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Algebra

Journal

2019

Articles 1 - 11 of 11

Full-Text Articles in Physical Sciences and Mathematics

Fibonacci And Lucas Identities From Toeplitz–Hessenberg Matrices, Taras Goy, Mark Shattuck Dec 2019

Fibonacci And Lucas Identities From Toeplitz–Hessenberg Matrices, Taras Goy, Mark Shattuck

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider determinants for some families of Toeplitz–Hessenberg matrices having various translates of the Fibonacci and Lucas numbers for the nonzero entries. These determinant formulas may also be rewritten as identities involving sums of products of Fibonacci and Lucas numbers and multinomial coefficients. Combinatorial proofs are provided of several of the determinants which make use of sign-changing involutions and the definition of the determinant as a signed sum over the symmetric group. This leads to a common generalization of the Fibonacci and Lucas determinant formulas in terms of the so-called Gibonacci numbers.

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An Admm-Factorization Algorithm For Low Rank Matrix Completion, Rahman Taleghani, Maziar Salahi Dec 2019

An Admm-Factorization Algorithm For Low Rank Matrix Completion, Rahman Taleghani, Maziar Salahi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose an Alternating Direction Method of Multipliers (ADMM) based algorithm that is taking advantage of factorization for the fixed rank matrix completion problem. The convergence of the proposed algorithm to the KKT point is discussed. Finally, on several classes of test problems, its efficiency is compared with several efficient algorithms from the literature.

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On Ordered (P; Q)-Lateral Ideals In Ordered Ternary Semigroups, Mohammad Y. Abbasi, Sabahat A. Khan, Akbar Ali Dec 2019

On Ordered (P; Q)-Lateral Ideals In Ordered Ternary Semigroups, Mohammad Y. Abbasi, Sabahat A. Khan, Akbar Ali

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study some useful results of ordered (p; q)-lateral ideals in ordered ternary semigroups. Also, some properties of (p; q)-lateral simple ordered ternary semigroup have been examined. Further, we characterize the relationship between minimal (resp., maximal) ordered (p; q)- lateral ideals and (p; q)-lateral simple ordered ternary semigroups.

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Hankel Rhotrices And Constructions Of Maximum Distance Separable Rhotrices Over Finite Fields, P. L. Sharma, Arun Kumar, Shalini Gupta Dec 2019

Hankel Rhotrices And Constructions Of Maximum Distance Separable Rhotrices Over Finite Fields, P. L. Sharma, Arun Kumar, Shalini Gupta

Applications and Applied Mathematics: An International Journal (AAM)

Many block ciphers in cryptography use Maximum Distance Separable (MDS) matrices to strengthen the diffusion layer. Rhotrices are represented by coupled matrices. Therefore, use of rhotrices in the cryptographic ciphers doubled the security of the cryptosystem. We define Hankel rhotrix and further construct the maximum distance separable rhotrices over finite fields.

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2-Local Derivations On Virasoro Algebras, Shavkat Ayupov, Bakhtiyor Yusupov Nov 2019

2-Local Derivations On Virasoro Algebras, Shavkat Ayupov, Bakhtiyor Yusupov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The present paper is devoted to study 2-local derivations on infinite-dimensional Lie algebras over a field of characteristic zero. We show that every derivation on Virasoro algebra is inner and prove that all 2-local derivations on this algebra is a derivation. We give an example of infinite-dimensional Lie algebra with a 2-local derivation which is not a derivation.

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Beauty, Bees, And God: The Fibonacci Sequence As A Theological Springboard In Secondary Mathematics, John D. Brahier Oct 2019

Beauty, Bees, And God: The Fibonacci Sequence As A Theological Springboard In Secondary Mathematics, John D. Brahier

Journal of Catholic Education

Catholic schools primarily should be in the business of making saints. This article identifies and explores a meaningful, engaging point of contact between mathematics and theology for high school math classes, the Fibonacci Sequence. This sequence serves as an engaging introduction to sequences and series; more importantly, the topic can be used as a springboard to theological discussions. The paper will provide a brief historical background to the Fibonacci Sequence, an explanation of how it can be used in a high school math classroom, and an exploration of three different theological touchpoints that the Fibonacci Sequence offers.

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Cubic Interior Ideals In Semigroups, G. Muhiuddin Jun 2019

Cubic Interior Ideals In Semigroups, G. Muhiuddin

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we apply the cubic set theory to interior ideals of a semigroup. The notion of cubic interior ideals is introduced, and related properties are investigated. Characterizations of (cubic) interior ideals are established, and conditions for a semigroup to be left (right) simple are provided.

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Solvable Leibniz Superalgebras Whose Nilradical Is A Lie Superalgebra Of Maximal Nilindex, Abror Khudoyberdiyev, Manuel Ladra, Khosiat Muratova Mar 2019

Solvable Leibniz Superalgebras Whose Nilradical Is A Lie Superalgebra Of Maximal Nilindex, Abror Khudoyberdiyev, Manuel Ladra, Khosiat Muratova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we investigate solvable Leibniz superalgebras whose nilradical is a Lie superalgebra with maximal nilindex.It should be noted that Lie superalgebra with a maximal nilindex only exists in the variety of Lie2,m when m is odd. We give the classification of all solvable Leibniz superalgebras such that even part is a Lie algebra and nilradical is a Lie superalgebra with a maximal index of nilpotency.

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Monoidal Supercategories And Superadjunction, Dene Lepine Mar 2019

Monoidal Supercategories And Superadjunction, Dene Lepine

Rose-Hulman Undergraduate Mathematics Journal

We define the notion of superadjunction in the context of supercategories. In particular, we give definitions in terms of counit-unit superadjunctions and hom-space superadjunctions, and prove that these two definitions are equivalent. These results generalize well-known statements in the non-super setting. In the super setting, they formalize some notions that have recently appeared in the literature. We conclude with a brief discussion of superadjunction in the language of string diagrams.

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Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant Mar 2019

Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant

Rose-Hulman Undergraduate Mathematics Journal

Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code C can be represented by its neural ideal JC. In turn, the polynomials in JC can be used to determine the relationships among the receptive fields of the neurons. In a paper by Curto et al., three such relationships, known as the Type 1-3 relations, were linked to the neural ideal by three if-and-only-if statements. Later, Garcia et al. discovered the Type 4-6 relations. These new relations differed from the first three in that they were …

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Parametric Natura Morta, Maria C. Mannone Mar 2019

Parametric Natura Morta, Maria C. Mannone

The STEAM Journal

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.

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