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- (Cubic) interior ideal (1)
- (Cubic) left (right) ideal (1)
- (Cubic) subsemigroup (1)
- (p; q)-lateral simple elements (1)
- (p; q)-lateral simple ordered ternary semigroup (1)
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- Alternating direction method of multipliers (1)
- Convex optimization (1)
- Factorization (1)
- Fibonacci sequence (1)
- Finite field (1)
- Hankel matrix (1)
- Hankel rhotrix (1)
- Lucas sequence (1)
- Matrix completion (1)
- Maximal ordered (p; q)-lateral ideals (1)
- Maximum distance separable rhotrix (1)
- Minimal ordered (p; q)- lateral ideals (1)
- Multinomial coefficient (1)
- Ordered (p; q)-lateral ideal (1)
- Ordered ternary semigroup (1)
- Toeplitz–Hessenberg matrix (1)
- Total ordered ternary semigroup (1)
- Trudi’s formula (1)
Articles 1 - 5 of 5
Full-Text Articles in Algebra
Fibonacci And Lucas Identities From Toeplitz–Hessenberg Matrices, Taras Goy, Mark Shattuck
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.
An Admm-Factorization Algorithm For Low Rank Matrix Completion, Rahman Taleghani, Maziar Salahi
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.
On Ordered (P; Q)-Lateral Ideals In Ordered Ternary Semigroups, Mohammad Y. Abbasi, Sabahat A. Khan, Akbar Ali
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.
Hankel Rhotrices And Constructions Of Maximum Distance Separable Rhotrices Over Finite Fields, P. L. Sharma, Arun Kumar, Shalini Gupta
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.
Cubic Interior Ideals In Semigroups, G. Muhiuddin
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.