scholarly journals The weighted estimates for the operators Vα(−ΔG+V)−β and Vα∇G(−ΔG+V)−β on the stratified Lie group G

2009 ◽  
Vol 349 (1) ◽  
pp. 235-244 ◽  
Author(s):  
Yu Liu
Keyword(s):  
Lie Group ◽  
Stratified Lie Group ◽  
Weighted Estimates

scholarly journals The Higher Order Riesz Transform andBMOType Space Associated with Schrödinger Operators on Stratified Lie Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yu Liu ◽  
Jianfeng Dong
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Riesz Transform ◽  
Integral Operators ◽  
Higher Order ◽  
Reverse Hölder Class ◽  
Stratified Lie Group ◽  
Homogeneous Dimension ◽  
Stratified Lie Groups ◽  
Reverse Hölder

Assume thatGis a stratified Lie group andQis the homogeneous dimension ofG. Let-Δbe the sub-Laplacian onGandW≢0a nonnegative potential belonging to certain reverse Hölder classBsfors≥Q/2. LetL=-Δ+Wbe a Schrödinger operator on the stratified Lie groupG. In this paper, we prove the boundedness of some integral operators related toL, such asL-1∇2,L-1W, andL-1(-Δ) on the spaceBMOL(G).

Weighted estimates for commutators of Hausdorff operators on the Heisenberg group

2020 ◽  
pp. 39-62
Author(s):  
Nguyen Minh Chuong ◽  
◽  
Dao Van Duong ◽  
Nguyen Duc Duyet ◽  
◽  
...  
Keyword(s):  
Heisenberg Group ◽  
Weighted Estimates ◽  
Hausdorff Operators

Divergence in the epidemiological estimates of traumatic brain injury in the United States: comparison of two national databases

2020 ◽  
pp. 1-10
Author(s):  
Brittany M. Stopa ◽  
Maya Harary ◽  
Ray Jhun ◽  
Arun Job ◽  
Saef Izzy ◽  
...  
Keyword(s):  
Traumatic Brain Injury ◽  
Emergency Department ◽  
Brain Injury ◽  
Data Bank ◽  
The United States ◽  
National Sample ◽  
Population Based ◽  
Weighted Estimates ◽  
True Incidence ◽  
Ed Visits

OBJECTIVETraumatic brain injury (TBI) is a leading cause of morbidity and mortality in the US, but the true incidence of TBI is unknown.METHODSThe National Trauma Data Bank National Sample Program (NTDB NSP) was queried for 2007 and 2013, and population-based weighted estimates of TBI-related emergency department (ED) visits, hospitalizations, and deaths were calculated. These data were compared to the 2017 Centers for Disease Control and Prevention (CDC) report on TBI, which used the Healthcare Cost and Utilization Project’s National (“Nationwide” before 2012) Inpatient Sample and National Emergency Department Sample.RESULTSIn the NTDB NSP the incidence of TBI-related ED visits was 59/100,000 in 2007 and 62/100,000 in 2013. However, in the CDC report there were 534/100,000 in 2007 and 787/100,000 in 2013. The CDC estimate for ED visits was 805% higher in 2007 and 1169% higher in 2013. In the NTDB NSP, the incidence of TBI-related deaths was 5/100,000 in 2007 and 4/100,000 in 2013. In the CDC report, the incidence was 18/100,000 in both years. The CDC estimate for deaths was 260% higher in 2007 and 325% higher in 2013.CONCLUSIONSThe databases disagreed widely in their weighted estimates of TBI incidence: CDC estimates were consistently higher than NTDB NSP estimates, by an average of 448%. Although such a discrepancy may be intuitive, this is the first study to quantify the magnitude of disagreement between these databases. Given that research, funding, and policy decisions are made based on these estimates, there is a need for a more accurate estimate of the true national incidence of TBI.

Symmetry properties of fractional order transport equations

2012 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
R.K. Gazizov ◽  
A.A. Kasatkin ◽  
S.Yu. Lukashchuk
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Group ◽  
Initial Conditions ◽  
Group Analysis ◽  
Equivalence Transformation ◽  
Point Change ◽  
Infinitesimal Operator ◽  
Symmetry Properties ◽  
Fractional Differential

In the paper some features of applying Lie group analysis methods to fractional differential equations are considered. The problem related to point change of variables in the fractional differentiation operator is discussed and some general form of transformation that conserves the form of Riemann-Liouville fractional operator is obtained. The prolongation formula for extending an infinitesimal operator of a group to fractional derivative with respect to arbitrary function is presented. Provided simple example illustrates the necessity of considering both local and non-local symmetries for fractional differential equations in particular cases including the initial conditions. The equivalence transformation forms for some fractional differential equations are discussed and results of group classification of the wave-diffusion equation are presented. Some examples of constructing particular exact solutions of fractional transport equation are given, based on the Lie group methods and the method of invariant subspaces.

ε‎-Invariance

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Lie Algebra ◽  
Lie Group

The discussions up to Chapter 4 have been concerned with the Lie group. In this chapter, the Lie algebra is constructed by defining the operators ∇ and ∇̃.

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