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Incompleteness of Arithmetic from the Viewpoint of Diophantine Set Theory
The authors analyze Diophantine sets and show that all recursively enumerable sets are Diophantine. Based on the classical results from the theory of...
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Isolated Diophantine Numbers
In this note, we discuss the topology of Diophantine numbers, giving simple explicit examples of Diophantine isolated numbers (among those with the...
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Linear Diophantine fuzzy substructures of ordered semigroups
As an extension of the fuzzy set, linear Diophantine fuzzy set (LDFS) was recently introduced. In this paper, we apply the concept of LDFS in ordered...
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Elliptic Curves Induced by Diophantine Triples
This chapter introduces elliptic curves induced by Diophantine triples and discusses their properties and applications. One of the main applications...
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(p, q)-Rung linear Diophantine fuzzy sets and their application in decision-making
The q -rung linear Diophantine fuzzy set is one of the effective generalizations of Diophantine fuzzy set for dealing with uncertainties in...
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Systems of Diophantine Equations over Finite Configurations
Under study are the finite systems of Diophantine equations over finite configurations. We propose some consistency verification procedure for such...
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Counting intrinsic Diophantine approximations in simple algebraic groups
We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple...
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Correlation coefficient measures and aggregation operators on interval-valued linear Diophantine fuzzy sets and their applications
Intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets are rudimentary concepts in computational intelligence, which have...
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On the metric theory of multiplicative Diophantine approximation
In 1962, Gallagher proved a higher-dimensional version of Khintchine’s theorem on Diophantine approximation. Gallagher’s theorem states that for any...
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Badly Approximable Matrices and Diophantine Exponents
AbstractThis paper is a survey of results concerning different kinds of Diophantine exponents. Special attention is paid to the transference...
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Effective equidistribution for multiplicative Diophantine approximation on lines
Given any line in the plane, we strengthen the Littlewood conjecture by two logarithms for almost every point on the line, thereby generalising the...
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Arithmetic statistics and diophantine stability for elliptic curves
We study the growth and stability of the Mordell–Weil group and Tate–Shafarevich group of an elliptic curve defined over the rationals, in various...
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Linear Diophantine Fuzzy Information Aggregation with Multi-criteria Decision-Making
Linear Diophantine fuzzy set (LDFS) is the integral part of decision-making process under uncertain environment, because of its amazing quality of...
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An Application of Linear Diophantine Fuzzy Sets to the Edge Detection Techniques
The utilization of fuzzy set theory within the domain of image processing provides a lot of advantages such as encompassing the management of...
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Intrinsic Diophantine approximation for overlap** iterated function systems
In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue of Khintchine’s...
