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INDONESIA
MATEMATIKA
Published by Universitas Diponegoro
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Core Subject : Education,
Mathematics
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Articles 7 Documents
 1 
Search results for , issue "Vol 16, No 1 (2013): Jurnal Matematika" : 7 Documents clear
ENDOMORFISMA L0 DARI BCH-ALJABAR Citra, Restia Sarasworo; ., Suryoto
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

BCH-algebras is an algebraic structure which built on a commutative group. In BCH-algebra there is a mapping from this structure to itself which called  a BCH-endomorphism. In BCH-algebra context, we denote L as a set of all left mapping and it contains L0 which the only non-identity BCH-endomorphism in L with some properties : the left map L0 is a center of BCH-endomorphism, L0 both be a periodic mapping dan an epimorphism on BCH-algebra. Such as a group with the fundamental group homomorphism theorem, in a BCH-algebra we have a fundamental BCH-algebra homomorphism theorem.
PERLUASAN HARNACK DAN SIFAT CAUCHY INTEGRAL HENSTOCK-DUNFORD PADA RUANG EUCLIDE ., Solikhin
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

In this paper we study Henstock-Dunford integral on the Euclidean space . We discuss some properties of the integrable. We prove  the Harnack Extension theorems and the Cauchy extension theorems for Henstock-Dunford integral on the Euclidean space .
PELABELAN GRACEFUL SISI BERARAH PADA GRAF GABUNGAN GRAF SIKEL DAN GRAF STAR Octafiani, Putri; Utomo, Robertus Heri Soelistyo
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Let G is simple and finite graph. Graph G is called a directed edge-gracefull graph  if there exists an orientation of G and bijective map  f : A(G) → {1,2, ..., q} such as a map g on V defined by g(v) = [f +(v) – f –(v)] (mod p) is bijective map, which is  f +(v) is the sum of the labels of arcs with v as a head and  f –(v) is the sum of the labels of all arc with v as a tail.  Graph with directed edge-gracefull labeling is called directed edge-gracefull graph. In this paper we will discussed about directed edge-gracefull labeling of cycle and star related graph
PATH KUAT TERKUAT DAN JARAK KUAT TERKUAT DALAM GRAF FUZZY Ekawati, Lusia Dini; Ratnasari, Lucia
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Fuzzy graph is a graph consists pair of vertex and edge that have degree of membership containing closed interval of real number [0,1] on each node and edge. A graph fuzzy  is connected if the strength of connectedness between nodes u and v larger than zero for each . This paper will be explained about ss-path and ss-distance. Strongest stong path (ss-path) between two nodes in connected fuzzy graph if path is a strongest path as well as strong path. If G is a connected fuzzy graph then for each  there exists a strongest strong path for u to v . While ss-distane between two nodes u and v in connected fuzzy graph as the reciprocal of  the strength of connectedness between nodes u and v. Using metric can be known that every connected fuzzy graph is ss-selfcentered
KONSTRUKSI, SIFAT DAN DIMENSI HIMPUNAN CANTOR MIDDLE THIRD Alfiana, Khoiroh; Khabibah, Siti; Utomo, Robertus Heri Soelistyo
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

This paper discussed about the construction of Cantor middle third set which is formed from unit interval . To construct the Cantor set, take a line and remove the middle third and remain two line segments. This Process is repeated infinite number of times. This process produces some interesting properties on Cantor middle third set, such as has uncountable many elements, contains no intervals, and is compact, perfect, and nowhere dense. By using Hausdorff dimension and self similar set, it discussed the dimension of Cantor middle third set which is a unique positive number
BILANGAN RADIO PADA GRAF GEAR Puspasari, Ambar; Irawanto, Bambang
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Let d(u,v) denote the distance between two distinct vertices of connected graph G, and diam (G) be the diameter of G. A radio labeling c of G is an assignment of positive integer to the vertices of G satisfying  d(u, v) + |c(u) − c(v)| ≥ diam(G) + 1.The maximum integer in the range of the labeling is its span. The radio number of G, rn(G), is the minimum possible span. Radio number of gear graph G’n , for n ≥ 4  is rn(G’n) ≥ 4n + 2, and n ≥ 7 is rn(G’n) ≤ 4n + 2. The labeling of gear graph G’n , n=4,5,6 is rn(G’4) = 18, rn(G’5) = 22, rn(G’6) = 26 than for n ≥ 4 , the radio number rn(G’n) is  4n + 2.
KINERJA SISTEM LUP TERTUTUP DENGAN PENGENDALI LINEAR QUADRATIC GAUSSIAN PADA SISTEM MASSA PEGAS ., Predesia; ., Widowati
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Linear Quadratic Gaussian (LQG) controller is one of the controllers used to stabilize a plant.  The plant is an object that is controlled.  The procedure to find this controller as follows; first, the plant is balanced so that controllability and observability Grammians is equal to square Hankel singular values diagonal matrix, then look for the controller gain and estimator gain that are solutions of Riccati equations.  Next, construct a state space realization of LQG controller.  To verify the performance of  the obtained controller, its was applied for the spring mass system.  Further, by using MATLAB program, the performance of the closed loop system with the LQG controller and the open loop system is compared.  The simulation results show that the closed loop system can be stabilized in less than 10 seconds, whereas the open loop system can be stabilized in 3000 seconds. This indicate that the performance of the closed loop system with LQG controller better than the open loop system

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