in Peka- nbaru. Monthly wind speed data from 2008 to 2017 are used in four wind speed models in the form of mixed probability density functions, that are Lindley distribution, Akash distribution, Shanker distribution, and Sujatha distribution. The maximu…
This thesis discusses the development of nutrition optimization model using goal programming to satisfy daily nutrition needs of adolescent. Objective function is designed to minimize deviations from the nutrients according to recommended daily nutrition needs. Nutrients needs are determined according to Indonesian Recommended Dietary Allowances (AKG) incorporated as goal constraints. This thes…
This study uses air pollution data with particulate matter 10 (PM10 ) pollutants in the Pekanbaru city in 2009 2015. Air pollution data was analyzed to obtain probability model for air pollution in the Pekanbaru city by using the Dagum distribution. This distribution is a special form of generalized beta II distribution with 3 parameters, namely b as a scale parameter and a, p as shap…
This thesis discusses the modifications of fuzzy algebra that are definition of positive and negative fuzzy number and arithmetic fuzzy number. Definition of positive and negative fuzzy number are obtained by comparing the area located on positive and negative x-axis. While, arithmetic fuzzy number is obtained using the formula of the multiplication of parametric function of fuzzy number. Modif…