scholarly journals k-ORDER FIBONACCI QUATERNIONS

2021 ◽  
Vol 21 (1) ◽  
pp. 29-38
Author(s):  
MUSTAFA ASCI ◽  
SULEYMAN AYDINYUZ
Keyword(s):  
Generating Function ◽  
Matrix Representation ◽  
Fibonacci Numbers ◽  
Summation Formula ◽  
The Matrix ◽  
Interesting Generalization

In this paper, we define and study another interesting generalization of the Fibonacci quaternions is called k-order Fibonacci quaternions. Then we obtain for Fibonacci quaternions, for Tribonacci quaternions and for Tetranacci quaternions. We give generating function, the summation formula and some properties about k-order Fibonacci quaternions. Also, we identify and prove the matrix representation for k-order Fibonacci quaternions. The matrix given for k-order Fibonacci numbers is defined for k-order Fibonacci quaternions and after the matrices with the k-order Fibonacci quaternions is obtained with help of auxiliary matrices, important relationships and identities are established.

scholarly journals Matrix Representation of Bi-Periodic Jacobsthal Sequence

2020 ◽  
pp. 1-12
Author(s):  
Sukran Uygun ◽  
Evans Owusu
Keyword(s):  
Generating Function ◽  
Initial Conditions ◽  
Matrix Representation ◽  
General Term ◽  
Identity Matrix ◽  
Summation Formulas ◽  
Matrix Sequence ◽  
Binet Formula ◽  
The Matrix ◽  
Generalized Matrix

In this paper, we bring into light the matrix representation of bi-periodic Jacobsthal sequence, which we shall call the bi-periodic Jacobsthal matrix sequence. We dene it as with initial conditions J0 = I identity matrix, . We obtained the nth general term of this new matrix sequence. By studying the properties of this new matrix sequence, the well-known Cassini or Simpson's formula was obtained. We then proceed to find its generating function as well as the Binet formula. Some new properties and two summation formulas for this new generalized matrix sequence were also given.

MRHS solver based on linear algebra and exhaustive search

2018 ◽  
Vol 12 (3) ◽  
pp. 143-157 ◽  
Author(s):  
Håvard Raddum ◽  
Pavol Zajac
Keyword(s):  
Linear Algebra ◽  
Matrix Representation ◽  
Equation System ◽  
Exhaustive Search ◽  
Binary Matrix ◽  
Algebraic Attacks ◽  
The Matrix ◽  
Speed Up ◽  
Symmetric Key

Abstract We show how to build a binary matrix from the MRHS representation of a symmetric-key cipher. The matrix contains the cipher represented as an equation system and can be used to assess a cipher’s resistance against algebraic attacks. We give an algorithm for solving the system and compute its complexity. The complexity is normally close to exhaustive search on the variables representing the user-selected key. Finally, we show that for some variants of LowMC, the joined MRHS matrix representation can be used to speed up regular encryption in addition to exhaustive key search.

Molecular and morphometric characterisation of Xiphinema globosum Sturhan, 1978 (Nematoda: Longidoridae) from Spain

Nematology ◽  
2011 ◽  
Vol 13 (1) ◽  
pp. 17-28 ◽  
Author(s):  
Blanca Landa ◽  
Carolina Cantalapiedra-Navarrete ◽  
Juan Palomares-Rius ◽  
Pablo Castillo ◽  
Carlos Gutiérrez-Gutiérrez
Keyword(s):  
Phylogenetic Trees ◽  
18S Rrna ◽  
Matrix Representation ◽  
Natural Environments ◽  
28S Rrna ◽  
Parsimony Method ◽  
Rdna Genes ◽  
Supertree Method ◽  
The Matrix ◽  
Relationship Of

AbstractDuring a recent nematode survey in natural environments of the Los Alcornocales Regional Park narrow valleys, viz., the renowned 'canutos' excavated in the mountains that maintain a humid microclimate, in southern Spain, an amphimictic population of Xiphinema globosum was identified. Morphological and morphometric studies on this population fit the original and previous descriptions and represent the first report from Spain and southern Europe. Molecular characterisation of X. globosum from Spain using D2-D3 expansion regions of 28S rRNA, 18S rRNA and ITS1-rRNA is provided and maximum likelihood and Bayesian inference analysis were used to reconstruct phylogenetic relationships within X. globosum and other Xiphinema species. A supertree solution of the different phylogenetic trees obtained in this study and in other published studies using rDNA genes are presented using the matrix representation parsimony method (MRP) and the most similar supertree method (MSSA). The results revealed a closer phylogenetic relationship of X. globosum with X. diversicaudatum, X. bakeri and with some sequences of unidentified Xiphinema spp. deposited in GenBank.

Leontev Input-Output Balance Model as a Dynamic System Control Problem

2021 ◽  
pp. 66-82
Author(s):  
S.N. Masaev
Keyword(s):  
Dynamic System ◽  
Matrix Representation ◽  
External Environment ◽  
Balance Model ◽  
System Control ◽  
Operational Mode ◽  
Input Output ◽  
System A ◽  
The Matrix ◽  
Research Show

The purpose of the study was to determine the problem of control of a dynamic system of higher dimension. Relying on Leontev input-output balance, we formalized the dynamic system and synthesized its control. Within the research, we developed a mathematical model that combines different working objects that consume and release various resources. The value of the penalty for all nodes and objects is introduced into the matrix representation of the problem, taking into account various options for their interaction, i.e., the observation problem. A matrix representation of the planning task at each working object is formed. For the formed system, a control loop is created; the influencing parameters of the external environment are indicated. We calculated the system operational mode, taking into account the interaction of the nodes of objects with each other when the parameters of the external environment influence them. Findings of research show that in achieving a complex result, the system is inefficient without optimal planning and accounting for the matrix of penalties for the interaction of nodes and objects of the dynamic system with each other. In a specific example, for a dynamic system with a dimension of 4.8 million parameters, we estimated the control taking into account the penalty matrix, which made it possible to increase the inflow of additional resources from the outside by 2.4 times from 130 billion conv. units up to 310 conv. units in 5 years. Taking into account the maximum optimization of control in the nodes, an increase of 3.66 times in the inflow of additional resources was ensured --- from 200.46 to 726.62 billion rubles

Matrix representation of formal polynomials over max-plus algebra

2020 ◽  
pp. 2150216
Author(s):  
Cailu Wang ◽  
Yuegang Tao
Keyword(s):  
Matrix Method ◽  
Polynomial Algorithm ◽  
Polynomial Function ◽  
Matrix Representation ◽  
Sufficient Condition ◽  
Polynomial Functions ◽  
Canonical Forms ◽  
Necessary And Sufficient Condition ◽  
The Matrix ◽  
Necessary And Sufficient

This paper proposes the matrix representation of formal polynomials over max-plus algebra and obtains the maximum and minimum canonical forms of a polynomial function by standardizing this representation into a canonical form. A necessary and sufficient condition for two formal polynomials corresponding to the same polynomial function is derived. Such a matrix method is constructive and intuitive, and leads to a polynomial algorithm for factorization of polynomial functions. Some illustrative examples are presented to demonstrate the results.

Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory

2009 ◽  
Vol 52 (1) ◽  
pp. 95-104 ◽  
Author(s):  
L. Miranian
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Classical Theory ◽  
Recurrence Relations ◽  
Matrix Representation ◽  
The Matrix ◽  
Classical Subject ◽  
First Time

AbstractIn the work presented below the classical subject of orthogonal polynomials on the unit circle is discussed in the matrix setting. An explicit matrix representation of the matrix valued orthogonal polynomials in terms of the moments of the measure is presented. Classical recurrence relations are revisited using the matrix representation of the polynomials. The matrix expressions for the kernel polynomials and the Christoffel–Darboux formulas are presented for the first time.

scholarly journals Hashing Based Answer Selection

2020 ◽  
Vol 34 (05) ◽  
pp. 9330-9337
Author(s):  
Dong Xu ◽  
Wu-Jun Li
Keyword(s):  
Question Answering ◽  
Matrix Representation ◽  
Matrix Representations ◽  
Binary Matrix ◽  
Large Memory ◽  
The Matrix ◽  
Novel Method ◽  
Online Prediction ◽  
Memory Cost ◽  
Vector Representations

Answer selection is an important subtask of question answering (QA), in which deep models usually achieve better performance than non-deep models. Most deep models adopt question-answer interaction mechanisms, such as attention, to get vector representations for answers. When these interaction based deep models are deployed for online prediction, the representations of all answers need to be recalculated for each question. This procedure is time-consuming for deep models with complex encoders like BERT which usually have better accuracy than simple encoders. One possible solution is to store the matrix representation (encoder output) of each answer in memory to avoid recalculation. But this will bring large memory cost. In this paper, we propose a novel method, called hashing based answer selection (HAS), to tackle this problem. HAS adopts a hashing strategy to learn a binary matrix representation for each answer, which can dramatically reduce the memory cost for storing the matrix representations of answers. Hence, HAS can adopt complex encoders like BERT in the model, but the online prediction of HAS is still fast with a low memory cost. Experimental results on three popular answer selection datasets show that HAS can outperform existing models to achieve state-of-the-art performance.

FERMI SYSTEMS, HUBBARD MODEL AND A SYMBOLICC++ IMPLEMENTATION

2001 ◽  
Vol 12 (02) ◽  
pp. 235-245 ◽  
Author(s):  
YORICK HARDY ◽  
WILLI-HANS STEEB
Keyword(s):  
Hubbard Model ◽  
Computer Algebra ◽  
Matrix Representation ◽  
Higher Order ◽  
Fermi Systems ◽  
The Matrix ◽  
Constants Of Motion

We show how the anticommutation relations for Fermi operators can be implemented with computer algebra using SymbolicC++. We describe applications to the Hubbard model. An important identity for Fermi operators is proved. Then, we test for higher order constants of motion for the Hubbard model. Finally, the matrix representation for the four point Hubbard model is calculated.

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