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<![CDATA[Levi Decomposition of Frobenius Lie Algebra of Dimension 6 ]]>
<![CDATA[Henti Henti]]>;
<![CDATA[Edi Kurniadi]]>;
<![CDATA[Ema Carnia]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i3.15656
<![CDATA[In this paper, we study notion of the Lie algebra of dimension 6. The finite dimensional Lie algebra can be expressed in terms of decomposition between Levi subalgebra and the maximal solvable ideal. This form of decomposition is called Levi decomposition. The work aims to obtain Levi decomposition of Frobenius Lie algebra of dimension 6. To achieve this aim, we compute Levi subalgebra and the maximal solvable ideal (radical) of with respect to its basis. To obtain Levi subalgebra and the maximal solvable ideal, we apply literature reviews about Lie algebra and decomposition Levi in Dagli result. For future research, decomposition Levi for higher dimension of Frobenius Lie algebra is still an open problem.]]>
<![CDATA[Mathematical Model of Iteroparous and Semelparous Species Interaction ]]>
<![CDATA[Arjun Hasibuan]]>;
<![CDATA[Asep Kuswandi Supriatna]]>;
<![CDATA[Ema Carnia]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i3.16447
<![CDATA[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.]]>
<![CDATA[Characteristic of Quaternion Algebra Over Fields ]]>
<![CDATA[Muhammad Faldiyan]]>;
<![CDATA[Ema Carnia]]>;
<![CDATA[Asep K. Supriatna]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.17625
<![CDATA[Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space with bases and the elements of the algebra are members of the field. Each element in quaternion algebra has an inverse, despite the fact that the ring is not commutative. Based on this, the purpose of this study is to obtain the characteristics of split quaternion algebra and determine how it interacts with central simple algebra. The research method used in this paper is literature study on quaternion algebra, field and central simple algebra. The results of this study establish the equivalence of split quaternion algebra as well as the theorem relating central simple algebra and quaternion algebra. The conclusion obtained from this study is that split quaternion algebra has five different characteristics and quaternion algebra is a central simple algebra with dimensions less than equal to four.]]>
<![CDATA[Characteristic of Quaternion Algebra Over Fields ]]>
<![CDATA[Faldiyan, Muhammad]]>;
<![CDATA[Carnia, Ema]]>;
<![CDATA[Supriatna, Asep K.]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v7i4.17625
<![CDATA[Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space with bases and the elements of the algebra are members of the field. Each element in quaternion algebra has an inverse, despite the fact that the ring is not commutative. Based on this, the purpose of this study is to obtain the characteristics of split quaternion algebra and determine how it interacts with central simple algebra. The research method used in this paper is literature study on quaternion algebra, field and central simple algebra. The results of this study establish the equivalence of split quaternion algebra as well as the theorem relating central simple algebra and quaternion algebra. The conclusion obtained from this study is that split quaternion algebra has five different characteristics and quaternion algebra is a central simple algebra with dimensions less than equal to four.]]>
<![CDATA[Levi Decomposition of Frobenius Lie Algebra of Dimension 6 ]]>
<![CDATA[Henti, Henti]]>;
<![CDATA[Kurniadi, Edi]]>;
<![CDATA[Carnia, Ema]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
Show Abstract
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DOI: 10.18860/ca.v7i3.15656
<![CDATA[In this paper, we study notion of the Lie algebra of dimension 6. The finite dimensional Lie algebra can be expressed in terms of decomposition between Levi subalgebra and the maximal solvable ideal. This form of decomposition is called Levi decomposition. The work aims to obtain Levi decomposition of Frobenius Lie algebra of dimension 6. To achieve this aim, we compute Levi subalgebra and the maximal solvable ideal (radical) of with respect to its basis. To obtain Levi subalgebra and the maximal solvable ideal, we apply literature reviews about Lie algebra and decomposition Levi in Dagli result. For future research, decomposition Levi for higher dimension of Frobenius Lie algebra is still an open problem.]]>
<![CDATA[Mathematical Model of Iteroparous and Semelparous Species Interaction ]]>
<![CDATA[Hasibuan, Arjun]]>;
<![CDATA[Supriatna, Asep Kuswandi]]>;
<![CDATA[Carnia, Ema]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
Show Abstract
|
Download Original
|
Original Source
|
Check in Google Scholar
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DOI: 10.18860/ca.v7i3.16447
<![CDATA[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.]]>
<![CDATA[On Properties of Five-dimensional Nonstandard Filiform Lie algebra ]]>
<![CDATA[Putra, Ricardo Eka]]>;
<![CDATA[Kurniadi, Edi]]>;
<![CDATA[Carnia, Ema]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v8i2.21018
<![CDATA[In this paper, we study the five-dimensional nonstandard Filiform Lie algebra and their basis elements representations. The aim of this research is to determine the basis elements of five-dimensional nonstandard Filiform Lie algebras representation in the form of real matrices. The method used in this study is by following Ceballos, Núñez, and Tenorio’s work. The results of this study are five real matrices as the realization of the basis elements of the five-dimensional nonstandard Filiform Lie algebra. We also discuss some results relate to five-dimensional nonstandard Filiform Lie algebra’s properties. The five-dimensional nonstandard Filiform Lie algebra is always nilpotent. For further research, it can be extended to five classes of Filiform Lie algebra, both standard and nonstandard with six dimensions. Moreover, it can be computed their split torus such that their direct sums are Frobenius Lie algebras.]]>
<![CDATA[Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields ]]>
<![CDATA[Faldiyan, Muhammad]]>;
<![CDATA[Carnia, Ema]]>;
<![CDATA[Supriatna, Asep Kuswandi]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v8i2.22881
<![CDATA[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.]]>
<![CDATA[Category of Discrete Dynamical System ]]>
<![CDATA[Permatasari, Ananda Ayu]]>;
<![CDATA[Carnia, Ema]]>;
<![CDATA[Supriatna, Asep Kuswandi]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/ca.v8i2.22711
<![CDATA[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.]]>
