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Articles 1 - 17 of 17
Full-Text Articles in Number Theory
(R1979) Permanent Of Toeplitz-Hessenberg Matrices With Generalized Fibonacci And Lucas Entries, Hacène Belbachir, Amine Belkhir, Ihab-Eddine Djellas
(R1979) Permanent Of Toeplitz-Hessenberg Matrices With Generalized Fibonacci And Lucas Entries, Hacène Belbachir, Amine Belkhir, Ihab-Eddine Djellas
Applications and Applied Mathematics: An International Journal (AAM)
In the present paper, we evaluate the permanent and determinant of some Toeplitz-Hessenberg matrices with generalized Fibonacci and generalized Lucas numbers as entries.We develop identities involving sums of products of generalized Fibonacci numbers and generalized Lucas numbers with multinomial coefficients using the matrix structure, and then we present an application of the determinant of such matrices.
(Si10-062) Comprehensive Study On Methodology Of Orthogonal Interleavers, Priyanka Agarwal, Shivani Dixit, M. Shukla, Gaurish Joshi
(Si10-062) Comprehensive Study On Methodology Of Orthogonal Interleavers, Priyanka Agarwal, Shivani Dixit, M. Shukla, Gaurish Joshi
Applications and Applied Mathematics: An International Journal (AAM)
Interleaving permutes the data bits by employing a user defined sequence to reduce burst error which at times exceeds the minimum hamming distance. It serves as the sole medium to distinguish user data in the overlapping channel and is the heart of Interleave Division Multiple Access (IDMA) scheme. Versatility of interleavers relies on various design parameters such as orthogonality, correlation, latency and performance parameters like bit error rate (BER), memory occupancy and computation complexity. In this paper, a comprehensive study of interleaving phenomenon and discussion on numerous interleavers is presented. Also, the BER performance of interleavers using IDMA scheme is …
Determinant Formulas Of Some Hessenberg Matrices With Jacobsthal Entries, Taras Goy, Mark Shattuck
Determinant Formulas Of Some Hessenberg Matrices With Jacobsthal Entries, Taras Goy, Mark Shattuck
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we evaluate determinants of several families of Hessenberg matrices having various subsequences of the Jacobsthal sequence as their nonzero entries. These identities may be written equivalently as formulas for certain linearly recurrent sequences expressed in terms of sums of products of Jacobsthal numbers with multinomial coefficients. Among the sequences that arise in this way include the Mersenne, Lucas and Jacobsthal-Lucas numbers as well as the squares of the Jacobsthal and Mersenne sequences. These results are extended to Hessenberg determinants involving sequences that are derived from two general families of linear second-order recurrences. Finally, combinatorial proofs are provided …
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.
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.
Adjoint Appell-Euler And First Kind Appell-Bernoulli Polynomials, Pierpaolo Natalini, Paolo E. Ricci
Adjoint Appell-Euler And First Kind Appell-Bernoulli Polynomials, Pierpaolo Natalini, Paolo E. Ricci
Applications and Applied Mathematics: An International Journal (AAM)
The adjunction property, recently introduced for Sheffer polynomial sets, is considered in the case of Appell polynomials. The particular case of adjoint Appell-Euler and Appell-Bernoulli polynomials of the first kind is analyzed.
On The Lucas Difference Sequence Spaces Defined By Modulus Function, Murat Karakaş, Tayfur Akbaş, Ayşe M. Karakaş
On The Lucas Difference Sequence Spaces Defined By Modulus Function, Murat Karakaş, Tayfur Akbaş, Ayşe M. Karakaş
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, firstly, we define the Lucas difference sequence spaces by the help of Lucas sequence and a sequence of modulus function. Besides, we give some inclusion relations and examine geometrical properties such as Banach-Saks type p, weak fixed point property.
Fibonacci And Lucas Differential Equations, Esra Erkus-Duman, Hakan Ciftci
Fibonacci And Lucas Differential Equations, Esra Erkus-Duman, Hakan Ciftci
Applications and Applied Mathematics: An International Journal (AAM)
The second-order linear hypergeometric differential equation and the hypergeometric function play a central role in many areas of mathematics and physics. The purpose of this paper is to obtain differential equations and the hypergeometric forms of the Fibonacci and the Lucas polynomials. We also write again these polynomials by means of Olver’s hypergeometric functions. In addition, we present some relations between these polynomials and the other well-known functions.
Simplifying Coefficients In A Family Of Ordinary Differential Equations Related To The Generating Function Of The Laguerre Polynomials, Feng Qi
Applications and Applied Mathematics: An International Journal (AAM)
In the paper, by virtue of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Laguerre polynomials.
Incomplete Generalized (P; Q; R)-Tribonacci Polynomials, Mark Shattuck, Elif Tan
Incomplete Generalized (P; Q; R)-Tribonacci Polynomials, Mark Shattuck, Elif Tan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we consider an extension of the tribonacci polynomial, which we will refer to as the generalized (p; q; r)-tribonacci polynomial, denoted by Tn;m(x).We find an explicit formula for Tn;m(x)which we use to introduce the incomplete generalized (p; q; r)-tribonacci polynomials and derive several properties. An explicit formula for the generating function of the incomplete generalized polynomials is determined and a combinatorial interpretation is provided yielding further identities.
On Circulant-Like Rhotrices Over Finite Fields, P. L. Sharma, Shalini Gupta, Mansi Rehan
On Circulant-Like Rhotrices Over Finite Fields, P. L. Sharma, Shalini Gupta, Mansi Rehan
Applications and Applied Mathematics: An International Journal (AAM)
Circulant matrices over finite fields are widely used in cryptographic hash functions, Lattice based cryptographic functions and Advanced Encryption Standard (AES). Maximum distance separable codes over finite field GF2 have vital a role for error control in both digital communication and storage systems whereas maximum distance separable matrices over finite field GF2 are used in block ciphers due to their properties of diffusion. Rhotrices are represented in the form of coupled matrices. In the present paper, we discuss the circulant- like rhotrices and then construct the maximum distance separable rhotrices over finite fields.
Generalizations Of Two Statistics On Linear Tilings, Toufik Mansour, Mark Shattuck
Generalizations Of Two Statistics On Linear Tilings, Toufik Mansour, Mark Shattuck
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study generalizations of two well-known statistics on linear square-and-domino tilings by considering only those dominos whose right half covers a multiple of , where is a fixed positive integer. Using the method of generating functions, we derive explicit expressions for the joint distribution polynomials of the two statistics with the statistic that records the number of squares in a tiling. In this way, we obtain two families of q -generalizations of the Fibonacci polynomials. When 1, our formulas reduce to known results concerning previous statistics. Special attention is payed to the case …
A New Approach For Computing Wz Factorization, Effat Golpar-Raboky
A New Approach For Computing Wz Factorization, Effat Golpar-Raboky
Applications and Applied Mathematics: An International Journal (AAM)
Linear systems arise frequently in scientific and engineering computing. Various serial and parallel algorithms have been introduced for their solution. This paper seeks to compute the WZ and the ZW factorizations of a nonsingular matrix A using the right inverse of nested submatrices of A. We introduce two new matrix factorizations, the QZ and the QW factorizations, and compute the factorizations using our proposed approach.
Q -Analogs Of Identities Involving Harmonic Numbers And Binomial Coefficients, Toufik Mansour, Mark Shattuck, Chunwei Song
Q -Analogs Of Identities Involving Harmonic Numbers And Binomial Coefficients, Toufik Mansour, Mark Shattuck, Chunwei Song
Applications and Applied Mathematics: An International Journal (AAM)
Recently, McCarthy presented two algebraic identities involving binomial coefficients and harmonic numbers, one of which generalizes an identity used to prove the Apéry number supercongruence. In 2008, Prodinger provided human proofs of identities initially obtained by Osburn and Schneider using the computer program Sigma. In this paper, we establish q -analogs of a fair number of the identities appearing in McCarthy (Integers 11 (2011): A37) and Prodinger (Integers 8 (2008): A10) by making use of q -partial fractions.
On Generalized Hurwitz-Lerch Zeta Distributions, Mridula Garg, Kumkum Jain, S. L. Kalla
On Generalized Hurwitz-Lerch Zeta Distributions, Mridula Garg, Kumkum Jain, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce a function which is an extension to the general Hurwitz-Lerch Zeta function. Having defined the incomplete generalized beta type-2 and incomplete generalized gamma functions, some differentiation formulae are established for these incomplete functions. We have introduced two new statistical distributions, termed as generalized Hurwitz-Lerch Zeta beta type-2 distribution and generalized Hurwitz-Lerch Zeta gamma distribution and then derived the expressions for the moments, distribution function, the survivor function, the hazard rate function and the mean residue life function for these distributions. Graphs for both these distributions are given, which reflect the role of shape and scale …
Rethinking Pythagorean Triples, William J. Spezeski
Rethinking Pythagorean Triples, William J. Spezeski
Applications and Applied Mathematics: An International Journal (AAM)
It has been known for some 2000 years how to generate Pythagorean Triples. While the classical formulas generate all of the primitive triples, they do not generate all of the triples. For example, the triple (9, 12, 15) can’t be generated from the formulas, but it can be produced by introducing a multiplier to the primitive triple (3, 4, 5). And while the classical formulas produce the triple (3, 4, 5), they don’t produce the triple (4, 3, 5); a transposition is needed. This paper explores a new set of formulas that, in fact, do produce all of the triples …
Signed Decomposition Of Fully Fuzzy Linear Systems, Tofigh Allahviranloo, Nasser Mikaeilvand, Narsis A. Kiani, Rasol M. Shabestari
Signed Decomposition Of Fully Fuzzy Linear Systems, Tofigh Allahviranloo, Nasser Mikaeilvand, Narsis A. Kiani, Rasol M. Shabestari
Applications and Applied Mathematics: An International Journal (AAM)
System of linear equations is applied for solving many problems in various areas of applied sciences. Fuzzy methods constitute an important mathematical and computational tool for modeling real-world systems with uncertainties of parameters. In this paper, we discuss about fully fuzzy linear systems in the form AX = b (FFLS). A novel method for finding the non-zero fuzzy solutions of these systems is proposed. We suppose that all elements of coefficient matrix A are positive and we employ parametric form linear system. Finally, Numerical examples are presented to illustrate this approach and its results are compared with other methods.