Results 51 to 60 of about 3,278,971 (302)

Quantitative unique continuation for Schrödinger operators [PDF]

Journal of Functional Analysis, 2019
We investigate the quantitative unique continuation properties of solutions to second order elliptic equations with singular lower order terms. The main theorem presents a quantification of the strong unique continuation property for $\Delta + V$.
Blair Davey
semanticscholar   +1 more source

Approximate Controllability of Sub-Diffusion Equation with Impulsive Condition

Mathematics, 2019
In this work, we study an impulsive sub-diffusion equation as a fractional diffusion equation of order α ∈ ( 0 , 1 ) . Existence, uniqueness and regularity of solution of the problem is established via eigenfunction expansion. Moreover,
Lakshman Mahto, Syed Abbas, Mokhtar Hafayed, Hari M. Srivastava   +3 more
doaj   +1 more source

A Hybridized High-Order Method for Unique Continuation Subject to the Helmholtz Equation

SIAM Journal on Numerical Analysis, 2020
We design and analyze an arbitrary-order hybridized discontinuous Galerkin method to approximate the unique continuation problem subject to the Helmholtz equation.
E. Burman, G. Delay, A. Ern
semanticscholar   +1 more source

Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations [PDF]

Advances in Mathematics, 2017
We study the strong unique continuation property backwards in time for the nonlocal equation in $\mathbb{R}^{n} \times \mathbb{R}$ \begin{equation}\label{one} (\partial_t - \Delta)^{s} u = V(x,t)u \end{equation} for $s \in (0,1)$.
Agnid Banerjee, N. Garofalo
semanticscholar   +1 more source

Multiscale Unique Continuation Properties of Eigenfunctions [PDF]

, 2015
Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schrödinger operators and control theory. We review recent results and announce new ones regarding quantitative unique continuation principles for partial differential equations with an underlying multiscale structure.
Borisov, Denis, Nakić, Ivica, Rose, Christian, Tautenhahn, Martin, Veselić, Ivan   +4 more
openaire   +3 more sources

Feasibility and Safety of Somato‐Cognitive Coordination Therapy for Cerebellar Ataxia Following Pediatric Brain Tumor Treatment

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Background Cerebellar ataxia after pediatric brain tumor treatment can cause persistent gait, balance, and speech impairment, yet no established rehabilitation strategy exists. Somato‐cognitive coordination therapy (SCCT) is a virtual reality–guided intervention designed to promote sensorimotor integration through visually constrained reaching
Masanobu Takeuchi, Takashi Matsuzawa, Jun Yamanishi, Masahiro Yoshitomi, Junji Ikeda, Shin‐Ichi Tsujimoto, Yasuteru Yamaguchi, Norio Shiba, Dhroov Pathare, Ayumi Kato, Masahiko Hara   +10 more
wiley   +1 more source

Estimating the Unique Information of Continuous Variables

Advances in neural information processing systems, 2021
The integration and transfer of information from multiple sources to multiple targets is a core motive of neural systems. The emerging field of partial information decomposition (PID) provides a novel information-theoretic lens into these mechanisms by identifying synergistic, redundant, and unique contributions to the mutual information between one ...
Ari Pakman, Amin Nejatbakhsh, Dar Gilboa, Abdullah Makkeh, Luca Mazzucato, Michael Wibral, Elad Schneidman   +6 more
openaire   +4 more sources

Sustained Therapeutic Efficacy of Intravenous Plasminogen Concentrate in Pediatric Patients With Type 1 Plasminogen Deficiency: An Analysis of Dosing Parameters and Clinical Outcomes

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Background Type 1 plasminogen deficiency (PLGD‐1) is an ultra‐rare autosomal recessive disorder caused by variants in the PLG gene and affects approximately 1.6 individuals per million. The condition is characterized by decreased plasminogen levels and impaired function, resulting in fibrin‐rich lesions on mucous membranes throughout the body.
Charles Nakar, Karen Thibaudeau, Mary Mathias, Heather McDaniel, Madlen Reschke, Klaus Tenbrock, Joseph M. Parker, Amy Shapiro   +7 more
wiley   +1 more source

Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem [PDF]

Mathematical physics, analysis and geometry, 2018
We prove the strong unique continuation property for many-body Schrödinger operators with an external potential and an interaction potential both in Llocp(ℝd)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts ...
Louis Garrigue
semanticscholar   +1 more source

Personalized Zebrafish Models for Fusion‐Positive Pediatric Sarcomas

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Clinical sequencing efforts have revolutionized our approaches to categorizing pediatric cancers in real time. This has dramatically improved our ability to profile pediatric tumors, identify actionable vulnerabilities, and influence clinical care.
Lisa H. Hall, Emma N. Harrison, Genevieve C. Kendall   +2 more
wiley   +1 more source