Results 31 to 40 of about 3,188,796 (338)
A Liouville-Type Theorem for an Elliptic Equation with Superquadratic Growth in the Gradient
Advanced Nonlinear Studies, 2020 We consider the elliptic equation -Δu=uq|∇u|p{-\Delta u=u^{q}|\nabla u|^{p}} in ℝn{\mathbb{R}^{n}} for any p>2{p>2} and q>0{q>0}. We prove a Liouville-type theorem, which asserts that any positive bounded solution is constant.
Filippucci Roberta +2 more
doaj +1 more source
Revisiting Gradient Clipping: Stochastic bias and tight convergence guarantees [PDF]
International Conference on Machine Learning, 2023 Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c>0$.
Anastasia Koloskova +2 more
semanticscholar +1 more source
Polarization-dependent tunneling of light in gradient optics [PDF]
Physical Review E, 2007 Reflection-refraction properties of photonic barriers, formed by dielectric gradient nanofilms, for inclined incidence of both S- and P-polarized electromagnetic (EM) waves are examined by means of exactly solvable models. We present generalized Fresnel formulae, describing the influence of the non-local dispersion on reflectance and transmittance of ...
Vladimir Kuzmiak +2 more
openaire +4 more sources
Quasilinear equations with dependence on the gradient
Nonlinear Analysis: Theory, Methods & Applications, 2009 Abstract We discuss the existence of positive solutions of the problem − ( q ( t ) φ ( u ′ ( t ) ) ) ′ = f ( t , u ( t ) , u ′ ( t ) ) for t ∈ ( 0 , 1 ) and u ( 0 ) = u ( 1 ) = 0 , where the nonlinearity f satisfies a superlinearity condition at 0 ...
Pedro Ubilla +3 more
openaire +4 more sources
Temperature dependence of spin currents in one- and three-dimensional insulators [PDF]
, 2011 The temperature dependence of spin currents in insulators at the finite temperature near zero Kelvin is theoretically studied. The spin currents are carried by Jordan-Wigner fermions and magnons in one- and three- dimensional insulators.
Nakata, Kouki
core +2 more sources
Gradient bounds for a thin film epitaxy equation [PDF]
, 2016 We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global wellposedness for initial
Li, Dong, Qiao, Zhonghua, Tang, Tao
core +1 more source
Pressure-dependence of the aortic valve gradient
Journal of the American College of Cardiology, 1998 Dipendenza lineare el gradiente transaortico dalla pressione sistolica aortica e dalle resistenze ...
LEONI, LOIRA +6 more
openaire +3 more sources
Confirming the Unusual Temperature Dependence of the Electric-Field Gradient in Zn
Crystals, 2022 The electric-field gradient (EFG) at nuclei in solids is a sensitive probe of the charge distribution. Experimental data, which previously only existed in insulators, have been available for metals with the development of nuclear measuring techniques ...
Heinz Haas +9 more
doaj +1 more source
On convergence of gradient-dependent integrands [PDF]
Applications of Mathematics, 2007 We study convergence properties of {υ(∇uk)}k∈ℕ if υ ∈ C(ℝm×m), |υ(s)| ⩽ C(1+|s|p), 1 < p < + ∞, has a finite quasiconvex envelope, uk → u weakly in W1,p (Ω; ℝm) and for some g ∈ C(Ω) it holds that ∫Ωg(x)υ(∇uk(x))dx → ∫Ωg(x)Qυ(∇u(x))dx as k → ∞. In particular, we give necessary and sufficient conditions for L1-weak convergence of {det ∇uk}k∈ℕ to det ∇u ...
openaire +2 more sources
Range dependent phase gradient autofocus [PDF]
IGARSS '98. Sensing and Managing the Environment. 1998 IEEE International Geoscience and Remote Sensing. Symposium Proceedings. (Cat. No.98CH36174), 1998 The Phase Gradient Autofocus (PGA) algorithm has been widely used in spotlight synthetic aperture radar (SAR) to remove motion-induced blurs in the images. The PGA algorithm has been proven to be a superior autofocus method. PGA assumes a narrow beam, which is valid for most SAR systems.
A.E. Robertson +4 more
openaire +2 more sources