scholarly journals On dendroids and their end-points and ramification points in the classical sense

1984 ◽  
Vol 124 (2) ◽  
pp. 99-108 ◽  
Author(s):  
Jacek Nikiel
2021 ◽  
Vol 24 (6) ◽  
pp. 1797-1830
Author(s):  
Chenkuan Li

Abstract The objective of this paper is, for the first time, to extend the fractional Laplacian (−△) s u(x) over the space Ck (Rn ) (which contains S(Rn ) as a proper subspace) for all s > 0 and s ≠ 1, 2, …, based on the normalization in distribution theory, Pizzetti’s formula and surface integrals in Rn . We further present two theorems showing that our extended fractional Laplacian is continuous at the end points 1, 2, … . Two illustrative examples are provided to demonstrate computational techniques for obtaining the fractional Laplacian using special functions, Cauchy’s residue theorem and integral identities. An application to defining the Riesz derivative in the classical sense at odd numbers is also considered at the end.


1962 ◽  
Vol 51 (3) ◽  
pp. 229-252 ◽  
Author(s):  
Janusz Charatonik

1991 ◽  
Vol 138 (2) ◽  
pp. 139-146
Author(s):  
J. Nikiel ◽  
E. Tymchatyn

2012 ◽  
Vol 40 (9) ◽  
pp. 5
Author(s):  
Michele G. Sullivan
Keyword(s):  

2011 ◽  
Vol 6 (1) ◽  
pp. 39
Author(s):  

Background:Since the first reported use of percutaneous transluminal coronary angioplasty, advances in the interventional cardiology arena have been fast paced. Developers and clinicians are adapting from the learning curve awarded by the time-course of drug-eluting stent (DES) evolution. BioMime™ sirolimus-eluting stent (SES) is a step towards biomimicry. The stent is built on a strut of ultra-low thickness (65μm), a cobalt–chromium platform using an intelligent hybrid of closed and open cells allowing for morphology-mediated expansion. It employs a well-known antiproliferative – sirolimus – that elutes from a known biodegradable copolymer formulation within 30 days. The resultant stent demonstrates almost 100% endothelialisation at 30 days in preclinical models.Methods:The meriT-1 was a prospective, single-arm, single-centre trial to evaluate the safety and efficacy of BioMime SES in 30 patients with a single de novo lesion in native coronary arteries. The primary safety and efficacy end-points were major adverse cardiac events (MACE) at 30 days and in-stent late lumen loss at eight months, as measured using quantitative coronary angiographic (QCA) method. Secondary safety and efficacy end-points included MACE at one and two years and angiographic binary restenosis at eight-month angiographic follow-up. Other end-points included the occurrence of stent thrombosis at acute, subacute, late and very late periods and the percentage of diameter stenosis by QCA.Results:No MACE were observed and the median in-stent late luminal loss in 20 (67%) subjects studied by QCA was 0.15mm, with 0% binary restenosis at eight-month follow-up. No stent thrombosis was observed up to one-year follow-up.Conclusions:In comparison to currently available DES, BioMime SES appears to have a considerable scientific basis for prevention of neointimal proliferation, restenosis and associated clinical events.


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