Coastal areas in the South Coast of West Java Province, Indonesia, have potential to develop marine ecotourism. One specific case is the Pangandaran area which must be transferred into economic value by not damaging natural resources. Marine ecotourism development is not only intended to raise foreign exchange for the local government, but is also expected to play a role in maintaining natural resources sustainably. This research aims to analyze the sustainable synergistic marine ecotourism development model. The method used in this research is the quantitative descriptive method. The quantitative descriptive method is used to describe the general condition of the research area, using primary and secondary data. The technique includes the taking of respondents using accidental sampling as many as 50 respondents, consisting of tourists, public figures, and fishermen who have side jobs as providers of marine ecotourism services. The analysis is carried out through the Rapfish modeling approach to measure the synergistic elements of sustainable development of marine ecotourism. Based on the results of the research the ecological dimension of environmental services are the most influential conditions, the economic dimension of marine ecotourism is a less influential condition. Meanwhile, marine ecotourism technology and the social dimension of marine ecotourism are least influential conditions. In regard to infrastructure and regulatory dimensions, the use of information technology is recommended to promote marine ecotourism optimally. It is also concluded that regulations are needed to establish marine ecotourism zoning rules and infrastructure improvements.

The paper reviews the applications of eigen value in different areas. One of the area is in the analysis of graphs coming from networks. The development of theory regarding the eigenvalues and its maximum eigenvalue of the adjacency matrix arising from a general graph is already well-established. Here we review some notions from different context, i.e. led by observation of some simple experiments regarding the relation between graph, cliques, and the eigen values of the adjacency matrix. We focus on regular graphs having one or more cliques in their graph structures. We do some numerical experiment on the computation of the eigen values of the adjacency matrix and show some patterns on the relation between the structure of the graph (e.g. the maximum cliques, chromatic number) and the eigen values of the adjacency matrix. By observing these patterns we find some conclusion, such as: i. the maximum clique of a complete graph is given by the largest eigen value plus one; ii. the maximum clique of a cycle graph (simple incomplete regular graph) equals the largest eigen value, in which the value is two; iii. the maximum multiplicity of the eigen values of a cycle graph is two. Future direction of the development is also presented based on the careful analysis of the existing development.

Graph is widely used in everyday life especially to describe model problem and describe it concretely and clearly. In addition graph is also used to facilitate solve various kinds of problems that are difficult to be solved by calculation. In Biology, graph can be used to describe the process of protein synthesis in DNA. Protein has an important role for DNA (deoxyribonucleic acid) or RNA (ribonucleic acid). Proteins are composed of amino acids. In this study, amino acids are related to genetics, especially the genetic code. The genetic code is also known as the triplet or codon code which is a three-letter arrangement of DNA nitrogen base. The bases are adenine (A), thymine (T), guanine (G) and cytosine (C). While on RNA thymine (T) is replaced with Urasil (U). The set of all Nitrogen bases in RNA is denoted by N = {C U, A, G}. This codon works at the time of protein synthesis inside the cell. This codon also encodes the stop signal as a sign of the stop of protein synthesis process. This paper will examine the process of protein synthesis through mathematical studies and present it in three-dimensional space or graph. The study begins by analysing the set of all codons denoted by NNN such that to obtain geometric representations. At this stage there is a matching between the sets of all nitrogen bases N with Z ₂ × Z ₂; . By matching the algebraic structure will be obtained such as group, group Klein-4,Quotien group etc. With the help of Geogebra software, the set of all codons denoted by NNN can be presented in a three-dimensional space as a multicube NNN and also can be represented as a graph, so that can easily see relationship between the codon.

Logika matematika adalah sebuah cabang matematika yang merupakan gabungan dari ilmu logika dan ilmu matematika. Logika matematika memberikan landasan bagaimana cara menyimpulkan. Hal yang paling penting dalam mempelajari logika matematika adalah kemampuan dalam mengambil dan menentukan kesimpulan yang benar atau salah. Materi logika matematika yang dipakai di antaranya disjungsi, konjungsi, tautologi, modus ponen. Sementara itu, DNA adalah makromolekul yang menyimpan segala informasi biologis yang sangat berperan dalam kehidupan organisme hidup. DNA tersusun atas tiga macam molekul, yaitu gula pentosa (deoksiribosa), asam fosfat, dan basa nitrogen. Dalam pembentukan DNA, terdapat berbagai proses yang terjadi di antaranya sintesis protein, replikasi DNA, dan proses hibridisasi yang diperlukan untuk membentuk ikatan antara DNA dengan DNA. Dengan logika matematika dan metode perluasan modus ponen pada proses hibridisasi, proses tersebut dapat disederhanakan. Pada artikel ini, dibahas aplikasi logika matematika dalam untai DNA pada proses hibridisasi

Mutations are changes in genetic material that can occur at the level of genes or chromosomes. Mutations at the gene level are structural changes in the genetic code. In this paper we will investigate the necessary and sufficient conditions for an endomorphism called autumorphism. The method used in this research paper is a review of literature conducted by collecting literature from previous studies in accordance with the study discussed. Mathematically, genetic mutations can be viewed with an endomorphism and automorphism f in the vector space which maps the standard genetic code sequence of wild-type genes into mutant genes. In the endomorphism there is a matrix called the endomorphism representation matrix.Keywords: authomorphism, endomophism, mutation Matriks Representasi Endomorfisma Dari Kode Genetik StandarABSTRAKMutasi merupakan perubahan pada materi genetik yang dapat terjadi pada tingkat gen maupun kromosom. Mutasi pada tingkat gen merupakan perubahan struktur dalam kode genetik. Pada penelitian ini akan dibahas syarat perlu dan syarat cukup sebuah endomorfisma disebut automorfisma. Metode yang digunakan dalam makalah penelitian ini adalah tinjauan literatur yang dilakukan dengan mengumpulkan literatur dari penelitian-penelitian sebelumnya sesuai dengan penelitian yang dibahas. Secara matematis, mutasi genetik dapat ditinjau dengan sebuah endomorfisma dan automorfisma pada ruang vektor yang memetakan barisan kode genetik standar gen wild-type ke dalam gen mutan. Pada endomorfisma tersebut terdapat sebuah matriks yang disebut matriks representasi endomorfisma.Kata kunci: Automorfisma, endomorfisma, mutasi GenetikMutations are changes in genetic material that can occur at the level of genes or chromosomes. Mutations at the gene level are structural changes in the genetic code. In this paper we will investigate the necessary and sufficient conditions for an endomorphism called autumorphism. The method used in this research paper is a review of literature conducted by collecting literature from previous studies in accordance with the study discussed. Mathematically, genetic mutations can be viewed with an endomorphism and automorphism f in the vector space which maps the standard genetic code sequence of wild-type genes into mutant genes. In the endomorphism there is a matrix called the endomorphism representation matrix.Keywords: authomorphism, endomophism, mutation Matriks Representasi Endomorfisma Dari Kode Genetik StandarABSTRAKMutasi merupakan perubahan pada materi genetik yang dapat terjadi pada tingkat gen maupun kromosom. Mutasi pada tingkat gen merupakan perubahan struktur dalam kode genetik. Pada penelitian ini akan dibahas syarat perlu dan syarat cukup sebuah endomorfisma disebut automorfisma. Metode yang digunakan dalam makalah penelitian ini adalah tinjauan literatur yang dilakukan dengan mengumpulkan literatur dari penelitian-penelitian sebelumnya sesuai dengan penelitian yang dibahas. Secara matematis, mutasi genetik dapat ditinjau dengan sebuah endomorfisma dan automorfisma pada ruang vektor yang memetakan barisan kode genetik standar gen wild-type ke dalam gen mutan. Pada endomorfisma tersebut terdapat sebuah matriks yang disebut matriks representasi endomorfisma.Kata kunci: Automorfisma, endomorfisma, mutasi Genetik

DNA (deoxyribonucleic acid,) terdiri dari beberapa komponen yaitu gugus gula deoksiribosa, gugus fosfat, dan gugus basa nitogren. Himpunan basa nitrogen dapat ditulis sebagai Kombinasi dari tiga buah elemen membentuk kode triplet (kodon) yang ditranslasikan menjadi asam amino. Dalam pembentukan DNA terdapat berbagai proses yang terjadi yaitu sintesis protein, replikasi DNA, dan proses hibridisasi. Untuk membentuk suatu ikatan antara DNA dengan DNA diperlukan proses hibridisasi.Proses Hibridisasi adalah pembentukan ikatan dupleks stabil antara dua rangkaian nukleotida yang saling komplementer melalui perpasangan basa Nitrogen. Kajian proses Hibridisasi sering ditemui dalam komputasi DNA yang menggunakan sistem Pakar. Paper ini akan mengkaji langkah-langkah yang diperlukan pada proses hibridisasi dalam merepresentasikan aturan hasil perhitungan indeks massa tubuh dengan aturan tertentu.Langkah-langkah tersebut dapat digunakan untuk pengukran gizi dan yang mempengaruhinya