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On aggregating two linear Diophantine equations [PDF]
Discrete Applied Mathematics, 1998 Given two diophantine equations \[ \sum_{j\in \mathbb{N}} a_{1j}x_j= b_1,\;\sum_{j\in \mathbb{N}}a_{2j}x_j= b_2, \quad x_j\geq 0\text{ for all }j\in \mathbb{N}= \{1,\dots, n\}, \tag{1} \] the problem is to find relatively prime integers \(t_1,t_2\), so that \[ \sum_{j\in \mathbb{N}} (t_1a_{1j}+ t_2a_{2j})x_j= t_1b_1+ t_2b_2 \tag{2} \] has the same ...
Kevin Broughan
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Geometry of the Minimal Solutions of a Linear Diophantine Equation [PDF]
SIAM Journal on Discrete Mathematics, 2021 Let a1, . . . , an and b1, . . . , bm be fixed positive integers, and let S denote the set of all nonnegative integer solutions of the equation x1a1 + . . . + xnan = y1b1 + . . . + ymbm. A solution (x1, . . . , xn, y1, . . .
P. Sissokho
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Non-Linear Diophantine Equation
International Journal For Multidisciplinary Research, 2023 This paper is an important study about these Non-Linear Equation which have integer solution exists. i.e., Non-Linear Diophantine Equation, which have named by the famous Greek Mathematician Diophantus of Alexandria.
J. -, S. .
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International Mathematical Forum, 2022 The all current methods of solving linear Diophantine equation and system of linear Diophantine equations have three shortcomings. Based on function thinking we put forward minimum principles to solve them, so that we can solve Generalized Chinese ...
Ming Xiong
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AppliedMathThis paper introduces a digital adaptive control framework for large-scale multivariable systems, integrating matrix linear Diophantine equations with block pole placement.
Belkacem Bekhiti +4 more
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Linear diophantine equations and local cohomology
Inventiones Mathematicae, 1982 If \(\mathbb R\), \(\mathbb Q\), \(\mathbb Z\), \(\mathbb N\) and \(\mathbb P\) have the usual meanings and if \(\Phi\) is an \(r\times n\) matrix over \(\mathbb Z\), then \(E = E^0\), where \(E^\alpha = \{\beta\in\mathbb N^n\mid \Phi\beta = \alpha\).
Richard P Stanley, Stanley Richard P
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The mathematical analysis of Linear Diophantine equations with two and three variables and Its Applications [PDF]
The Egyptian International Journal of Engineering Sciences and Technology, 2023 Linear Diophantine equation are introduced to determine and search for integral solutions according to the associated variables. In this paper, the mathematical techniques are approached to solve Linear Diophantine equation with two, three unknowns and ...
Rania Amer
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An Introduction to Refined Neutrosophic Number Theory [PDF]
Neutrosophic Sets and Systems, 2021 Number theory is concerned with properties of integers and Diophantine equations. The objective of this paper is dedicated to introduce the basic concepts in refined neutrosophic number theory such as division, divisors, congruencies, and Pell's equation
Mohammad Abobala, Muritala Ibrahim
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Neutrosophic Linear Diophantine Equations with Two Variables [PDF]
Neutrosophic Sets and Systems, 2020 This paper studies for the first time the neutrosophic linear Diophantine equations with two variables in the neutrosophic ring of integers, and refined neutrosophic ring of integers.
Hasan Sankari, Mohammad Abobala
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Asian journal of control, 2023 Multifrequency steady‐state visual evoked potentials (SSVEPs) have been developed to extend the capability of SSVEP‐based brain‐machine interfaces (BMIs) to complex applications that have large numbers of targets.
Jing Mu, Ying Tan, D. Grayden, D. Oetomo
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