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Measles is an acute highly contagious disease caused by Paramyxovirus. Measles is considered as a dangerous disease because it cause complications, brain and other organs damage, lifelong disability, paralysis and even death. In the previous studies, it was known that the spread of measles highly dependent on number of infected individuals so it is necessary to control measles through treatment. In this paper, we study about the application of the optimal control theory on the system of differential equations of the SIR endemic model. Determination of the optimal control is obtained through the application of the Pontryagin minimum principle. The main target in this paper is to find a unique optimal control where the optimal control can be described as an efficiency rate of treatment in individuals infected with measles to decrease the number of infected individuals.

Sequence spaces is one of interesting topic of analysis research. Some of that are convergent and bounded sequence. In this paper we define some releated BK spaces (????,?????)?, (????,?????), dan (????,?????)0 some characteristics releated to them. Moreover we determine their ?-dual.

A ternary semiring is an additive commutative semigroup with a ternary multiplication which satisfying some condition. This paper will be discuss about prime bi-ideal radikal in semiring ternary with definition and some theorem. If B is a bi-ideal in semiring ternary T, then radical prime bi-ideal of B in semiring ternary T is an intersection of all prime bi-ideal in semiring ternary T which containing B.

The data obtained in banking and financial research is often in the form of panel data, while panel data is a combination of cross section and time series data. The aim of this paper is to apply panel data regression analysis to obtain an appropriate model. The case taken is the analysis of the influence of the ratio of Loan to Deposit Ratio (LDR) and Non Performing Loan (NPL) to the Return On Assets (ROA) of Bank for Regional Development (BPD) in Indonesia in the period 2012 to 2016. From the model specification test results obtained that the fit model is the Fixed Effect Model (FEM). The empirical test result between individual and time effect showed that fit model is is individual effect model, i.e. slope coefficients constant but the intercept varies across 20 bank of BPD samples. The main LDR and NPL variables have no significant effect on ROA. While individual Bank BPD which has significant effect on ROA is BPD of DIY, BPD of Central Sulawesi, BPD of Southeast Sulawesi BPD of West Java BPD, BPD of East Java, and BPD of South Kalimantan.

HIV/AIDS is a very dangerous disease. The transmission of HIV/AIDS can be in three ways and one of them through a syringe. In this paper we describe SIR and SEIR Host-Vector model transmission of HIV/AIDS amongst populations of injecting drug users. From the existing model we obtained disease-free equilibrium point and endemic equilibrium point. Then we study the stability conditions and sensitivity analysis of the . The analysis shows if then the disease-free equilibrium point is stable and if then the endemic equilibrium point will be stable. We also obtained that parameter of probality host-vector infected with HIV/AIDS affects the increase of number infected HIV/AIDS. Keywords: HIV/AIDS, Host-Vector Transmission, The Stability of Equilibrium Point.

Abstract: Rizza-negativity of holomorphic vector bundle is a sufficient condition for the negativity of . In the present paper, we shall discuss that as a special case, using the Rizza metric which is derived from a Hermitian metric also implies the negativity of . Further we showed that for the negative holomorphic vector bundle there is a pseudo-convex Finsler metric with negative curvature. Keywords: Hermitian metric, Rizza metric, Rizza-negativity.

The object of the present paper is to initiate the study contact CR- submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric semi metric connection. For this, some properties of CR- submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric semi metric connection are investigated which conclude that CR- submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric semi metric connection exists with respect to the ?????horizontal and ?????vertical.

Songket is one of the Indonesian arts and culture into community characteristics Palembang. Palembang songket motifs influenced by Islamic culture, in general, Palembang songket motifs shaped flowers. In this paper are given motif fractal Palembang songket motifs Sadum Tumpal Ulos. This motif is formed from the set of Julia with , with z = a + ib and n = 5.5; n = 6 and n = z.

Mangrove forest or known as bakau forest is important forest as a natural wave barrier or tsunami wave mitigation. Some advantages of mangrove forest to reduce the water waves are already studied. Mangrove forest in north coast of Bali’s island, Buleleng regency, Indonesia is in damaged condition. The aim of this paper is to present the importance of mangrove forest as the water wave mitigation in numerical simulation point of view. Moreover, the results also show the effect of tsunami propagation to the coastal area with and without mangrove resistance. Here, the nonlinear shallow water equations are used to govern the model of numerical simulation.

This paper is study about the existence of ethnomathematics on the Bali woven handicraft. Ethnomathematics is mathematics that grow and develop in a particular culture. Unconsciously, the society use tesselation concepts in making woven handicraft. A tessellation is a special type of pattern that consists of geometric figures that fit without gaps or overlaps to cover the plane. The existence of ethnomathematics on woven handicraft can be used as a source of learning and of course can make learners better understand how their cultural relate with mathematics.

This paper shows the initial research about the design of optimal investment policy of the public company in resource conservation, by using optimal control model. The mathematical bioeconomics model in using of mathematical modeling for resource conservation is a dynamics problem. The successfull of resource conservation management must fully take account of the time dimension for sustained equilibrium bioeconomics. The design of a dynamic optimization model is solved by optimal control strategy via maximum principle Pontryagin of Hamiltonian expressi. We have the conclusion that the optimization of present value for resource conservation very dependent of time domain, how long stock optimal can be sustained for is given initial stock.

The aim of this paper is to determine a new location of junior high school at Klungkung, using Fuzzy Subtractive Clustering Algorithm. The new location of the junior high school is depending on the graduate number of elementary school, the distance between location of candidates, and distance between the candidates’ location and existing junior high school. To measure the distance, it is used an Euclidean distance. At the beginning of calculation, the locations of elementary schools are used as the location candidates. Then, the density value of each location candidates is calculated using Fuzzy Subtractive Clustering Algorithm. The location candidate which has the highest density will be chosen to become a starting location. The results of calculation show that the location candidate at 8°32'5.70"S, 115°24'20.64"E has the highest density value, it is at SD Negeri 1 Semarapura Kangin. So the location for the new junior high school is at around SD Negeri 1 Semarapura Kangin.

Kejadian ekstrim pada bidang finansial pada periode 2008/2009 telah menyadarkan para praktisi maupun peneliti di bidang finansial untuk mengevaluasi kembali teknik-teknik pemodelan risiko finansial. Ini menegaskan bahwa diperlukan model-model matematika atau teknik pemodelan yang lebih baik di bidang manajemen risiko finansial yang dapat mengatisipasi adanya kejadian-kejadian yang jarang muncul seperti pada periode tahun tersebut di atas. Metode yang paling sesuai dalam menangani kejadian kejadian ekstrim seperti ini adalah Extreme Value Theory (EVT). Dalam pemodelan Value at Risk(VaR), tingkat pengembalian (return) suatu data finansial biasanya ditaksir menggunakan suatu pendekatan yang mengasumsikan bahwa data tersebut terdistrubusi secara normal. Namun asumsi ini tidak merefleksikan perilaku nilai return yang sesungguhnya, sebab distribusi data finansial menunjukkan adanya ekor distribusi yang lebih gemuk (heavy-tail), yaitu ekor distribusi turun lebih pelan dibandingkan dengan ekor distribusi normal. Ini berarti peluang munculnya nilai ekstrim lebih besar. Sehingga pendekatan secara konvensional dianggap mengabaikan nilai-nilai ekstrim ini. Paper ini membahas penerapkan EVT pada data finansial. Kemudian menghitung nilai VaR dinamis dari nilai indeks IHSG (Jakarta Stock Exchange) periode 28 Desember 2007-28 Desembar 2012. EVT dipakai untuk memprediksi VaR statis dan EVT-GARCH(1,1) dipakai untuk memprediksi VaR dinamis.

It is common in practice to evaluate the correctness of an assumed linear regression model by conducting a model-check method in which the residuals of the observations are investigated. In the asymptotic context instead of observing the vector of the residuals directly, one investigates the partial sums of the observations. In this paper we derive a functional central limit theorem for a sequence of residual partial sums processes when the observations come from heteroscedastic spatial linear regression models. Under a mild condition it is shown that the limit process is a function of Brownian sheet. Several examples of the limit processes are also discussed. The limit theorem is then applied in establishing an asymptotically Kolmogorov type test concerning the adequacy of the fitted model. The critical regions of the test for finite sample sizes are constructed by Monte Carlo simulation.

This paper aims to model and determine the service cycle completion time of noncyclic fork-join queueing networks with infinite buffer capacity, using max-plus algebra. The finding show that the dynamics of the noncyclic fork-join queuing networks with infinite buffer capacity can be modeled into a matrix equation over max-plus algebra. We can also show that the service cycle completion time of queuing networks is a max-plus eigenvalues of the matrix in the equation.slklsklslsllsllllllllllllllllllllll

Control diffusion processes has been found in a wide field of applications as in stochastic optimal control and in mathematical finance via the theory of hedging and nonlinear pricing theory for imperfect markets. In this paper we discuss the control diffusion process with time and space dependent coefficients and local Lipschitz continuity of the drift. The results show that the controlled process Xs;;u t is independent of control u for a constant.