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Ema Carnia
Departemen Matematika, FMIPA, Universitas Padjadjaran
Agriculture, Biological Sciences & Forestry Arts Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Mathematical Model of Iteroparous and Semelparous Species Interaction Hasibuan, Arjun; Supriatna, Asep Kuswandi; Carnia, Ema
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i3.16447

Abstract

A species can be categorized based on its reproductive strategy, including semelparous and iteroparous. Semelparous species is a species that reproduces only once in its lifetime shortly before dying, while iteroparous species is a species that reproduces in its lifetime more than once. In this paper, we examine multispecies growth dynamics involving both species categories focusing on one semelparous species and one iteroparous species influenced by density-dependent also harvesting in which there are two age classes each. We divided the study into two models comprising competitive and non-competitive models of both species. Competition in both species can consist of competition within the same species (intraspecific competition) and competition between different species (interspecific competition). Our results show that the level of competition both intraspecific and interspecific affects the co-existence equilibrium point and the local stability of the co-existence equilibrium point.
Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields Muhammad Faldiyan; Ema Carnia; Asep Kuswandi Supriatna
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v8i2.22881

Abstract

Quaternions are extensions of complex numbers that are four-dimensional objects. Quaternion consists of one real number and three complex numbers, commonly denoted by the standard vectors  and . Quaternion algebra over the field is an algebra in which the multiplication between standard vectors is non-commutative and the multiplication of standard vector with itself is a member of the field. The field considered in this study is the quadratic field and its extensions are biquadratic and composite. There have been many studies done to show the existence of split properties in quaternion algebras over quadratic fields. The purpose of this research is to prove a theorem about the existence of split properties on three field structures, namely quaternion algebras over quadratic fields, biquadratic fields, and composite of  quadratic fields. We propose two theorems about biquadratic fields and composite of  quadratic fields refer to theorems about the properties of the split on quadratic fields. The result of this research is a theorem proof of three theorems with different field structures that shows the different conditions of the three field structures. The conclusion is that the split property on quaternion algebras over fields exists if certain conditions can be met.
Category of Discrete Dynamical System Ananda Ayu Permatasari; Ema Carnia; Asep Kuswandi Supriatna
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v8i2.22711

Abstract

A dynamical system is a method that can describe the process, behavior, and complexity of a system. In general, a dynamical system consists of a discrete dynamical system and a continuous dynamical system. This dynamical system is very interesting if seen from the algebraic side. One of them is about category theory. Category theory is a very universal theory in mathematical concepts. In this research, the dynamical system used is a discrete dynamical system represented as a directed graph with nodes in the graph called states. This discrete dynamical system has a height which is shown on the dynamical map in which the number of states at each height is called a profile. In this research, it will be proved whether the discrete dynamical system with the same profile is a category. Also, why category theory is needed in discrete dynamical systems will be investigated. The result of this study shows that the discrete dynamical system with the same profile is a category with its morphism is an evolution from one state to another state in different dynamical systems. Furthermore, category theory is needed for discrete dynamical systems to know about the properties and structure of discrete dynamical system.
Quasi-Associative Algebras on the Frobenius Lie Algebra M_3 (R)⊕gl_3 (R) Henti, Henti; Kurniadi, Edi; Carnia, Ema
Al-Jabar: Jurnal Pendidikan Matematika Vol 12 No 1 (2021): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v12i1.8485

Abstract

In this paper, we study the quasi-associative algebra property for the real Frobenius  Lie algebra  of dimension 18. The work aims  to prove that  is a quasi-associative algebra and to compute its formulas explicitly. To achieve this aim, we apply the literature reviews method corresponding to Frobenius Lie algebras, Frobenius functionals, and the structures of quasi-associative algebras. In the first step, we choose a Frobenius functional determined by direct computations of a bracket matrix of  and in the second step, using an induced symplectic structure, we obtain the explicit formulas of quasi-associative algebras for . As the results, we proved that  has the quasi-associative algebras property, and we gave their formulas explicitly. For future research, the case of the quasi-associative algebras on   is still an open problem to be investigated. Our result can motivate to solve this problem.  
A COMPARISON OF CENTRALITY MEASURES IN SUSTAINABLE DEVELOPMENT GOALS Ariesandy, Sena; Carnia, Ema; Napitupulu, Herlina
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 14 No 3 (2020): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1092.17 KB) | DOI: 10.30598/barekengvol14iss3pp309-320

Abstract

The Millennium Development Goals (MDGs), which began in 2000 with 8 goal points, have not been able to solve the global problems. The MDGs were developed into Sustainable Development Goals (SDGs) in 2015 with 17 targeted goal points achieved in 2030. Until now, methods for determining the priority of SDGs are still attractive to researchers. Centrality measure is one of the tools in determining the priority goal points on a network by using graph theory. There are four measurements of centrality used in this paper, namely degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality. The calculation results obtained from the four measurements are compared dan analyzed, to conclude which goal points are the most prior and the least prior. Furthemore, in this paper we present other example with simple graph to show that each different centrality calculation possibly resulted different priority node, the calculation of this illustration is done using a Python’s library named NetworkX
STABILITY ANALYSIS OF TUNGRO DISEASE SPREAD MODEL IN RICE PLANT USING MATRIX METHOD Maryati, Ati; Anggriani, Nursanti; Carnia, Ema
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 1 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (840.713 KB) | DOI: 10.30598/barekengvol16iss1pp215-226

Abstract

Rice is one of the staple foods produced from the rice plant. Rice productivity is increased by carrying out efforts to control diseases that usually attack rice plants. Tungro is one of the most destructive diseases of rice plants. Mathematical models can help solve problems in the spread of plant diseases. In this paper, the development of a mathematical model for the spread of tungro disease in rice plants with 6 compartments is developed involving rice in the vegetative and generative phases. Furthermore, stability analysis is carried out on the obtained model by using the Basic Reproduction Number ( ) search through the matrix method, especially through the search for transition matrices and transmission matrices. The analytical results show that when 1 the non-endemic equilibrium point is stable and when >1 the endemic equilibrium point is stable. Numerical results showed that rice plants in the generative phase were more infected than rice plants in the vegetative phase.
ALGEBRAIC STRUCTURES ON A SET OF DISCRETE DYNAMICAL SYSTEM AND A SET OF PROFILE Permatasari, Ananda Ayu; Carnia, Ema; Supriatna, Asep Kuswandi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss1pp0065-0074

Abstract

A discrete dynamical system is represented as a directed graph with graph nodes called states that can be seen on the dynamical map. This discrete dynamical system is symbolized by , where is a finite set of states and the function g is a function from to . In the dynamical map, the discrete dynamical system has a height where the number of states in each height is called a profile. The set of discrete dynamical systems has an addition operation defined as a disjoint union on the graph and a multiplication operation defined as a tensor product on the graph. The set of discrete dynamical systems and the set of profiles are very interesting to observe from the algebraic point of view. Considering operation on the set of discrete dynamical systems and the set of profiles, we can see their algebraic structure. By recognizing the algebraic structure, it will be easy to solve the polynomial equation in the discrete dynamical system and in the profile. In this research, we will investigate the algebraic structure of discrete dynamical systems and the set of profiles. This research shows that the set of discrete dynamical system has an algebraic structure, which is a commutative semiring and the set of profiles has an algebraic structure, which is a commutative semiring and -semimodule. Moreover, both sets have the same property, which is isomorphic to the set of non-negative integers.
THE LEVI DECOMPOSITION OF THE LIE ALGEBRA M_2 (R)⋊gl_2 (R) Kurniadi, Edi; Henti, Henti; Carnia, Ema
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0717-0724

Abstract

The idea of the Lie algebra is studied in this research. The decomposition between Levi sub-algebra and the radical can be used to define the finite dimensional Lie algebra. The Levi decomposition is the name for this type of decomposition. The goal of this study is to obtain a Levi decomposition of the Lie algebra of dimension 8. We compute its Levi sub-algebra and the radical of Lie algebra with respect to its basis to achieve this goal. We use literature studies on the Levi decomposition and Lie algebra in Dagli result to produce the radical and Levi sub-algebra. It has been shown that can be decomposed in the terms of the Levi sub-algebra and its radical. In this resulst, it has been given by direct computations and we obtained that the explicit formula of Levi decomposition of the affine Lie algebra whose basis is is written by with is is the Levi sub-algebra of .
Co-Authors Agus Supriatna Ananda Ayu Permatasari Ariesandy, Sena Arjun Hasibuan Asep K. Supriatna Asep K. Supriatna Asep Kuswandi Supriatna Basuki , Basuki Basuki Dwindi Agryanti Johar Edi Kurniadi Edi Kurniadi Edi Kurniadi Edi Kurniadi Edi Kurniadi Elah Dewia Endang Rusyaman Faldiyan, Muhammad Faurani, Nuraesa Nufus Hafizhah, Nur Hasibuan, Arjun Henti Henti Henti Henti Henti, Henti Herlina Napitupulu Irawati Irawati Isah . Aisah Isah Aisah Isah Aisah Kankan Parmikanti Maryati, Ati Muhammad Deni Johansyah Muhammad Faldiyan Nuraesa Nufus Faurani Nursanti Anggriani Permatasari, Ananda Ayu Setiadji, Setiadji Sisilia Sylviani Sri Wahyuni Sukono . Supriatna, Agus Valerie ​Valerie Valerie ​Valerie Yurio Windiatmoko Yurio Windiatmoko, Yurio