Rafik Hariri philanthropic and developmental contributions are countless. The most remarkable being the multifaceted support to educate more than 36,000 Lebanese university students within Lebanon, and beyond.
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STEEPEST DESCENT ON A UNIFORMLY CONVEX SPACE
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Mohamad M. ZAHRAN
|
Univ. |
University of North Texas |
Spec. |
Mathematics |
Dip. |
Year |
# Pages |
|
Ph.D. |
1995 |
65 |
This paper contains four main ideas: First, it shows global existence for the steepest descent in the uniformly convex setting.
Secondly, it shows existence of critical points for convex functions defined on uniformly convex spaces.
Thirdly, it shows an isomorphism between the dual space of H1,P[0,1] and the space H1,q [0,1], where p > 2 and 1/p +1/q = 1.
Fourthly, it shows how the Beurling-Denny theorem can be extended to find a useful function from H1,P[0,1] to LP[0,1], where p > 2 and addresses the problem of using that function to establish a relationship between the ordinary and the Sobolev gradients. The paper contains some numerical experiments and two computer codes.
