Computation of Graphical Derivative for a Class of Normal Cone Mappings under a Very Weak Condition

2017 ◽  
Vol 27 (1) ◽  
pp. 190-204 ◽  
Author(s):  
Nguyen Huy Chieu ◽  
Le Van Hien
Keyword(s):  
Normal Cone ◽  
Weak Condition ◽  
Graphical Derivative

Proximal Normal Cone Analysis on Smooth Banach Spaces and Applications

2014 ◽  
Vol 24 (1) ◽  
pp. 363-384 ◽  
Author(s):  
Xi Yin Zheng ◽  
Kung Fu Ng
Keyword(s):  
Banach Spaces ◽  
Normal Cone ◽  
Proximal Normal Cone

VARIATIONAL PRINCIPLE FOR SUBADDITIVE SEQUENCE OF POTENTIALS IN BUNDLE RANDOM DYNAMICAL SYSTEMS

2009 ◽  
Vol 09 (02) ◽  
pp. 205-215 ◽  
Author(s):  
XIANFENG MA ◽  
ERCAI CHEN
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Multifractal Analysis ◽  
Weak Condition ◽  
Random Dynamical Systems ◽  
Topological Pressure ◽  
Set Up

The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in the study of multifractal analysis for random version of nonconformal dynamical systems.

scholarly journals In what spaces is every closed normal cone regular?

1970 ◽  
Vol 17 (2) ◽  
pp. 121-125 ◽  
Author(s):  
C. W. McArthur
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Unconditional Basis ◽  
Normal Cone ◽  
Closed Subspace ◽  
Locally Convex Space ◽  
Regular Part ◽  
Fréchet Space ◽  
Sequential Completeness ◽  
Locally Convex

It is known (13, p. 92) that each closed normal cone in a weakly sequentially complete locally convex space is regular and fully regular. Part of the main theorem of this paper shows that a certain amount of weak sequential completeness is necessary in order that each closed normal cone be regular. Specifically, it is shown that each closed normal cone in a Fréchet space is regular if and only if each closed subspace with an unconditional basis is weakly sequentially complete. If E is a strongly separable conjugate of a Banach space it is shown that each closed normal cone in E is fully regular. If E is a Banach space with an unconditional basis it is shown that each closed normal cone in E is fully regular if and only if E is the conjugate of a Banach space.

JOHN LOCKE ON THE CARE OF THE NEWBORN INFANT (1684)

PEDIATRICS ◽  
1979 ◽  
Vol 64 (2) ◽  
pp. 237-237
Author(s):  
T. E. C.
Keyword(s):  
Olive Oil ◽  
Newborn Infant ◽  
John Locke ◽  
Red Wine ◽  
Weak Condition ◽  
Newborn Baby ◽  
Almond Oil ◽  
Human Understanding ◽  
Essay Concerning Human Understanding ◽  
Medical Interest

John Locke (1632-1704), physician and philosopher, is best known for his Essay Concerning Human Understanding (1690). His reputation as a philosopher has overshadowed the extent of his medical interests. Locke's journals between 1678 and 1698 contain thousands of items of medical interest. An entry in his journal for September 1684 contained the following recommendations for the care of the newborn infant.1 1. Soon after birth the baby can be given 1 or 2 spoonfuls of syrup of violets with almond oil, to loosen the bowels and keep it from convulsive colic. Or else distilled olive oil can be mixed with sugar. 2. If the newborn baby is in a weak condition you can blow on it the smell of chewed onions and cloves; smear its nostrils and lips with Cinnamon water; press warm slices of meat on its head and anus; wrap in bandages soaked in red wine and place in a bath composed of water or beer and fresh butter. If the baby is lively give a little after a mixture of 1 spoonful of distilled almond oil and syrup of Cowslip flowers and ½ spoonful of wine tempered with sugar, so that it can purge itself properly. 3. As soon as it begins to feed on pap, give it for the first few days a little powder of Marchion. 4. If it is weak apply to the region of the heart a cloth coaked with warm Embryon. The best ways to stimulate its strength are baths, putting warm wine on its head, placing hot meat on its chest, smearing its nose and lips with cinnamon water, putting onions near its nostrils, etc.

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