Jurnal Ilmiah Matematika dan Terapan
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PEMODELAN WAKTU TUNGGU PENUMPANG PADA JALUR ANGKUTAN DALAM KOTA PALU MENGGUNAKAN ALJABAR MAX-PLUS
Full text linkPassenger waiting time is the time required by passengers starting from the stops until getting transport. The purpose of this research is to get the model of waiting time passengers on the freight line in the Palu city. The first step is the preparation of directed graphs based on the existring routes, then calculate the mileage and travel time using synchronization rules and power algorithm with initial vector = 0 obtained the value = 2, = 1 and = 102by using the appplication rock Scilab 5.5.2 and Map-Plus Toolbox obtained eigenvalues as the departure period of 102 and eigenvektor as the initial departure time.Keywords : Eigenvalues, Eigenvectors, Max-Plus Algebra, Waiting Time
POTRET KESEHATAN MASYARAKAT DI KOTA PADANG DENGAN METODE WAJAH CHERNOFF
Full text linkChernoff Face Method is a method used to represent multiple variable data in the form of a cartoon face with 20 specific facial features. In this study, we will show how the use of the Chernoff face method to see a portrait of public health in the city of Padang. Health indicators will be paired with specific facial features of Chernoff's face using Principal Component Analysis (PCA). The results of this study are expected to provide an overview of public health protection for each sub-district in Padang City and Padang City as a whole. Keywords : Chernoff Face Method, Health Indicators, Principal Component Ananlysis
DIMENSI PARTISI GRAF THORN DARI GRAF RODA W3 DAN W4
Full text linkLet = (, ) be a connected graph and ⊆ (). For a vertex v ∈ V(G) and an ordered k-partition Π = {1 , 2 , … , } of (), the representation of v with respect to Π is the k-vector (| = ((, 1), (, 2), . . . , (, )), where d(v,Si) denotes the distance between v and Si. The k-partition Π is said to be resolving if for every two vertices , (), the representation (|П) (|Π). The minimum k for which there is a resolving k-partition of () is called the partition dimension of , denoted by (). The wheel graph + 1 vertices with () = {0, 1, . . . , }. Let 2 ,2 ,… ,be non-negative integers, ≥ 1, for {0,1,2, . . . , }. The thorn graph of the graph Wn, with parameters 0 ,1 ,… , is obtained by attaching li new vertices of degree one to the vertex vi of the graph Wn. The thorn graph is denoted by ℎ(,0 ,1 ,… ,). In this paper we give the upper bounds for the partition dimension of 3 and 4 denoted by (ℎ(3 ,0 ,1 ,2 ,3 )) and (ℎ(4 ,0 ,1 ,2 ,3 ,4 )). Keywords : Partition Dimension, Resolving Partition, Thorn Graph, Wheel Graph
KENDALI OPTIMAL MODEL PENYEBARAN PENYAKIT BLOOD DESEASE BACTERIUM (BDB) PADA TANAMAN PISANG KEPOK DENGAN INOKULASI BAKTERI ENDOFIT
Full text linkBanana plants are the most widely grown plants in Indonesia. In its growth period, banana plants can experience an attack of the disease Blood Desease Bacterium (BDB) caused by Ralstonia solanacearum Phylotipe IV which is the main cause of the loss of banana yield in Indonesia. BDB can cause plant death and crop failure. To represent this phenomenon a mathematical model was developed to reperents the spread BDB of Kepok banana plants by inoculating endophytic bacteria. Adapted 2 SEI epidemic models for banana and SI plant populations for the insect population trigona spp. The SEI model of banana population is divided into 3 subclasses, namely the BDB susceptible population class (ℎ), exposed population class (ℎ), and population class infected with BDB disease (ℎ). It was also observed the class of banana population that received treatment ( ). This group was a class of banana population that was given endophytic bacteria. The SI model was adapted for the insect population trigona spp. which are grouped into 2 subclasses, namely the vulnerable population class to infect BDB ( ), and the population class is ready to infect BDB ( ). Analysis of the stability of the model is carried out at a critical point then an optimal control of the spread of BDB disease through inoculation of endophytic bacteria is carried out. Controlling the rate of suppression of BDB transmission in bananas is done by keep the β parameters (isolates of endophytic bacteria inoculated into banana plants) for the purpose of reducing the incidence of BDB in banana plants. The simulation are carried out for optimal control design, using the principle of minimum Pontryagin, optimal solutions are obtained which show that controlling BDB disease with endophytic bacterial inoculation is said to be successful because it can reduce the number of infected banana plant populations.Keywords : BDB Disease, Endophytic bacteri, Inoculation, Ralstonia Solanacearum Phylotipe IV , Trigona spp., The Minimum Principle of Pontryagin
TEOREMA KONVOLUSI PADA TRANSFORMASI FOURIER FRAKSIONAL QUATERNION SISI KIRI DAN SIFAT-SIFATNYA
Full text linkFourier transform (FT) is growing very rapidly and applying in various fields such as analyzing and decomposing signals in the frequency domain. FT has been extended to quaternion algebra known as the Quaternion Fourier Transform (QFT). The purpose of this paper are to formulate the definition and properties of the left sided Quaternion Fractional Fourier Transform (QFFT), to formulate the definition and convolution theorem for left sided QFFT. Firstly, the results showed the formulation of the left sided QFFT definition and some of the properties such as linearity, translation, modulation and scalar. Secondly, its showed the formulation of convolution theorem for left sided QFFT and also the left sided QFFT of conjugate and translation convolution
MODEL PENGENDALIAN ALAMI PENYAKIT EMBUN JELAGA OLEH JAMUR CAPNADIUM SP PADA TANAMAN CENGKEH MENGGUNAKAN KUMBANG HELM CYCLONEDA SPP SEBAGAI PREDATOR KUTU DAUN (COCCOUS VIRIDIS GREEN
Full text linkSoot dew disease is one of the clove plant diseases caused by fungi Capnadium sp. fungus Capnadium sp living on filth of aphids Coccous Viridis Green. The fungus is spread by vectors of black ants that exist on a clove vulnerable. To control the disease naturally, people utilize the helmet beetles Cycloneda spp as a pest predator of aphids Coccous Viridis Green. The mathematical models that represent the natural control of the disease was adapted from the SI model. The model provides 9 exiting critical points which describes the state of the system. The results of the stability analysis of the critical points using the method of Linearization and Routh-Hurwitz shows that there are 4 disease-free critical points such that the solution can be maintained in the neighbourhood of the critical points. All endemic critical points are unstable such that the solution will leave the critical points. Simulation at the endemic critical points indicates the existence of helmet beetles Cycloneda spp population that able to suppress the spread of this disease by preying aphids Coccus Viridis Green.Keywords : Dew Soot, Helmet Beetles, Aphids, Mathematical Models
PENERAPAN METODE FUZZY MAMDANI UNTUK MEMPREDIKSI JUMLAH PRODUKSI KARET (STUDI KASUS: DATA PERSEDIAAN DAN PERMINTAAN PRODUKSI KARET PADA PTP NUSANTARA XIV (PERSERO) KEBUN AWAYA, TELUK ELPAPUTIH, MALUKU-INDONESIA)
Full text linkGood corporate management will determine the development of a company. In addition, the necessary production planning is also required to achieve maximum profit. This study uses data from PTP Nusantara XIV (Persero) Awaya Garden, Teluk Elpaputih, Maluku Province Indonesia, which is engaged in the production of raw rubber. This research uses Fuzzy Mamdani method to predict the amount of rubber production based on the demand data, inventory and production of rubber per day in April 2016. From the research result obtained the exact amount of rubber production with the percentage of truth value equal to 87,83% and the resultant error is 12,17%.Keywords : Demand, Fuzzy Logic Mamdani Method, Inventory, Production
ANALISIS MODEL ANTRIAN MULTIPLE CHANNEL MULTIPLE PHASE SERVICE DALAM PROSES PEMBUATAN KARTU MAHASISWA (KTM) PADA BANK BNI UNTAD
Full text linkThe queue is a common situation that is common in our daily lives as consumers waited in front of the booth to get a turn to the service or service facilities. One example is the manufacture queue Student Identity Card (KTM) Tadulako in Bank BNI UNTAD. The purposes of this research is to analyze the characteristics of the making of queue Student Identity Card (KTM) Tadulako in Bank BNI of UNTAD. By calculating the probability were no queues (0 ),the average customer in the queue (),the average customer in the system ( ),the average waiting time for customers in the queue (Wa ),the average time waiting for customers in the system (W ). The results showed that the model type of queue that is used in the manufacture of Student Card (KTM) Tadulako in Bank BNI UNTAD is a model of multiple channels-multiple phase (M / M / S) with a Poisson arrival pattern distribution and exponential distribution service time. The analysis shows the performance characteristics of a queuing system manufacture KTM BANK BNI of UNTAD can be said to have been effective, because of the steady state in each stage. On Wednesday, the value of (0 ) at CS is 0,145 and the teller is 0.8879,for the value of () in CS is 1.8821 and the teller customer is a customer 0.0004 tothe value ( ) 3.4948is the customer, to the value of (Wa ) on CS is 33.5373 minutes and the teller was 0.0075 minutes, to the value of (W ) is 74.1952 minutes. On Thursday, the value of (0 ) on CS was 0.121 and the teller is 0.8837,for the value of () in CS is 2.4998 and the teller customer is a customer 0.0005 tothe value ( ) 4.1918is the customer, to the value of (Wa ) on CS is 42.4061 minutes and the teller was 0.0081 minutes, to the value of (W ) is 71.1808 minutes.Keywords : Exponential Distribution, Poisson Distribution, Queue Multi Phas
KONTROL OPTIMAL PADA PEYEBARAN TUBERKULOSIS DENGAN EXOGENOUS REINFECTION
Full text linkTuberculosis is a disease caused by Mycobacterium tuberculosis. Tuberculosis can be controlled through treatment, chemoprophylaxis and vaccination. Optimal control of treatment in the exposed compartment can be done in an effort to reduce the number of exposed compartments individual into the active compartment of tuberculosis. Optimal control can be completed by the Pontryagin Maximum Principle Method. Based on numerical simulation results, optimal control of treatment in the exposed compartment can reduce the number of infected compartments individual with active TB.Keywords : Exogenous Reinfection, Optimal Control, Pontryagin's Maximum Principle, Spread Of Tuberculosis
KONDISI MINIMAL IDEAL KIRI TERURUT PADA SEMIGRUP TERNER TERURUT PARSIAL
Full text linkTernary semigroups is obtained from a nonempty set that given a mapping with a multiplication operation ternary that satisfied closed and associative properties. So, generally a ternary semigroup is an abstraction of a semigroup structure. Meanwhile, partially ordered ternary semigroups is an ordered semigroup that satisfies the properties for each , , , ∈ if ≤ then () ≤ () and () ≤ (). In a ternary semigroups there is also concept of left ideals. This study was conducted to examine the characteristics of ordered left ideals on partially ordered ternary semigroups. Furthermore, it will be discussed about the characteristics of minimal ordered left ideals on partially ordered semigroups.Keywords : Ternary Semigroups, Ordered Ternary Semigroups, Left Ideals, Ordered Left Ideals, Minimal of Ordered Left Ideals