scholarly journals Hardy Inequalities on Homogeneous Groups

2019 ◽  
Author(s):  
Michael Ruzhansky ◽  
Durvudkhan Suragan
Keyword(s):  
Hardy Inequalities ◽  
Homogeneous Groups

scholarly journals Hardy inequalities on metric measure spaces

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180310
Author(s):  
Michael Ruzhansky ◽  
Daulti Verma
Keyword(s):  
Integral Form ◽  
Hyperbolic Spaces ◽  
Hadamard Manifolds ◽  
Metric Measure Spaces ◽  
Differentiable Structure ◽  
Hardy Inequalities ◽  
Homogeneous Groups ◽  
Measure Spaces

In this note, we give several characterizations of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy's original inequality. We give examples obtaining new weighted Hardy inequalities on R n , on homogeneous groups, on hyperbolic spaces and on Cartan–Hadamard manifolds. We note that doubling conditions are not required for our analysis.

A Note on Hardy Inequalities on Homogeneous Groups

2018 ◽  
Vol 51 (3) ◽  
pp. 425-435 ◽  
Author(s):  
Nguyen Lam
Keyword(s):  
Hardy Inequalities ◽  
Homogeneous Groups

scholarly journals Hardy inequalities on metric measure spaces, II: the case p  >  q

2021 ◽  
Vol 477 (2250) ◽  
pp. 20210136
Author(s):  
Michael Ruzhansky ◽  
Daulti Verma
Keyword(s):  
Integral Form ◽  
Hyperbolic Spaces ◽  
Hadamard Manifolds ◽  
Metric Measure Spaces ◽  
Differentiable Structure ◽  
Hardy Inequalities ◽  
Homogeneous Groups ◽  
Link Type ◽  
Measure Spaces

In this paper, we continue our investigations giving the characterization of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy’s original inequality. This is a continuation of our paper (Ruzhansky & Verma 2018. Proc. R. Soc. A 475 , 20180310 ( doi:10.1098/rspa.2018.0310 )) where we treated the case p  ≤  q . Here the remaining range p  >  q is considered, namely, 0 <  q  <  p , 1 <  p  < ∞. We give several examples of the obtained results, finding conditions on the weights for integral Hardy inequalities on homogeneous groups, as well as on hyperbolic spaces and on more general Cartan–Hadamard manifolds. As in the first part of this paper, we do not need to impose doubling conditions on the metric.

Self-monitoring and leadership in culturally heterogeneous and homogeneous groups

2003 ◽  
Author(s):  
Magdalene Hsien Chen Pua ◽  
Lynn R. Offermann ◽  
Catina M. Smith ◽  
Mary Sass ◽  
Craig R. Seal ◽  
...  
Keyword(s):  
Self Monitoring ◽  
Homogeneous Groups

The early stages of spontaneous forest regeneration on poor soils and continental sand dunes in northern Belgium

1983 ◽  
Vol 49 ◽  
Author(s):  
M. Van Miegroet
Keyword(s):  
Scots Pine ◽  
Age Differences ◽  
Forest Regeneration ◽  
Sand Dunes ◽  
Mixed Forest ◽  
Pedunculate Oak ◽  
White Poplar ◽  
Technical Problems ◽  
Homogeneous Groups ◽  
Invading Species

Spontaneous  natural regeneration under variable conditions on sandy soils and continental  sand dunes were analysed in 5 locations in N.E. Belgium.     The number of seedlings varies between 14.000 and 522.000/ha. The most  prominent invading species are red oak, pedunculate oak and Scots pine.    Two principal types of regeneration are recognized : homogeneous groups of  oak or pine and mixtures, predominantly composed by the same species.  Pioneers such as birch, willow, white poplar and wild black cherry do not  play an important role.    Social differentiation sets in quite early and is mainly provoked by age  differences. Therefore early silvicultural intervention is advisable. The  growth relationships between the species indicate that Scots pine is not in  danger of spontaneous elemination by other species. Because of the density  and variability of spontaneous forest regeneration, the conversion of pure  pine stands into mixed forest, using group regeneration to this end, poses no  real technical problems.

scholarly journals An analysis of COVID-19 clusters in India

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Pooja Sengupta ◽  
Bhaswati Ganguli ◽  
Sugata SenRoy ◽  
Aditya Chatterjee
Keyword(s):  
Public Health ◽  
Cluster Analysis ◽  
Population Density ◽  
Case Studies ◽  
Compartment Model ◽  
Health Interventions ◽  
Disease Spread ◽  
Second Phase ◽  
Public Health Interventions ◽  
Homogeneous Groups

Abstract Background In this study we cluster the districts of India in terms of the spread of COVID-19 and related variables such as population density and the number of specialty hospitals. Simulation using a compartment model is used to provide insight into differences in response to public health interventions. Two case studies of interest from Nizamuddin and Dharavi provide contrasting pictures of the success in curbing spread. Methods A cluster analysis of the worst affected districts in India provides insight about the similarities between them. The effects of public health interventions in flattening the curve in their respective states is studied using the individual contact SEIQHRF model, a stochastic individual compartment model which simulates disease prevalence in the susceptible, infected, recovered and fatal compartments. Results The clustering of hotspot districts provide homogeneous groups that can be discriminated in terms of number of cases and related covariates. The cluster analysis reveal that the distribution of number of COVID-19 hospitals in the districts does not correlate with the distribution of confirmed COVID-19 cases. From the SEIQHRF model for Nizamuddin we observe in the second phase the number of infected individuals had seen a multitudinous increase in the states where Nizamuddin attendees returned, increasing the risk of the disease spread. However, the simulations reveal that implementing administrative interventions, flatten the curve. In Dharavi, through tracing, tracking, testing and treating, massive breakout of COVID-19 was brought under control. Conclusions The cluster analysis performed on the districts reveal homogeneous groups of districts that can be ranked based on the burden placed on the healthcare system in terms of number of confirmed cases, population density and number of hospitals dedicated to COVID-19 treatment. The study rounds up with two important case studies on Nizamuddin basti and Dharavi to illustrate the growth curve of COVID-19 in two very densely populated regions in India. In the case of Nizamuddin, the study showed that there was a manifold increase in the risk of infection. In contrast it is seen that there was a rapid decline in the number of cases in Dharavi within a span of about one month.

scholarly journals Sufficient Criteria for Obtaining Hardy Inequalities on Finsler Manifolds

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
Ágnes Mester ◽  
Ioan Radu Peter ◽  
Csaba Varga
Keyword(s):  
Finsler Manifolds ◽  
Hardy Inequalities
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