ABSTRACT This final project formulates premium of contingent term life insurance based on Makeham’s law for two persons at the age x and y years old. Contingent life insurance is an insurance whose payment are based on the sequence of the deceased insured. In determining the order in which death is delayed, the compound contingent function is used. In this final project, term life annuit…
ABSTRACT This nal project discusses the Hungarian method to solve assignment problems with generalized interval arithmetic. This problem aims to optimize decision making in assignment placement by minimizing costs for n jobs completed by m employees. Interval assignments are performed by converting each table entry into the form of midpoint and width. Then the Hungarian method in the ass…
ABSTRACT This final project discusses some properties of B-algebra and the ideal, complete ideal, n-ideal of B-algebra. There is a relation between ideal, complete ideal, and n-ideal that every ideal of B-algebra is complete ideal and every ideal of B-algebra is n-ideal. This project is a review of article of Abdullah and Athsan [Applied Mathematical Sciences, 11 (2017), 1705-1713]. Keywo…
ABSTRACT This final project discusses the properties of BN1-algebra and the relation- ship between BN1-algebra with BG-algebra, BCI-algebra and Coxeter-algebra. Then, by using the properties contained in BN1-algebra and some other alge- bras, several other related algebraic properties are derived. In final section, it is found that the conditions of some algebra in BN1-algebra are the same…
ABSTRACT This article discusses the development of the Japanese theorem for two circles in cyclic quadrilateral, with reconstruct two incircles of the triangle in Japanese theorem. The result obtained are the value of the incircles radii of the triangle in two cyclic quadrilateral and diagonal relationship of cyclic quadrilateral in two circles. Keywords: Cyclic quadrilateral, incircle of…
ABSTRACT This final project discusses the solution of assignment problems in the form of equally spread symmetric fuzzy numbers for minimization and maximization cases both balanced and unbalanced cases. The fuzzy numbers does not need to be converted into crisp numbers and then completed using the branch and bound method by forming branch in each step to construct a solution tree at the …
ABSTRACT This final project discusses the solution of assignment problems in the form of mixed objective assignment costs. The assignment costs used are triangular fuzzy numbers and crisp numbers. Triangular fuzzy numbers are converted to crisp numbers using the Yager’s ranking method, so that crisp number operations can be applied. Furthermore, to get the optimal solution of the problem…
ABSTRACT This paper discusses the problem of transporting trapezoidal fuzzy numbers with supply and demand approach. The coefficients of cost, supply and demand are in the form of fuzzy numbers because there is uncertainty. The simplex method is implemented to convert the fuzzy objective and constraint function in the fuzzy transportation problem to four form numbers in the transportation …
ABSTRACT This final project discusses a two-step iteration method without memory for solving absolute equations. The convergence analysis performed shows that the two-step iteration method without memory has a linear convergence order. Then a computation example is given to see the implementation of the algorithm discussed. At the end of the discussion, a numerical comparison is carried ou…
ABSTRACT This nal project discusses the properties of BM-algebra and the relation of BM-algebra with BCI -algebra, BF-algebra and Coxeter algebra. Their rela- tionship is proven by showing that the properties of BM-algebra, BCI -algebra, BF-algebra, Coxeter algebra are interrelated. Keywords: BM-algebra, BCI -algebra, BF-algebra, Coxeter algebra.
ABSTRACT This nal project discusses a new kind of lattice path and innite lower tria- ngular array with the given steps. By using lattice path the lower triangular array which is obtained has the sum of row on its diagonal. The sum of lat- tice path is found by generating function of the sum of row Riordan matrix. Then a combinatorial interpretation is obtained for the generalized tribon…
ABSTRACT This final project discusses the new Newton iterative method based on nonstan- dard difference for solving nonlinear equations. The proposed method is proven analytically to have the order of cubic convergence involving four evaluation functions. Several examples of numerical computation show that the resulting method is comparable to the class of existing methods. Keywords: Nonl…
ABSTRACT This nal project discusses the solution of the travelling salesman problem using the genetic algorithm method with MATLAB software. This discussion aims to nd the optimal solution of a route by a salesman. The best path result from a travel route are optained and it can be concluded that the genetic algorithm can be used as a method for solving the problem of travelling salesman…
ABSTRACT This final project discusses travel planning around the mainland of riau province using ant colony algorithm, utilizing the heuristic method, with Matlab software to a variative solution. This discussion aims to find the shortest route using data of distance, cost, and a combination of distance and cost. Optimization of the travel index is the shortest route using a combination da…
ABSTRACT This final project discusses the premium reserve of joint life status endowment life insurance based on Zillmer’s method for two insurance participants. The calculation of this reserve is obtained by using the prospective reserve principle and the size of Zillmer’s rate. The premium reserve is obtained by determining the single premium, annual premium, and life annuity based o…
ABSTRACT This nal project proposes a new single step iterative method for solving no- nlinear equations. This iterative method is derived using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence sho- ws that the order of convergence of the proposed iterative method for a simple root is four. To illustrate the advantages and performance of the propo…
ABSTRACT The nal project discusses some congruences on harmonic numbers and Berno- ulli nmubers. The study is completed using several harmonic identities, congru- ence modulo properties and algebraic calculations. Futhermore it can be proven that the congruence of the multiplication of the binomial sums and harmonic numbers with Bernoulli numbers. This is a review of article of He [Period…
The mathematical problem-solving ability of students was still relatively low, one of them caused by the application of models and the development of learning tools that are still not at all. This study aims to develop learning tools based on problem-based learning to facilitate the mathematical problem-solving ability for 10th-grade senior high school on equations and inequalities of one varia…
The results of the document review that the researcher conducted on the learning tools used by teachers in several Grade school in Pekanbaru City, obtained information that the learning tools used by teachers did not meet the rules contained in the 2013 Curriculum so they still needed to be improved. This study aims to produce learning tools based on Problem Based Learning on Plans and Scales m…