Global Lorentz estimates for hypoelliptic operators with drift on homogeneous group

2021 ◽  
Author(s):  
Yuexia Hou
Keyword(s):  
Homogeneous Group ◽  
Hypoelliptic Operators

scholarly journals Global Hölder Estimates via Morrey Norms for Hypoelliptic Operators with Drift

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Yuexia Hou ◽  
Pengcheng Niu
Keyword(s):  
Vector Fields ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Homogeneous Group ◽  
Hypoelliptic Operator ◽  
Real Vector ◽  
Constant Matrix ◽  
Hypoelliptic Operators ◽  
Hölder Estimates

Suppose thatX0,X1,…,Xmare left invariant real vector fields on the homogeneous groupGwithX0being homogeneous of degree two andX1,…,Xmhomogeneous of degree one. In the paper we study the hypoelliptic operator with drift of the kindL=∑i,j=1maijXiXj+a0X0,wherea0≠0and(aij)is a constant matrix satisfying the elliptic condition onRm. By proving the boundedness of two integral operators on the Morrey spaces with two weights, we obtain global Hölder estimates forL.

scholarly journals Experiments with high velocity positive ions V—Further experiments on the disintegration of boron

1936 ◽  
Vol 154 (881) ◽  
pp. 246-261 ◽  
Keyword(s):  
High Velocity ◽  
Ion Beam ◽  
Continuous Distribution ◽  
Homogeneous Group ◽  
Hydrogen Ions ◽  
Positive Ions ◽  
Mixed Beam ◽  
Magnetic Analysis ◽  
Α Particles

1—In a previous paper experiments on the disintegration of lithium, boron, and carbon by heavy hydrogen ions were described. The experiments on boron showed the presence of three proton groups of ranges 31, 58, and 92 cm for deuteron energies of 500 kv. They showed also a continuous distribution of α-particles between the ranges 5 cm and 15 cm, the distribution having a maximum at about 9 cm. There were also indications of a homogeneous group of α-particles at the end of the distribution, but the numbers of particles obtained were not sufficient to allow of its existence being definitely established. Since these experiments, we have been able to obtain heavy hydrogen of much higher purity, and have improved our source of ions, so that we have been able to determine the distribution in energy of the α-particles with much greater precision. A further improvement has been made by applying magnetic analysis to our ion beam, for in our original experiments with a mixed beam of protons and deuterons, the α-particles of range less than 4 cm resulting from deuteron transmutations were masked by the large number of α-particles due to proton disintegrations.

T-3 Uptake in Infants and Children

PEDIATRICS ◽  
1962 ◽  
Vol 30 (6) ◽  
pp. 1012-1013
Author(s):  
JAMES F. MARKS
Keyword(s):  
Statistical Difference ◽  
Age Groups ◽  
Homogeneous Group ◽  
Early Infancy ◽  
Infants And Children ◽  
Discrete Groups ◽  
In Infants And Children

The values obtained by Kundstadter and associates vary rather markedly from those obtained by ourselves and others. They found elevated T-3-RBC uptake at various periods throughout childhood, while our results showed an elevation only in early infancy. Even there Kundstadter et al. showed a much greater change than we did. Our work was in part misrepresented by the authors, when they stated that we did not distinguish among various age groups. We divided our infants under 18 months into a number of discrete groups. We grouped together children 1½ to 15 years of age because our data indicated these children represented a homogeneous group with respect to T-3 uptake. Indeed, observation of the authors' data for children 2 to 13 years suggests no real statistical difference among the three separate groups into which they have been divided.

The Empirical Heterogeneity of First Rank Symptoms in Schizophrenia

1982 ◽  
Vol 140 (5) ◽  
pp. 498-502 ◽  
Author(s):  
Richard Lewine ◽  
Robin Renders ◽  
Mark Kirchhofer ◽  
Ann Monsour ◽  
Norman Watt
Keyword(s):  
Psychiatric Symptoms ◽  
Empirical Studies ◽  
Reliability And Validity ◽  
Homogeneous Group ◽  
Schizophrenic Patients ◽  
First Rank Symptoms ◽  
The Relationship

SummaryFirst rank symptoms have assumed an important role in the assessment of schizophrenia. Only recently, however, have there been empirical studies of their reliability and validity. In this study, we examined the relationship between first rank and other psychiatric symptoms in 100 schizophrenic patients. The results are consistent with other research reports suggesting that first rank symptoms do not represent a homogeneous group of symptoms within an individual patient.

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