Judul: Biological Pest Control Strategies using Sterile Insect Technique and Natural Enemies
Abstrak: Indonesia adalah negara agraris sehingga pertanian memiliki peranan penting bagi Indonesia. Oleh sebab itu, masalah yang berkaitan dengan pertanian seperti serangan hama selalu menjadi topik yang penting pula. Pestisida kimia banyak digunakan dalam pengendalian hama ini, namun pestisida kimia memiliki banyak dampak negatif bagi lingkungan. Pengendalian Hama Terpadu (PHT) dikembangkan untuk mengurangi penggunaan pestisida kimia. Teknik dalam PHT yang digunakan pada karya ilmiah ini, yaitu SIT (Sterile Insect Technique) dan musuh alami. Dalam karya ilmiah ini, dilakukan pemodelan kontrol optimum untuk mengoptimalkan kepadatan populasi tanaman menggunakan strategi pelepasan serangga hama steril dan penambahan musuh alami ke area lahan tanaman sebagai variabel kontrolnya. Prinsip maksimum Pontryagin digunakan dalam penentuan syarat perlu optimalitas dan metode Runge-Kutta orde 4 serta backward-forward sweep method digunakan untuk mengetahui solusi numeriknya., Indonesia is an agricultural country, so agriculture has an important role for Indonesia. Therefore, problems related to agriculture, such as pests, always be an important topic. Chemical pesticides are highly used in controlling these pests, however chemical pesticides have lots of negative impacts on the environment. Integrated Pest Management (IPM) was developed to reduce the use of these chemical pesticides. There are techniques of IPM that are used in this paper, i.e. sterile insect technique (SIT) and natural enemies. In this paper, the optimum control modelling was carried out to optimize the density of the plant population using the strategy of releasing sterile insect pests and adding natural enemies to the crops area as control variables. Pontryagin’s maximum principle is used in determining the requirements for optimality, fourth-order Runge Kutta method and backward-forward sweep method are used to determine the numerical solution.
Keyword: optimal control, fourth-order Runge Kutta method, natural enemies, Pontryagin’s maximum principle, sterile insect technique

Judul: Masalah Kontrol Optimum Hama Secara Hayati
Abstrak: Pests are species that can attack crops and interfere farming activity. Effort to reduce the effect of pests is necessary. It can be accomplished either by chemical control through insecticides or by biological control using natural enemy intervention. In this work, pest control effort is formulated by a mathematical model, i.e., an optimal pest control problem. The primary objective of this work is to determine control strategies which maintain the density of the pest population in the equilibrium level below economic losses. Two-step control strategy is proposed by using the combination of chemical and biological controls; in the first step to speed-up pest reduction, and solely by using the biological control in the second step to maintain the admissible level. The control strategy is then applied to a predator-prey model which involves Anticarsia gemmatalis as a pest to soybean and Geocoris sp. as a natural enemy. It shows that the admissible level of 20 pest/m2 can be attained and maintained subsequently.
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Judul: Konstruksi Hukum Grup Kurva Eliptik Atas F3m
Abstrak: Elliptic curves upon F3m can be divided in two cases, i.e. supersingular and nonsupersingular case. Based on group laws on elliptic curves, a new arithmetic upon F3m can be formulated as an addition process of two random points on the curve. This addition process can then be applied to the ElGamal algorithm.
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