Sapto W. Indratno

Inversion of the Laplace Transform from the Real Axis Using an Adaptive Iterative Method

A new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function 𝑓 ( 𝑡 ) is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to 𝑓 ( 𝑡 ) , are proposed in this paper.

Dynamical systems method for solving ill-conditioned linear algebraic systems

A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving Ill-Conditioned Linear Algebraic System (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new iterative scheme for solving ICLAS is proposed. This iterative scheme is based on the DSM solution. An a posteriori stopping rules for the proposed method is justified. This paper also gives an a posteriori stopping rule for a modified iterative scheme developed in A.G. Ramm, Jour. Math. Anal. Appl., Vol. 330 (2007), pp.1338-1346, and proves convergence of the solution obtained by the iterative scheme.

Creating materials with a desired refraction coefficient: numerical experiments

A recipe for creating materials with a desired refraction coefficient is implemented numerically. An error estimate is given for the approximate solution of the many-body scattering problem in the case of small scatterers. This result is used for the estimate of the minimal number of small particles to be embedded in a given domain D in order to get a material whose refraction coefficient approximates the desired one with the relative error not exceeding a desired small quantity.

An iterative method for solving Fredholm integral equations of the first kind

The purpose of this paper is to give a convergence analysis of the iterative scheme: u δ n = qu δ n−1 + (1 − q)T −1 a n K* f δ, u δ 0 = 0, where T := K*K, Ta := T + aI, q ∈ (0, 1), an := α0q n, α0 > 0, with finite-dimensional approximations of T and K* for solving stably Fredholm integral equations of the first kind with noisy data.

A visual formalism for weights satisfying reverse inequalities

In this expository article we introduce a diagrammatic scheme to represent reverse classes of weights and some of their properties.

Study of behavior and determination of customer lifetime value(CLV) using Markov chain model

Customer Lifetime Value or CLV is a restriction on interactive marketing to help a company in arranging financial for the marketing of new customer acquisition and customer retention. Additionally CLV can be able to segment customers for financial arrangements. Stochastic models for the fairly new CLV used a Markov chain. In this model customer retention probability and new customer acquisition probability play an important role. This model is originally introduced by Pfeifer and Carraway in 2000 [1]. They introduced several CLV models, one of them only involves customer and former customer. In this paper we expand the model by adding the assumption of the transition from former customer to customer. In the proposed model, the CLV value is higher than the CLV value obtained by Pfeifer and Caraway model. But our model still requires a longer convergence time.

Estimation of the Basic Reproductive Ratio for Dengue Fever at the Take-Off Period of Dengue Infection

Estimating the basic reproductive ratio ℛ 0 of dengue fever has continued to be an ever-increasing challenge among epidemiologists. In this paper we propose two different constructions to estimate ℛ 0 which is derived from a dynamical system of host-vector dengue transmission model. The construction is based on the original assumption that in the early states of an epidemic the infected human compartment increases exponentially at the same rate as the infected mosquito compartment (previous work). In the first proposed construction, we modify previous works by assuming that the rates of infection for mosquito and human compartments might be different. In the second construction, we add an improvement by including more realistic conditions in which the dynamics of an infected human compartments are intervened by the dynamics of an infected mosquito compartment, and vice versa. We apply our construction to the real dengue epidemic data from SB Hospital, Bandung, Indonesia, during the period of outbreak Nov. 25, 2008–Dec. 2012. We also propose two scenarios to determine the take-off rate of infection at the beginning of a dengue epidemic for construction of the estimates of ℛ 0: scenario I from equation of new cases of dengue with respect to time (daily) and scenario II from equation of new cases of dengue with respect to cumulative number of new cases of dengue. The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans. Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa. We conclude that the second approach is more realistic, compared with our first approach and the previous work.

A comparison of binary and continuous genetic algorithm in parameter estimation of a logistic growth model

Genetic algorithm is an optimization method based on the principles of genetics and natural selection in life organisms. The algorithm begins by defining the optimization variables, defining the cost function (in a minimization problem) or the fitness function (in a maximization problem) and selecting genetic algorithm parameters. The main procedures in genetic algorithm are generating initial population, selecting some chromosomes (individual) as parents individual, mating, and mutation. In this paper, binary and continuous genetic algorithms were implemented to estimate growth rate and carrying capacity parameter from poultry data cited from literature. For simplicity, all genetic algorithm parameters (selection rate and mutation rate) are set to be constant along implementation of the algorithm. It was found that by selecting suitable mutation rate, both algorithms can estimate these parameters well. Suitable range for mutation rate in continuous genetic algorithm is wider than the binary one.

Application of multi response optimization with grey relational analysis and fuzzy logic method

Multi-response optimization is an optimization process by considering multiple responses simultaneously. The purpose of this research is to get the optimum point on multi-response optimization process using grey relational analysis and fuzzy logic method. The optimum point is determined from the Fuzzy-GRG (Grey Relational Grade) variable which is the conversion of the Signal to Noise Ratio of the responses involved. The case study used in this research are case optimization of electrical process parameters in electrical disharge machining. It was found that the combination of treatments resulting to optimum MRR and SR was a 70 V gap voltage factor, peak current 9 A and duty factor 0.8.

A measure for objects clustering in principal component analysis biplot: A case study in inter-city buses maintenance cost data

This article presents the application of the principal component analysis (PCA) biplot for the needs of data mining. This article aims to simplify and objectify the methods for objects clustering in PCA biplot. The novelty of this paper is to get a measure that can be used to objectify the objects clustering in PCA biplot. Orthonormal eigenvectors, which are the coefficients of a principal component model representing an association between principal components and initial variables. The existence of the association is a valid ground to objects clustering based on principal axes value, thus if m principal axes used in the PCA, then the objects can be classified into 2m clusters. The inter-city buses are clustered based on maintenance costs data by using two principal axes PCA biplot. The buses are clustered into four groups. The first group is the buses with high maintenance costs, especially for lube, and brake canvass. The second group is the buses with high maintenance costs, especially for tire, and f...