This final project discusses solving the traveling salesman problem in the form of an octagonal fuzzy number. The process is started by converting the octagonal fuzzy number into crisp numbers using the Robust’s ranking method , then to get the optimal solution the Hungarian method is used. To understand the process of getting the optimal solution, an example is given. This final project …
This nal project discusses a method for solving a quadratic fractional programming (QFP) problems. The method is called the decomposition method based on linear programming (LP) problem for nding an optimal solution to a quadratic fractional programming (QFP) problem, where both the numerator and the denominator of the objective function can be fatorized into two linear functions. The me…
This nal project discusses the solution of triangular fuzzy number linear programming. The method for solving triangular fuzzy number linear programming is called Mehar's method. Mehar's method is done by conversion the objective function and the fuzzy constraint functions based on the fuzzy linear programming problem to crips number based on operation of fuzzy number linear programming a…
This final project discusses new estimators for population variance using two auxilary informations. This estimator ratio is completed by simple random sampling without replacement method. The result of this method is to get efficiency of estimators. Then to determine an efficient estimator is done by comparing the MSE (Mean Square Error) for estimator ˆ S2 rpG1 dan ˆ S2 rpG2 and varia…
This nal project discusses how to solve the problem of traveling salesman in fuzzy triangles using dynamic programming. The process to obtain the solution begins by converting the fuzzy triangle numbers into crisp numbers using the Yager's ranking method and then the optimal solution is determined using dynamic programming. This nal project is a review of the article Mythili et al. [Inte…
This final project discusses the stability between predator and prey in the modified Lotka-Volterra. This model uses a modified rational Lotka-Volterra model with one predator and one prey. In this model, there are two nonnegative equilibrium points and stability positive equilibrium in the parameters. Furtheremore, a simulation is given for each case that describes the behavior and stabil…
This nal project discusses the stability analysis of predator-prey models with ratio-dependent functional responses and harvesting in predator populations. The stability of the system around the equilibrium point is determined by the linearization method in order to obtain the characteristic equation and the eigenvalue which is a reference for determining the stability properties. The mod…
This final project discusses the generalized composite Bernstein quadrature formula derived by approximating the function that are integrated using Bernstein polynomial to calculate the integral of a function. The process of deriving the method starts by defining the Bernstein operator and its error, then proceed by applying it to estimate the integral function so that the generalized comp…
This article discusses the generalization of the Euler formula having an expansion resembling a Fourier series. This formula can be applied in calculating the value of an in_nite series of real numbers. In addition, the given identity of the generalization formula Euler that can be applied to the sum of in_nite series algebra, and the process of integrating the Brownian motion and Brownian …
This final project discusses the iterative method without involving derivatives derived using a progressive interpolation to solve a nonlinear equation. Analytically it is shown that the discussed method is of order 3 ・ 2m−3, where m is the number of function evaluations. From computational test on some functions by setting the number of function evaluations fixed it can be seen that this m…
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…
The background of this research is motivated by the limited number of mathematics learning devices that can be used as references by teachers in developing learning devices independently in accordance with the demands of the 2013 curiculum. The purpose of this study is to produce a learning devices with a problem based learning model on the material of the size concentration and disseminat…