In this Thesis the identity of k-Tribonacci numbers in modular ring Z6 and in modular ring Z8 are discussed and their relationship with the k-Tribonacci number of factors of 6 and the factor of 8 are analysed using the method carried out by Layendekkers and Shannon [Notes on Number Theory and Discrete Mathematics, 19 (2013), 66-72]. Our computational experiment results show that (i) for k ≡ 1…
This thesis discusses the solution of a dual fully fuzzy linear system with fuzzy trapezoidal numbers for positive fuzzy number solutions and negative fuzzy numbers. The general form of the dual fully fuzzy linear equation system is ˜ A⊗ ˜x⊕˜b = ˜ C ⊗ ˜x⊕ ˜ d. The general form of the fully fully fuzzy dual equation system is transformed into the form of ˜ A⊗˜x = ˜ C ⊗˜x⊕…
The identity of Fibonacci numbers and Lucas numbers in modulo 7 and modulo 8 can be determined using congruence in modulo tables. In Modulo 8 the relationship of Fibonacci numbers and Lucas numbers can be analyzed in modulo 2 and modulo 4. Fibonacci numbers, and Lucas numbers in modulo 8 can be obtained from Fibonacci numbers and Lucas numbers in modulo 2 and modulo 4. Twice Fibonacci numbers a…
The Cross’ theorem is basically for triangles. Some authors have developed in rectangles and used rectangles on side of triangle. This thesis discusses the modification Cross’ theorem on triangle which is expanded once more by constructing a square outside direction on each side of the Cross’ theorem triangle. The proof process is done in a very simple way using congruence. Besides, the m…
Tsunami is a series of ocean waves that can propagate at speeds of up to more than 900 km/hour. Aceh Province experienced an earthquake disaster on December 26, 2004 at 7:58:53 WIB with the power of 9 Richter scale. The earthquake in Aceh caused a tsunami disaster with a height of up to 30 m, and caused 250,000 deaths. This study has used data from the 2004 tsunami in Aceh. Tsunami wave height …
This thesis discusses two three-step iterative methods which are derived by combining the iterative methods that contain the function and first derivative with Newton’s method. The process of the combination uses the principle of an undetermined coefficient method by allowing only one additional function evaluation that may occur in the process. By combining the methods proposed by Khattri an…
The sequence of base plane on the heptagonal and octagonal is the sum of elements on the base of each heptagonal and octagonal pyramid level. This thesis constructs the form of the base sequence of each heptagonal and octagonal and the pyramid of sides by using a pattern of sequences formed on the base sequence tetrahedron,pyramid, pentagonal pyramid or hexagonal pyramid. Additionally, by regis…
This thesis discusses a formula to reconstruct the P-position of three-pile Fraenkel game by using mex operator. P-position is a dynamic position where a gamer can decide his victory. The result shows that P-position of three-pile Fraenkel game is a series (An;j ,Bn;j ,Cn;j), with the value of An;j is the smallest positive integer which does not exist in (Ai;j ,Bi;j ,Ci;j) with 0 ≤ i < n, whi…
The sequences of base side is sequences obtained from the arrangement of the number of integers in one of the base side of the pyramid space. This the- sis discussess the sequences of base side on heptagonal and octagonal pyramids pyramids base facests with making a three dimensional sketch and method of _nding the number pattterns formed on sequences base side of pentagonal, he xagonal, heptag…
In general the Van Aubel's theorem is constructed from any quadrilateral. Some authors develop the Van Aubel's theorem on any triangle. This thesis discusses another form of the Van Aubel's theorem on triangle. In this study the author makes proof by using congruence, similarity, and concurrent. The results obtained in this thesis are three pairs of parallel lines, equal in length and perpendic…
This thesis presents a modi_cation of the third-order Runge-Kutta method based on the convex combination of the Lehmer mean, and its local truncation error. Stability analysis of the proposed methods show that the stability areas of the discussed method are the same as the stability area of the third order Runge Kutta method based on the arithmetic mean. Then the discussed methods are applied t…
Menelaus' theorem basically applicable for triangles. Some authors have developed it in quadrilateral. This thesis develops Menelaus' theorem for the pentagon. The prooving process is done in a very simple way that is by using Menelaus' theorem on the triangle by partitioning the pentagon into several triangles, area comparison of the triangle, and similarity. The results obtained are the _ve p…
This thesis discusses the development of the Ceva’s theorem on the pentagon in various cases including for the convex pentagon and the nonconvex pentagon. The Ceva’s theorem discusses the case of one-point concurrent in the pentagon. The prooving process is done in a simple way that is by using area proportion. The results obtained from this thesis are the existence of five lines from each …
Stirling numbers are divided into two types namely Stirling's numbers of the _rst kind s(n; k) and Stirling's numbers of the second kind S(n; k). The tribonacci number is a generalization of a Fibonacci number which has a unique and eisily recognizable shape, since each subsequent tribe is obtained by summing the three previous tribes beginning with the tribes 0, 0 and 1. Stirling's matrix of t…
One of generalisation of Fibonacci sequences is the -Fibonacci. This sequence can be constructed by Pascal 2-triangle. -Fibonacci sequences if operated in modulo arythmatic can produce a unique sequence that is the recurring numbers. The repetition of thus numbers is called Pissano Period Length, denoted by . The -Fibonacci sequences have the same period length if and . So, we can produce new f…
The purpose of this study is to explain the techniques in detecting the outlier of the ordinal data by using the regression coefficients. Identification data derives from the sport tests of Junior High Schools Students (SMP) in Pekanbaru. The ordinal logistic regression is combined with the proportional odds model. As the attraction of the modulus ordinal regressions interest, the jackknife tec…
Morley’s Theorem generally applies in a triangle. In this thesis Morley’s Theorem is proved in a quadrilateral and special rectangles and also the side length of Morley’s quadrilateral is determined. Quadrilaterals discussed in this paper are square, rectangle, rhombus, kite and isosceles trapezium. Simpler ways are used to prove by applying congruence concept and trigonometric concepts. …
The tetranacci number is a generalization of Fibonacci numbers whose form consists of the sum of the four previous term having begin with 0, 0, 0 and 1. Pascal’s triangle shape is geometrically obtained from the coefficients of the powers of summation of the two numbers, i.e. can be arranged in the from of a triangle. The numbers that exist in every row of the Pascal’s triangle is the coeff…
This thesis discusses a problem in the management of blood supply chain at the blood banks with perishability characteristics especially for the red blood cells and platelet. Focus of this discussion is to minimize the total cost, shortage and wastage levels of the blood unit. Stochastic integer programming approach is used to solve this problem by the following assumptions blood group and some…
This thesis discusses Napoleon's Theorem at hexagon having three pairs of parallel sides in same lengths with two cases (i) regularly built toward outside and (ii) regularly built toward inside. Provided proofs use the congruence and trigonometric concepts. At the end of the discussion, the development of Napoleon's Theorem by using geogebra applications is presented. Keywords: Napoleon's The…