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The purpose of this paper is to investigate the existence, uniqueness, and stability solution to a non-linear system of integro-differential equations by using both methods Picard approximation and Banach fixed point theorem. The existence, uniqueness, and stability theorems are established under necessary and sufficient conditions of closed and bounded domain.

This article presented some theorems on a novel non-linear multiple Integro-differential equations of boundary T-system. It has been studied the numerical-analytic method and Banach fixed point theorem for the existence and approximation of the solutions over considered boundary system in compact space. In this work, we demonstrate that the mention methods can be discussed and analyzed for the existence and uniqueness, of a solution for the vector system. The paper satisfies the Hölder condition.

Endowment insurance with a participating policy is an insurance contract that offers death benefits that increase every year. This paper analyzes a single and monthly premiums of participating policy endowment life insurance using the Vasicek interest rate model. The increase in benefits is highly dependent on the performance of the insurance company's investment portfolio. The model in this study assumes that market interest rates move stochastically following the Vasicek model and the company's investment portfolio follows the geometric brownian motion (GBM) model. This study assumes that the participant is a man aged 30 years and buys an insurance contract for 20 years with non-participation benefits of Rp. 100,000,000.00. As a result, the premium that must be paid by the man is IDR 37,832,555.84 for a single premium and if the insurance participant chooses to pay monthly, the premium is IDR 240,915.59. The insurance premium with a participation policy is influenced by the participation coefficient, the asset volatility of the investment portfolio, the minimum guarantee interest rate and the entry age of the insurance participant.

In this paper we study the existence and uniqueness solution for a first kind fractional Volterra boundary value problem involving Hadamard type and three-point boundary conditions. Our analysis is based on Krasnoselskii-Zabreiko’s fixed point theorem and Banach contraction principle. As an application we discuss a Hadamard type boundary value problem with fractional integral boundary conditions. We emphasize that our results are new in the context of Hadamard fractional calculus and are well illustrated with the aid of examples.

In this paper, we present a novel approach to data-driven neuro-fuzzy modeling, which aims to create accurate monthly inflow and outflow forecast of money (M0) in Bali Province. The data is monthly time series included some religious ceremony identification variables and a monthly dummy variable from January 2011 to March 2019. Well known, Bali Province has unique cultures, the only one province which Hinduism majority religion in Indonesia, and listed as top tourism destination in the world. The neuro-fuzzy models were created using ANFIS architecture and sliding window time series analysis, then simulated using walk forward validation, interpreted using MAPE, and NRMSE. Based on the simulation of the last 24 months, the model of inflow obtained MAPE 23.33% (worth considering) and NRMSE 18.68% (accurate). Meanwhile, the model of outflow obtained MAPE 19.24% (accurate) and NRMSE 8.71% (very accurate). These models and their pieces of information could assist the central bank in Bali Province to prepare cash for money (M0) outflow and managed technic for counting money (M0) inflow.

Agriculture in Bali has profound importance, namely as a natural tourist attraction and is one of the sectors with the most workers absorb as well the largest contributor to regional income for Bali Province. Currently, the agriculture sector in Bali is experiencing the problem of decreasing the workforce due to the reluctance of future generations to continue farming inherited from their families. The purpose of this paper is to identify the factors causing the reluctance of future generations to continue family farming and to study the causality of these factors to the reluctance for continuing family farming. This study uses a variance-based structural equation modeling (PLS-SEM). Internal and external motivation to continue family farming as well the perception of agricultural works are the exogenous variables, and the reluctance to continue family farming is the endogenous variable on the model. The data in this study obtained from interviewing 115 respondents in the Jembrana Regency of Bali. The study’s result justifies that internal factors, external factors, and perceptions of agricultural work influenced the reluctance to continue family farming.

In this paper, it is discussed about giving control variable to dynamic systems to process the spread of viruses on computers. The dynamic model describes the process of spreading viruses on the computer, where susceptible can be instantly removed and infected can instantly become susceptible. And through qualitative analysis on the model is given a control and completed using the Pontryagin Maximum Principle (PMP) method on infected interactions so that the infected computer can be minimized. Dynamic models that have been given control are simulated using MATLAB software and the results show the infected computer is reduced enough significan.

Influence of radiation and non-uniform heat source on unsteady, magneto-hydrodynamic free convection flow of viscous incompressible fluid past an infinite vertical heated plate embedded in porous medium of an optically thin environment with time dependent suction and viscous dissipation is investigated in this paper. Analytical solutions of the coupled non-linear equations are obtained for the velocity field and temperature distribution using oscillating time-dependent perturbation technique. Expressions for skin-friction and heat transfer rate are also derived. The effects of the material parameters on velocity, temperature, skin-friction, and rate of heat transfer are discussed quantitatively.

The characteristics of a function are usually investigated by looking at the continuity of the function. But what happens if a function does not have continuous properties? To what extent can the characteristics of continuous function be maintained for discontinuous cases? The stochastic function that is widely involved in solving problems in the field of average financial mathematics is a discontinuous function. This is reflected by the acquisition of a smooth curve from the modeling drawing obtained. Today, the nature of continuous functions in [a, b] has been widely studied and developed. Some properties of the continuous function can be extended to the appropriate discontinuous function. In this paper, there will be some integral reviews for discontinuous functions which are closely related to stochastic functions.

In this article, we established the existence, uniqueness and stability solutions for a nonlinear system of integro-differential equations of Volterra type in Banach spaces. Krasnoselskii Fixed point theorems and Picard approximation method are the main tool used here to establish the existence and uniqueness results. A simple example of application of the main result of this paper is presented.

Ordinary differential equation is one form of differential equations that are often found in everyday life. One form of ordinary differential equations which has non–constant coefficients is the Cauchy–Euler differential equation. In the nonhomogeneous Cauchy–Euler differential equations, the undetermined coefficient and the parameter variation were the most method that often used to find the particular solution. This paper aimed to show a new solution that was shorter than the previous methods for nonhomogeneous Cauchy–Euler differential equations with the right side was a logarithmic form. The new solution had been proven to produce the same solution as the ordinary solution sought using the undetermined coefficient method.

In the inventory system is given operational policies relating to product inventory control, such as how much is ordered, when to order with the aim of minimizing storage and ordering costs. Customer demand and lead time affect the inventory system. This study aims to determine the densitas distribution of demand data, total inventory costs and optimal coconut supply for the two order periods using the stochastic inventory model. Stochastic inventory models can be used if there is variable uncertainty. This paper discusses the optimization of coconut inventories using a stochastic model with uncertainty about demand and lead time. It is known that demand data is uniformly distributed, based on the realization value of random variable requests can be formed in 49 scenarios. Obtained an optimal total inventory cost for the two planning periods is Rp. 45,672,910, optimal supply for period one was 26031 coconuts. Inventory levels in two period for any scenarios are

In this paper, a model of the spread of computer viruses with security classification and nonlinear infection rates is formulated. From the short analysis, is found that the model does not have a virus-free equilibrium point. This show that the virus will always exist in the system and increasingly that can not be avoided. Therefore, control strategy by installing antivirus on subpopulation susceptible low-security level and infective subpopulation aims to minimize the number of infective computers, and minimize the cost related to these strategies. Hence, an important tool, in this case is, optimal control theory. The system solved numerically by using Forward-Backward Sweep method in combination with the fourth-order Runge-Kutta method. Based on the simulation results, the combination of the two controls is effective in suppressing the spread of computer viruses. However, controlling by installing an antivirus on an infected computer has a great influence in suppressing the spread of the computer virus.

In this paper we determine the total edge irregularity strength of , that is a complete graph in which one of its edge has been removed. To do so, we make three cases. In two cases, the labelling of equals to the labelling of the complete graph such that no re-labelling is necessary. Meanwhile, the third case could not happen. As a result, the total edge irregularity strength of equals to the total edge irregularity strength of Kn

This paper presents a unit-linked insurance which is a modern insurance. The policyholders will get benefits of insurances and investment. The aim of this research is to analysis of unit link insurance products in Indonesia. Especially to analysis the mortality cost, premium, return, and profit of the product. The method used is a stochastic profit testing method and the results of the study show that mortality cost offered by the three unit link companies selected as the sample of this study are greater than the insurance costs calculated based on the Indonesian Mortality Table. From comparing different unit linked insurance plans, only one plan is sufficient to fund the guarantee. While others have to do a Top-up premium.

A Four-tank system is a multi-input multi-output (MIMO) system consisting of four interconnected water tanks and two pumps. This paper deals with the control design of the four-tank system using model predictive control (MPC) based filter Kalman. The objective of the control design is to regulate the output of the system towards the desired values. In this work, the optimal control to the system is determined by means MPC controller where both output and input constraints to the system are explicitly considered. The filter Kalman is used to estimate the state of the system. Simulations by using Matlab are performed to verify the performance of the proposed control design. Simulation results show that the proposed control design can regulate the output of the system towards the desired values.

Temperature is an important factor in the production of agricultural commodities. For this reason, goverments needs to protect farmers in order to continue their farming. Climate-based agricultural insurance is an alternative to climate-related risk management. Insurance premium is given when the temperature index lower than the pre determined trigger index. The purpose of this study is to determine the stages and assumptions in determining the value of agricultural insurance premiums based on surface temperature index on cocoa commodities using the method of burn analysis. The temperature index was determined using the burn analysis method with the temperature as the climate parameter. Trigger values ??are determined based on long run times. In this paper, the result is that when the temperature index lower than the determined trigger value, trigger payments as much as Rp.10.931.960,40 / Ha based on trigger index as many 26.145 ° C, so amount of premium payment equals Rp 215.776.

Development of human causes the increasing of the demand of energy for living. Sea wave energy is one of the alternative energy sources which is renewable and sustainable, no impact on environmental pollution. The goal of this paper is to simulate the level of water wave using shallow water equation for generating energy oscillating water column. The solution of the equation is approximated using LaxFriedrich scheme and will be compared with the analytic solution in standing wave problem. Simulation is used to obtain the results of the energy in the form of electrical power generated by ocean wave. The results of the error of numerical validation is obtained 0.32%. Moreover, the results of the potential energy depend on the height of the surface waves is found 1574.46 Watts the average of water level is 0.881 meters.

This paper introduces the joint life satatus for married couples with independent and dependent mortality models. Using Frank copula and Indonesia Life Tables 2011, we evaluate the impact of dependent future lifetimes on the net single and level premium. The results show premium rates are reduced if models of dependent future lifetime are used compared to the models using an assumption of independence.

In this paper we determine the total edge irregularity strength of , that is a complete graph in which one of its edge has been removed. To do so, we make three cases. In two cases, the labelling of equals to the labelling of the complete graph such that no re-labelling is necessary. Meanwhile, the third case could not happen. As a result, the total edge irregularity strength of equals to the total edge irregularity strength of Kn

Blurring is one of the basic image processing technique in order to reduce the noise in a image. In this paper two methods of blurring which are called mean and weighted average method will be elaborated. Three different sizes of mask (3 × 3, 5 × 5 and 7 × 7) are given for each method. Moreover, three different of resolution images 1000 × 1000, 700 × 700, and 400 × 400 pixels are used. From the experiment result, the output image by mean method is shown a darker than the weighted average method. Additionally, run time of CPU using mean method is around 77.78 % shorter than weighted average method.

Holding option contracts are considered as a new way to invest. In pricing the option contracts, an investor can apply the binomial tree method. The aim of this paper is to present how the European option contracts are calculated using binomial tree method with some different choices of strike prices. Then, the results are compared with the Black-Scholes method. The results obtained show the prices of call options contracts of European type calculated by the binomial tree method tends to be cheaper compared with the price of that calculated by the Black-Scholes method. In contrast to the put option prices, the prices calculated by the binomial tree method are slightly more expensive.

Binomial tree is a method that can be used to determine price option contracts. In this method, the stock price movement is presented in the form of a tree with each branch representing the probability of the stock price to move up or move down. The purpose of this paper was to determine the price of the options contracts with the American type on Binomial Tree method and compare the three methods that is variance matching, proportional , and risk neutral of determining the value of price option contracts used in Binomial Tree method with Black-Schole method. The result of this research was the value of the options contract using the variance matching more similar with the value of the Black-Scholes contract.

One of multivariate analysis application was used to see the relationship between two or more quantitative variable and objects within. Multivariate analysis which used in this case is correspondence analysis. This paper will be done correspondence analysis application in order to see the characteristic of tourism business in Bali. In this study it can be seen the characteristic of tourism business in Bali in a form of illustration of tourism business situation of each regencies which mapped in two dimensional plots. The result was Karangasem, Buleleng, Gianyar, Jembrana, Tabanan, and Klungkung were in a group because they have the same development of tourism area business and accommodation service business. However tourism business that was developed in Denpasar and Badung was tour and travel and food and beverage business.

Pension plan is an effort to anticipate the life of old on the day. In the pension program, there are two methods of normal due’s calculation to be paid by the insured each year, the Entry Age Normal method, namely calculation of normal dues with constant premiums and projected unit credit method, namely calculation of normal dues with Premium Increases Each year or is not constant. This paper wants to develop an inconstant premium calculation method with constant premium increase annually. Where the pension plan participants’ age when he joined the pension plan is 19 years and the retirement age on this contract is 55 years, with premium increases of 5% of the normal dues early. The large ratio of premiums is, for dues normal at the age of 19 years until the age of 28 years, but for dues normal at the age of 29 years to the age of 33 years and to normal dues at the age of 34 years old until the age of one year before retirement.

The aim of this paper is to forecast the numbers of Australian tourist to Bali using multivariate fuzzy time series method (MFTS). MFTS method is development from fuzzy time series (FTS). The defferent betwen FTS and MFTS method is showed by factor in used. In FTS method using one factor, but in MFTS method using more than one factor. In this peper there was three factor used in this research, it was number of Australian tourist, Indonesian Inflation, and change rate of AUD to IDR. At the beginning, the speed of each factor was calculated. For each factor given weight, 0,999 for numbers of Australian tourist, -0,90 for Indonesian inflation, and 0,21 for change rate of AUD to IDR. The result showed that Australian tourist at July 2014 would visit Bali as much 91.056 tourist, with average error rate 6.87%.

This paper aimed to determine long-run equilibrium the tourist arrivals, inflation, exchange rate and gross domestic regional product (GDRP) of Bali Province used Johansen’s cointegration test. First examined whether each stationary variables using augmented dickey fuller (ADF) test. ADF test showed GDRP of Bali, tourist arrivals, and exchange rate are not stationary, so it is assumed stationary in first lag or I(1). While inflation is stationary in level or I(0). Johansen’s cointegration test showed the tourist arrivals, inflation, exchange rate and GDRP of Bali are not cointegrated. Notice that there is no long-run equilibrium, it can not be concluded for structural equation models.

This paper aimed to elaborates and compares the performance of Fuzzy Time Series (FTS) model with Markov Chain (MC) model in forecasting the Gross Regional Domestic Product (GDRP) of Bali Province. Both methods were considered as forecasting methods in soft modeling domain. The data used was quarterly data of Bali’s GDRP for year 1992 through 2013 from Indonesian Bureau of Statistic at Denpasar Office. Inspite of using the original data, rate of change from two consecutive quarters was used to model. From the in-sample forecasting conducted, we got the Average Forecas­ting Error Rate (AFER) for FTS dan MC models as much as 0,78 percent and 2,74 percent, respec­tively. Based-on these findings, FTS outperformed MC in in-sample forecasting for GDRP of Bali’s data.

One of functions of multivariate analysis is to group data. Multivariate analysis often used in grouping data are cluster analysis and biplot analysis. In this paper, a comparative analysis will be made between clusters analysis and biplot analysis for grouping the data. Technique used in the cluster analysis is k-mean method and biplot analysis used two-dimensional display. The results ware that biplot analysis produces are better in grouping accuracy than clusters analysis. But in general, biplot analysis can not be said to be better than clusters analysis in grouping the data and vice versa.

The Poisson regression analysis is one of the regression methods used for count data and has the assumption of equidispersion. However, it is the overdispersion and then underestimate standard errors will be obtained. If the data are overdispersed and more data is zero then ZIP (Zero Inflated Regression) regression is used. ZIP regression model is more appropriate to be used to analyze the amount of Senior High School/Madrasah Aliyah who do not pass the exam with five independent variables, because a lot of data failure is zero. In this paper, data are overdispersed on Poisson regression, so ZIP regression are used. ZIP regression models obtained are only influenced by the proportion of Senior High School/Madrasah Aliyah classroom were damaged (X3), is and .