Results 51 to 60 of about 220,140 (287)

Solving Elliptic Diophantine Equations Avoiding Thue Equations and Elliptic Logarithms [PDF]

Experimental Mathematics, 1998
We determine the solutions in integers of the equation y2 = (x + p)(x2 + p2) for p = 167, 223, 337, 1201. The method used was suggested to us by Yu. Bilu, and is shown to be in some cases more efficient than other general purpose methods for solving such equations, namely the elliptic logarithms method and the use of Thue equations.
openaire   +4 more sources

Critical Sets of Elliptic Equations [PDF]

Communications on Pure and Applied Mathematics, 2014
Given a solution u to a linear, homogeneous, second‐order elliptic equation with Lipschitz coefficients, we introduce techniques for giving improved estimates of the critical set 𝒷(u)u {x :|δu|(x) = 0}, as well as the first estimates on the effective critical set 𝒷r(u), which roughly consists of points x such that the gradient of u is small somewhere ...
Cheeger J, Naber A, Valtorta D
openaire   +4 more sources

Enhancing Corrosion Resistance and Mechanical Strength of 3D‐Printed Iron Polylactic Acid for Marine Applications via Laser Surface Texturing

Advanced Engineering Materials, EarlyView.
Laser surface texturing significantly improves the corrosion resistance and mechanical strength of 3D‐printed iron polylactic acid (Ir‐PLA) for marine applications. Optimal laser parameters reduce corrosion by 80% and enhance tensile strength by 25% and ductility by 15%.
Mohammad Rezayat, Mojtaba Karamimoghadam, Mohammadreza Lalegani Dezaki, Ali Zolfagharian, Giuseppe Casalino, Antonio Mateo, Mahdi Bodaghi   +6 more
wiley   +1 more source

Picone-type inequalities for nonlinear elliptic equations with first-order terms and their applications

Journal of Inequalities and Applications, 2006
Picone-type inequalities are established for nonlinear elliptic equations which are generalizations of nonself-adjoint linear elliptic equations, and Sturmian comparison theorems are derived as applications.
Takaŝi Kusano, Yoshida Norio, Jaroš Jaroslav   +2 more
doaj  

$C^{1,\alpha}$ regularity for elliptic equations with the general nonstandard growth conditions [PDF]

Mathematica Bohemica
We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on $\Omega$. We prove the global $C^{1, \alpha}$ regularity of bounded weak solutions of these equations with the Dirichlet boundary ...
Sungchol Kim, Dukman Ri
doaj   +1 more source

Spatial pseudoanalytic functions arising from the factorization of linear second order elliptic operators

, 2011
Biquaternionic Vekua-type equations arising from the factorization of linear second order elliptic operators are studied. Some concepts from classical pseudoanalytic function theory are generalized onto the considered spatial case.
Berglez, Bers, Castillo Perez, Elkins, Gürlebeck, Korn, Kravchenko, Kravchenko, Kravchenko, Kravchenko, Kravchenko, Kravchenko, Kravchenko, Malonek, Sprössig, Vekua   +15 more
core   +1 more source

A Bohr Phenomenon For Elliptic Equations [PDF]

Proceedings of the London Mathematical Society, 2001
This article is devoted to the generalization of the well-known theorem of Bohr about the existence of a number \(r\in(0,1)\) such that if a power series \(\sum^\infty_{\nu=0}c_\nu z^\nu\) converges in the unit disk and the modulus of its sum is less than 1, then \(\sum^\infty_{\nu=0}|c_\nu z^\nu|
Aizenberg, Lev A., Tarkhanov, Nikolai Nikolaevich   +1 more
openaire   +4 more sources

Subgrain and Cavity Development during Creep of Al‐3.85%Mg

Advanced Engineering Materials, EarlyView.
Al‐3.85%Mg does form subgrains if crept at very high strains. This fact allows the unification of the creep description in two different alloys such as pure Al and Al–Mg alloys. It is classically considered that the creep mechanisms for type M (e.g., pure Al) and type A alloys (e.g., Al–Mg alloys) are different.
Augusta Isaac, Itziar Serrano‐Munoz, Aleksander Kostka, Martinus Putra Widjaja, Gaspar González‐Doncel, Giovanni Bruno, Ricardo Fernández   +6 more
wiley   +1 more source

Picone-type inequalities for nonlinear elliptic equations and their applications

Journal of Inequalities and Applications, 2001
Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are ...
Takaŝi Kusano, Yoshida Norio, Jaroš Jaroslav   +2 more
doaj  

Elliptic triad

Physics Letters B
The triad refers to embedding the Macdonald polynomials into the Noumi-Shiraishi functions and their reduction to solutions of simple linear equations at particular values of t. It provides an alternative definition of Macdonald theory.
A. Mironov, A. Morozov, A. Popolitov, Z. Zakirova   +3 more
doaj   +1 more source