Results 61 to 70 of about 3,530,646 (225)
Symmetric Diophantine Equations
Rocky Mountain Journal of Mathematics, 2004 The author describes a method to obtain infinite parametric solutions of some Diophantine equations of type \(f(x,y)=f(u,v)\) where \(f\) is a form (usually the product of some linear and quadratic forms) with rational coefficients. The main idea is to apply a non-singular linear transformation \(x=\alpha u+\beta v\), \(y=\gamma u+\delta v\) such that ...
openaire +2 more sources
Optimising Wave Energy Plant Location Through Neutrosophic Multi‐Criteria Group Decision‐Making
CAAI Transactions on Intelligence Technology, Volume 11, Issue 1, Page 167-189, February 2026.ABSTRACT The global shift towards sustainable energy has intensified research into renewable sources, particularly wave energy. Pakistan, with its long coastline, holds significant potential for wave energy development. However, identifying optimal locations for wave energy plants involves evaluating complex, multi‐faceted criteria.
Hafiz Muhammad Athar Farid +4 more
wiley +1 more source
A note on the ternary Diophantine equation x2 − y2m = zn
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 − y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.
Bérczes Attila +3 more
doaj +1 more source
A universal example for quantitative semi‐uniform stability
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We characterise quantitative semi‐uniform stability for C0$C_0$‐semigroups arising from port‐Hamiltonian systems, complementing recent works on exponential and strong stability. With the result, we present a simple universal example class of port‐Hamiltonian C0$C_0$‐semigroups exhibiting arbitrary decay rates slower than t−1/2$t^{-1/2}$.
Sahiba Arora +3 more
wiley +1 more source
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
The Davenport–Heilbronn method: 80 years on
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.
Tim Browning
wiley +1 more source
On the Diophantine equation x2+p2k+1=4yn
International Journal of Mathematics and Mathematical Sciences, 2002 It has been proved that if p is an odd prime, y>1, k≥0, n is an integer greater than or equal to 4, (n,3h)=1 where h is the class number of the field Q(−p), then the equation x2+p2k+1=4yn has exactly five families of solution in the positive integers x ...
S. Akhtar Arif, Amal S. Al-Ali
doaj +1 more source
The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
wiley +1 more source
Combinatorics on number walls and the P(t)$P(t)$‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 1, January 2026.Abstract In 2004, de Mathan and Teulié stated the p$p$‐adic Littlewood conjecture (p$p$‐LC) in analogy with the classical Littlewood conjecture. Let Fq$\mathbb {F}_q$ be a finite field P(t)$P(t)$ be an irreducible polynomial with coefficients in Fq$\mathbb {F}_q$. This paper deals with the analogue of p$p$‐LC over the ring of formal Laurent series over
Steven Robertson
wiley +1 more source
On the Diophantine equation Ax2+22m=yn
International Journal of Mathematics and Mathematical Sciences, 2001 Let h denote the class number of the quadratic field ℚ(−A) for a square free odd integer A>1, and suppose that n>2 is an odd integer with (n,h)=1 and m>1.
Fadwa S. Abu Muriefah
doaj +1 more source