Results 11 to 20 of about 268 (182)
On Using Linear Diophantine Equations for in-Parallel Hiding of Decision Tree Rules [PDF]
Entropy, 2019 Data sharing among organizations has become an increasingly common procedure in several areas such as advertising, marketing, electronic commerce, banking, and insurance sectors.
Georgios Feretzakis +2 more
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Advances in Mechanical Engineering, 2023 Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets.
Mudassir Shams +3 more
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On aggregating two linear Diophantine equations
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 A Broughan
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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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On Some Algorithms for Solving Different Types of Symbolic 2-Plithogenic Algebraic Equations [PDF]
Neutrosophic Sets and Systems, 2023 The main goal of this paper is to study three different types of algebraic symbolic 2-plithogenic equations. The symbolic 2-plithogenic linear Diophantine equations, symbolic 2-plithogenic quadratic equations, and linear system of symbolic 2-plithgenic ...
Ahmad Khaldi +4 more
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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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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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Sparse Solutions of Linear Diophantine Equations [PDF]
SIAM Journal on Applied Algebra and Geometry, 2017 We present structural results on solutions to the Diophantine system $A{\boldsymbol y} = {\boldsymbol b}$, ${\boldsymbol y} \in \mathbb Z^t_{\ge 0}$ with the smallest number of non-zero entries. Our tools are algebraic and number theoretic in nature and include Siegel's Lemma, generating functions, and commutative algebra.
Iskander Aliev +3 more
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Linear Diophantine equations in several variables [PDF]
Linear Algebra and its Applications, 2022 Let $R$ be a ring and let $(a_1,\dots,a_n)\in R^n$ be a unimodular vector, where $n\geq 2$ and each $a_i$ is in the center of $R$. Consider the linear equation $a_1X_1+\cdots+a_nX_n=0$, with solution set $S$. Then $S=S_1+\cdots+S_n$, where each $S_i$ is naturally derived from $(a_1,\dots,a_n)$, and we give a presentation of $S$ in terms of generators ...
Quinlan, R., Shau, M., Szechtman, F.
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