Criteria for the Boundedness and Complete Continuity of Certain Imbedding Operators

1971 ◽  
pp. 101-105
Author(s):  
V. L. Oleinik ◽  
B. S. Pavlov
Keyword(s):  
Complete Continuity

scholarly journals The complete continuity property in Bochner function spaces

1993 ◽  
Vol 117 (4) ◽  
pp. 1109-1109 ◽  
Author(s):  
Narcisse Randrianantoanina ◽  
Elias Saab
Keyword(s):  
Function Spaces ◽  
Continuity Property ◽  
Complete Continuity

On a Non-linear Boundary-Layer Problem for the Fractional Blasius-Type Equation

2018 ◽  
Vol 19 (5) ◽  
pp. 493-498
Author(s):  
Ramiz Tapdigoglu ◽  
Berikbol T. Torebek
Keyword(s):  
Type Equation ◽  
Linear Integral Equation ◽  
Linear Boundary ◽  
Complete Continuity ◽  
Existence Of A Solution ◽  
Boundary Layer Problem ◽  
Blasius Equation ◽  
Non Linear ◽  
Linear Integral ◽  
Layer Problem

AbstractIn this paper, we consider a non-linear sequential differential equation with Caputo fractional derivative of Blasius type and we reduce the problem to the equivalent non-linear integral equation. We prove the complete continuity of the non-linear integral operator. The theorem on the existence of a solution of the problem for the Blasius equation of fractional order is also proved.

A Compact Imbedding Theorem for Functions without Compact Support

1971 ◽  
Vol 14 (3) ◽  
pp. 305-309 ◽  
Author(s):  
R. A. Adams ◽  
John Fournier
Keyword(s):  
Sobolev Space ◽  
Compact Support ◽  
Unbounded Domains ◽  
Bounded Domains ◽  
Complete Continuity ◽  
Compact Imbedding ◽  
Compactness Theorems ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Made In

The extension of the Rellich-Kondrachov theorem on the complete continuity of Sobolev space imbeddings of the sort1to unbounded domains G has recently been under study [1–5] and this study has yielded [4] a condition on G which is necessary and sufficient for the compactness of (1). Similar compactness theorems for the imbeddings2are well known for bounded domains G with suitably regular boundaries, and the question naturally arises whether any extensions to unbounded domains can be made in this case.

scholarly journals Ancient mitogenomes show plateau populations from last 5200 years partially contributed to present-day Tibetans

2020 ◽  
Vol 287 (1923) ◽  
pp. 20192968 ◽  
Author(s):  
Manyu Ding ◽  
Tianyi Wang ◽  
Albert Min-Shan Ko ◽  
Honghai Chen ◽  
Hui Wang ◽  
...  
Keyword(s):  
Mitochondrial Dna ◽  
Deep Learning ◽  
Tibetan Plateau ◽  
High Altitude ◽  
Simulation Models ◽  
The Tibetan Plateau ◽  
Limited Evidence ◽  
Complete Continuity ◽  
Genetic Origins ◽  
Low Altitude

The clarification of the genetic origins of present-day Tibetans requires an understanding of their past relationships with the ancient populations of the Tibetan Plateau. Here we successfully sequenced 67 complete mitochondrial DNA genomes of 5200 to 300-year-old humans from the plateau. Apart from identifying two ancient plateau lineages (haplogroups D4j1b and M9a1a1c1b1a) that suggest some ancestors of Tibetans came from low-altitude areas 4750 to 2775 years ago and that some were involved in an expansion of people moving between high-altitude areas 2125 to 1100 years ago, we found limited evidence of recent matrilineal continuity on the plateau. Furthermore, deep learning of the ancient data incorporated into simulation models with an accuracy of 97% supports that present-day Tibetan matrilineal ancestry received partial contribution rather than complete continuity from the plateau populations of the last 5200 years.

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