Results 111 to 120 of about 416,500 (289)

A short proof of Weyl's law for fractional differential operators

, 2013
We study spectral asymptotics for a large class of differential operators on an open subset of $\R^d$ with finite volume. This class includes the Dirichlet Laplacian, the fractional Laplacian, and also fractional differential operators with non ...
Geisinger, Leander
core   +1 more source

Local Elliptic Regularity for the Dirichlet Fractional Laplacian [PDF]

, 2017
We prove the Wloc2⁢s,p${W_{{\mathrm{loc}}}^{2s,p}}$ local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of ℝN${\mathbb{R}^{N}}$. The key tool consists in analyzing
U. Biccari, M. Warma, E. Zuazua
semanticscholar   +1 more source

On fractional powers of singular perturbations of the Laplacian [PDF]

Journal of Functional Analysis, 2018
We qualify a relevant range of fractional powers of the so-called Hamiltonian of point interaction in three dimensions, namely the singular perturbation of the negative Laplacian with a contact interaction supported at the origin. In particular we provide an explicit control of the domain of such a fractional operator and of its decomposition into ...
Vladimir Georgiev, Vladimir Georgiev, Raffaele Scandone, Alessandro Michelangeli   +3 more
openaire   +5 more sources

Use of PopPK and E‐R Analyses toward Explaining Causal Link Between ADAMTS13 in Recombinant vs. Plasma‐Based Therapies and Clinical Effects in cTTP

Clinical Pharmacology &Therapeutics, EarlyView.
Congenital thrombotic thrombocytopenic purpura (cTTP) is an ultra‐rare, potentially life‐threatening condition caused by a deficiency of the blood enzyme ADAMTS13. Until now, ADAMTS13 replacement has been achieved with infusions of plasma or plasma‐based therapies (PBT).
Munjal Patel, Huijuan Xu, Olivier Barriere, Paul Diderichsen, Parth Patwari, Andy Z. X. Zhu, Jean François Marier, Thomas Peyret, Linda T. Wang, Björn Mellgård, Wenping Wang, Indranil Bhattacharya   +11 more
wiley   +1 more source

Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity

Journal of Function Spaces, 2018
We consider the following fractional p-Laplacian equation: -Δpαu+V(x)up-2u=f(x,u)-Γ(x)uq-2u,  x∈RN, where N≥2, pα⁎>q>p≥2, α∈(0,1), -Δpα is the fractional p-Laplacian, and Γ∈L∞(RN) and Γ(x)≥0 for a.e. x∈RN. f has the subcritical growth but higher than Γ(x)
Huxiao Luo, Shengjun Li, Wenfeng He
doaj   +1 more source

Fractional powers and singular perturbations of quantum differential Hamiltonians

, 2018
We consider the fractional powers of singular (point-like) perturbations of the Laplacian, and the singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure for resolvents
Michelangeli, Alessandro, Ottolini, Andrea, Scandone, Raffaele   +2 more
core   +1 more source

Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian [PDF]

Mathematics of Computation, 2019
For the discretization of the integral fractional Laplacian $(-\Delta)^s$, $0 < s < 1$, based on piecewise linear functions, we present and analyze a reliable weighted residual a posteriori error estimator.
M. Faustmann, J. Melenk, D. Praetorius
semanticscholar   +1 more source

The role of artificial intelligence in pharmacy: Revolutionizing drug development and beyond

Journal of Intelligent Medicine, EarlyView.
This comprehensive review explores the integration of artificial intelligence (AI) in the field of pharmacy, covering advancements in drug discovery, personalized medicine, medication management, and patient care. It synthesizes current research, methodologies, and future prospects, offering insights into how AI technologies are reshaping ...
Usman Shettima Usman, Farogh Ahsan, Muhammad Alanjiro, Saidu Yahaya Bataba, Jibrin Abdullahi Dallatu, Tarique Mahmood, Shahzadi Bano, Jamal Akhtar Ansari, Saba Parveen   +8 more
wiley   +1 more source

On the Solvability of Caputo -Fractional Boundary Value Problem Involving -Laplacian Operator

Abstract and Applied Analysis, 2013
We consider the model of a Caputo -fractional boundary value problem involving -Laplacian operator. By using the Banach contraction mapping principle, we prove that, under some conditions, the suggested model of the Caputo -fractional boundary value ...
Hüseyin Aktuğlu, Mehmet Ali Özarslan
doaj   +1 more source

Odometer of long-range sandpiles in the torus: mean behaviour and scaling limits [PDF]

, 2018
In \cite{Cipriani2016}, the authors proved that with the appropriate rescaling, the odometer of the (nearest neighbours) Divisible Sandpile in the unit torus converges to the bi-Laplacian field.
Chiarini, Leandro, Jara, Milton, Ruszel, Wioletta   +2 more
core   +1 more source