Browsing by Author "Sirait, Asli"

Now showing 1 - 20 of 21
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    BEBERAPA HUKUM URUTAN TERBALIK PADA INVERS GRUP DARI PERKALIAN DUA MATRIKS
    (2016-04-27) Elvina; Sirait, Asli; Musraini
    This paper discusses some equivalent conditions for reverse order law of group inverses of product of two matrices. Several sufficient conditions which enable both (AB)# = B(1,2)A(1,2) and (AB)# = B(1,2)A(1,2) hold are also given.
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    BEBERAPA SIFAT ALJABAR GENERALIZED INVERSE PADA MATRIKS
    (2014-03-25) Risa, Erma; Gemawati, S.; Sirait, Asli
    This article discusses some of the algebraic properties of the generalized inverse matrix on the addition operation, which is derived using the properties of the sum of the rank of matrices. Generalized inverse of the sum of two matrices can be obtained if the range space of the sum of two matrices is disjoint. At the end of the discussion, an example of how to get a generalized inverse matrix is given
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    Developing A Direct Search Algorithm for Solving The Capacitated Open Vehicle Routing Problem
    (2017-10-26) Aziskhan; Pane, Rolan; Natsir, M; Sirait, Asli; Kho, Johannes
    In open vehicle routing problems, the vehicle are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacited vehicle routing problem (CVRP). The strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method and the notion of superbasics, has been developed for efficienty requirments, this strategy is used to force the appropriate non-integer basic veriables to move to their neighbourhood integer points. A study of criteria fr choosing a nonbasic variable to work with in the inegerizing strategy has also been made. Succesful implementation of these algorithms was achieved on various test problem
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    HUBUNGAN ANTARA BILANGAN PRIMA DAN GRUP POS
    (2016-04-27) Abduh, Muhammad; Gemawati, Sri; Sirait, Asli
    Group perfect order subset (POS) is a group that is characterized by the number elements in the group having the same order that divides the group order. This article discusses the relationship between the properties of the POS group to the number of elements related to prime numbers which have a positive power order of the group POS.
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    Ketaksamaan Nilai Singular Pada Products Hadamard
    (2017-10-16) Sirait, Asli; Pane, Rolan; Natsir, M
    Misalkan M m,n merupakan ruang dari matriks kompleks m x n , dimana A , B M n , n dan merupakan product Hadamard ( atau Schur) dari A dan B oleh A o B , Untuk A Mn, n maka merupakan nilai singular terurut dan menyusut terurut menurut baris Euclidean dan panjang kolom dari A terhadap r1 (A ) ≥ r2(A ) ≥ .. rm (A ) ≥ dan c1 (A ) ≥ c2(A ) ≥ .. cn (A) Akan ditunjukkan bahwa untuk suatu A , B M n , n berlaku hubungan , dengan k = 1 , 2 , ….. , min { m,n }
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    Linierisasi Sistem Dinamik Dalam Bidang Datar
    (2017-10-16) Firdaus; Sirait, Asli; Natsir, M
    Pada makalah ilmiah ini dibahas tentang teori linierisasi suatu sistem persamaan diferensial non linier dari sistem dinamik berdasarkan aturan dan definisi terkait . Untuk sistem Linier 2 dimensi, , n=2, diperoleh linierisasi dari Persamaan dengan r = Trace A , , Beberapa kriteria perilaku penyelesaian yang mungkin tergantung pada tanda yang tergambar pada struktur eigen dari sistem planar dalam ruang parameter .
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    Matriks Fuzzy Nilpoten
    (2013-02-26) Sirait, Asli; Efendi, Riistam
    Dalam penelitian ini dibahas tentang masalah matriks fuzzy nilpoten, yaitu dibuktikan beberapa sifat dari matriks fiizzy nilpoten yang berkaitan dengan nilai eigen. Selanjutnya untuk jumlah hingga matriks fuzzy ditentukan karakterisasi dari mlpoten simultannya. Operasi yang digunakan adalah operasi aljabar maks-min.
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    MENENTUKAN INVERS SUATU MATRIKS DENGAN MENGGUNAKAN METODE AUGMENTASI DAN REDUKSI
    (2013-07-20) Wati, S. E.; Muhammad, Imran; Sirait, Asli
    We discuss a method to obtain an inverse of a nonsingular matrix, called Augmenta- tion and Reduction Method. The total computational cost of this method to obtain an inverse of a matrix is the same as those of Gauss-Jordan method. However this method to be applied needs more storage than those of Gauss-Jordan method.
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    MENENTUKAN NILAI EIGEN DAN VEKTOR EIGEN DARI MATRIKS TRIDIAGONAL PADA KASUS n GENAP
    (2016-04-27) Purwanti, Tannia; Gemawati, Sri; Sirait, Asli
    This article discusses how to obtain eigenvalues and their corresponding eigenvectors of tridiagonal matrices of the form                            a b c a b a b c b c A n n n   1 1 2 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0               where , , a,b and c are complex number, for the case when n is even.
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    MENGHITUNG BANYAKNYA BILANGAN PRIMA YANG LEBIH KECIL DARI ATAU SAMA DENGAN SUATU BILANGAN BULAT n
    (2016-02-04) Polorida; Sirait, Asli; Musraini
    This articel studies the explicit formula for a function to enumerate the number of primes less than or equal to n called Prime Counting Function, where n is natural number. Prime Counting Function is denoted by π(n). Explicit formula of π(n) is constructed by arithmetic function φ(n) and δ(n) with the help of notation of sum and the oor function.
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    MENGHITUNG DETERMINAN SUATU MATRIKS DENGAN MENGGUNAKAN METODE CORNICE
    (2013-03-16) Gusriansyah; Gemawati, Sri; Sirait, Asli
    ݊ × ݊ (݊ ≥ 5) matrices by reducing their sizes by four, it is known as the Cornice Method. A determinant of matrices with the exception of the first and the last entries, the entries of the 2nd row and (݊ − 1) − ‫ݐ‬h row, as well as the 2nd column and (݊ − 1) − ‫ݐ‬h column are all zero. This called “Cornice Determinants” and note as |‫ܥ‬௡×௡ |(݊ ≥ 5). To obtain the form of this Cornice Ma
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    PELABELAN TOTAL SISI AJAIB SUPER PADA GRAF CORONA-LIKE UNICYCLIC
    (2013-06-25) Kurniawan; Pane, Rolan; Sirait, Asli
    We discuss the super edge magic total labeling in the corona-like unicyclic graph by reordering the grid points on the trajectory, followed by the transformation to the edges. A new variation is obtained from the super edge magic total labeling.
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    Pengembangan dan Penerapan Teorema Pappus dalam Berbagai Kasus
    (2013-03-21) Hasriati; Sirait, Asli
    In this paper we discuss about The Pappus theorem with colinearitas of three points which is the intersection of six points on two different lines. Furthermore, if there are four lines that intersect and form a triangles, the triangle formed through the orthocenter is show coliniearitas
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    PREMI ASURANSI JIWA BERJANGKA MENGGUNAKAN MODEL TINGKAT BUNGA VASICEK
    (2014-03-25) Muslim; Hasriati; Sirait, Asli
    This paper discusses a single premium of term life insurance using interest rate Vasicek model. The calculation of premium in this model is affected by the equilibrium point of interest rate β and the acceleration of interest rate wich lead to the equilibrium point α. The Values of β and α are obtained using estimation of maximum likelihood method of Vasicek model. Futhermore, a numerical example is given to explain the problem discussed
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    SIFAT-SIFAT KESETARAAN PADA MATRIKS SECONDARY NORMAL
    (2014-03-25) Nursyahlina, Nursyahlina; Gemawati, S.; Sirait, Asli
    A square matrix A is called a secondary normal matrix if AAθ = Aθ A, where Aθ is a secondary conjugate transpose of the matrix A, which is different from the conjugate transpose matrix. In this paper, we discuss some equivalent conditions of a secondary normal matrix that is if A is a secondary normal matrix then it exists a secondary unitary matrix P obtained by diagonalization and Gram-Schmidt process, such that Pθ A P = D, where D is a diagonal matrix. More over if A = VP and V is a secondary uniter matrix then A is a secondary normal matrix.
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    SIFAT-SIFAT SEMIGRUP SIMETRIS INTERVAL
    (2013-03-26) Yusman, Rizan Febri; Gemawati, Sri; Sirait, Asli
    Interval set is a set from an object whose elements consist of intervals. A set of all one-to-one and onto mappings from interval set to the other for all with composition operation which from a semigrup is called interval semigroup. In this paper some symmetric semigroup on certain intervals were discused. Some of the properties discused were isomorphic, S-interval symmetric semigroup, S-weakly cyclic interval symmetric semigroup and S-weakly commutative interval symmetric semigroup which are expressed in some theorems
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    Solusi Alternatif Persamaan Diferensial Biasa
    (2017-10-31) Sirait, Asli; Natsir, M; Pane, Rolan
    Pada makalah ini akan ditunjukkanpenyelesaian sistem persamaan diferensial x’ = Ax diformulasikan oleh persamaan , dengan menentukan nilai ( v1 , v2 , …., vn ) yang merupakan eigenvektor yang berkoresponden dengan eigen value λ dari matriks A .Matriks modal P = ( v1 , v2 , …. , vn ) , dipenuhi oleh transformasi bentuk kanonik Jordan P-1AP = J , Untuk nilaieigen berbeda penyelesaian x! = Ax diberikan oleh dan Beberapa metode alternatif dalam menyelesaikan persamaan x! = Ax antara lain metode Silvester dan metode langsung
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    SOLUSI REFLEKSIF DAN ANTI-REFLEKSIF DARI PERSAMAAN MATRIKS AX = B
    (2016-02-04) Arrohman; Gemawati, Sri; Sirait, Asli
    This article studies the necessary and sufficient conditions to determine the solutions of the matrix equation AX=B, which can be either reflexive and anti-reflexive matrix. An n × n complex matrix A is said to be a reflexive (or anti-reflexive) if A = PAP (or A = −PAP) where an n × n complex matrix P is said to be a generalized reflection matrix if PH = P and P2 = I.
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    Solving A Class of Stochastic Multiobjective Integer Linear Programming Problems
    (2017-10-16) Kho, Johannes; Pane, Rolan; Aziskhan; Sirait, Asli; Natsir, M
    In this paper we propose a method for solving a multi objective chance constrained integer programming problem. We assume that there is randomness in the right-hand sides of the constraints only and that the random variables are normally distributed. The stochastic model is transformed in a deterministic equivalent for using covariance technique. Then we propose an interactive approach for solving the deterministic mode
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    SYARAT PERLU DAN CUKUP SISTEM PERSAMAAN LINEAR BERUKURAN m × n MEMPUNYAI SOLUSI
    (2016-02-04) Zainuri, Aryan; Syamsudhuha; Sirait, Asli
    This article discusses the necessary and sufficient condition for the system of linear equations Ax = b where A is an m × n matrix, with m < n and b is an n × 1 vector to have a solution. The discussion involves determining the number of single variables by looking at columns lowering rank and determining the value of the single variables.