scholarly journals Global Hölder estimates for hypoelliptic operators with drift on homogeneous groups

2012 ◽  
Vol 13 (2) ◽  
pp. 337 ◽  
Author(s):  
Yuexia Hou ◽  
Xiaojing Feng ◽  
Xuewei Cui
Keyword(s):  
Hypoelliptic Operators ◽  
Homogeneous Groups ◽  
Hölder Estimates

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.

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 On the Gevrey index for some hypoelliptic operators

1986 ◽  
Vol 26 (3) ◽  
pp. 387-402
Author(s):  
Takashi Ōkaji
Keyword(s):  
Hypoelliptic Operators

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 Evaluating performance of health care facilities at meeting HIV-indicator reporting requirements in Kenya: an application of K-means clustering algorithm

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Milka Bochere Gesicho ◽  
Martin Chieng Were ◽  
Ankica Babic
Keyword(s):  
Clustering Algorithm ◽  
Distinct Pattern ◽  
Health Care Facilities ◽  
Health Facilities ◽  
Hiv Care ◽  
Care Providers ◽  
Homogeneous Groups ◽  
Reporting Requirements ◽  
Low Middle Income Countries ◽  
Over Time

Abstract Background The ability to report complete, accurate and timely data by HIV care providers and other entities is a key aspect in monitoring trends in HIV prevention, treatment and care, hence contributing to its eradication. In many low-middle-income-countries (LMICs), aggregate HIV data reporting is done through the District Health Information Software 2 (DHIS2). Nevertheless, despite a long-standing requirement to report HIV-indicator data to DHIS2 in LMICs, few rigorous evaluations exist to evaluate adequacy of health facility reporting at meeting completeness and timeliness requirements over time. The aim of this study is to conduct a comprehensive assessment of the reporting status for HIV-indicators, from the time of DHIS2 implementation, using Kenya as a case study. Methods A retrospective observational study was conducted to assess reporting performance of health facilities providing any of the HIV services in all 47 counties in Kenya between 2011 and 2018. Using data extracted from DHIS2, K-means clustering algorithm was used to identify homogeneous groups of health facilities based on their performance in meeting timeliness and completeness facility reporting requirements for each of the six programmatic areas. Average silhouette coefficient was used in measuring the quality of the selected clusters. Results Based on percentage average facility reporting completeness and timeliness, four homogeneous groups of facilities were identified namely: best performers, average performers, poor performers and outlier performers. Apart from blood safety reports, a distinct pattern was observed in five of the remaining reports, with the proportion of best performing facilities increasing and the proportion of poor performing facilities decreasing over time. However, between 2016 and 2018, the proportion of best performers declined in some of the programmatic areas. Over the study period, no distinct pattern or trend in proportion changes was observed among facilities in the average and outlier groups. Conclusions The identified clusters revealed general improvements in reporting performance in the various reporting areas over time, but with noticeable decrease in some areas between 2016 and 2018. This signifies the need for continuous performance monitoring with possible integration of machine learning and visualization approaches into national HIV reporting systems.

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