Results 111 to 120 of about 22,960 (196)

Isolated points of Diophantine sets

, 2020
Let $ \in(0;\frac{1}{2}), \geq 1$ and define the "$ , $ Diophantine set" as: $$D_{ , }:=\{ \in (0;1): ||q ||\geq\frac {q^ }\quad\forall q\in\Bbb{N}\},\qquad ||x||:=\inf_{p\in\Bbb{Z}}|x-p|.$$ We analyze the topology of these sets and we show that generally they have isolated points.
openaire   +2 more sources

Diophantine approximation and badly approximable sets

Advances in Mathematics, 2006
Let (X,d) be a metric space and ( , d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of . Loosely speaking, these consist of points in which `stay clear' of some given set of points in X.
Kristensen, S., Thorn, R., Velani, S.
openaire   +3 more sources

Plank theorems and their applications: A survey

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
wiley   +1 more source

Algebraic Principles as a Tool for Energy Saving

Chemical Engineering Transactions, 2020
This paper discusses algebraic approaches of control design for a set of Single Input – Single Output (SISO) delayed systems that are further developed and discussed.
Roman Prokop, Jirí Korbel, Libor Pekar
doaj   +1 more source

Report on some recent advances in Diophantine approximation [PDF]

, 2009
A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex number, as well as
Waldschmidt, Michel
core   +3 more sources

Intersective sets and Diophantine approximation

Michigan Mathematical Journal, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

On the integral values of a curious recurrence

, 2014
We discuss a problem initially thought for the Mathematical Olympiad but which has several interpretations. The recurrence sequences involved in this problem may be generalized to recurrence sequences related to a much larger set of diophantine ...
Dvornicich, Roberto, Veneziano, Francesco, Zannier, Umberto   +2 more
core  

From Diophantian Equations to Matrix Equations (Iv) - Diophantian Equations of Higher Degree [PDF]

Educaţia 21
In the context of training and developing the skills of teachers, students and children to solve exercises and problems in Mathematics, in this paper we propose to continue the steps started in the first three papers with the same generic title and ...
Teodor Dumitru Vălcan
doaj   +1 more source

NON-DIOPHANTINE SETS IN RINGS OF FUNCTIONS

The Journal of Symbolic Logic
Abstract Except for a limited number of cases, a complete classification of the Diophantine (i.e., positive existentially definable) sets of polynomial rings and fields of rational functions seems out of reach at present. We contribute to this problem by proving that several natural sets and relations over these structures are not ...
Garcia-Fritz, Natalia, Pasten, Hector, Pheidas, Thanases   +2 more
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Non-Salem Sets in Multiplicative Diophantine Approximation

International Mathematics Research Notices
Abstract In this paper, we answer a question of Cai–Hambrook in arXiv$\colon $ 2403.19410. Furthermore, we compute the Fourier dimension of the multiplicative $\psi $-well approximable set $$ \begin{align*} &M_2^{\times}(\psi)=\left\{(x_1,x_2)\in [0,1]^{2}\colon \|qx_1\|\|qx_2\|<\psi(q) \textrm{ for infinitely many}\ q\in ...
Tan, Bo, Zhou, Qing-Long
openaire   +2 more sources