scholarly journals The Gaussian Double-Bubble and Multi-Bubble Conjectures

2022 ◽  
Vol 195 (1) ◽  
Author(s):  
Emanuel Milman ◽  
Joe Neeman
Keyword(s):  
Double Bubble

scholarly journals Polyurethane-Coated Implants for Prevention of Double-Bubble Effect in Breast Augmentation

2021 ◽  
Vol 7 ◽  
pp. 2513826X2110289
Author(s):  
Vitali Bagirov
Keyword(s):  
United States ◽  
Breast Augmentation ◽  
Cosmetic Surgery ◽  
The United States ◽  
Treatment Result ◽  
Lower Pole ◽  
Common Complication ◽  
Breast Volume ◽  
Double Bubble ◽  
Growing Body

Breast augmentation is the most frequently performed cosmetic surgery in the United States, with approximately 279,000 patients every year. The so-called double-bubble effect (DBE) is a common complication in breast augmentation. This complication is characterized by folds running along the lower pole of the breast, forming distinct bubble-like protrusions above and below the fold. Factors that increase the risk of DBE include bulbous breasts and a large native breast volume. There is evidence that polyurethane-coated (PU) implants may help to reduce the risk of DBE. We describe here the case of a 47-year old patient for whom DBE has recurred in each of 4 tandem breast surgeries. PU implants ultimately appeared to prevent the DBE, leading to an aesthetically satisfying treatment result for the patient. This case adds weigh to the growing body of evidence that supports the use of polyurethane implants to prevent DBE.

Duodenal atresia: not always a double bubble

2014 ◽  
Vol 44 (8) ◽  
pp. 1031-1034 ◽  
Author(s):  
Jonathan M. Latzman ◽  
Terry L. Levin ◽  
Suhas M. Nafday
Keyword(s):  
Duodenal Atresia ◽  
Double Bubble

Physical properties of biaxially oriented PA6 film for simultaneous stretching and sequential processing

2011 ◽  
Vol 31 (1) ◽  
Author(s):  
Masao Takashige ◽  
Toshitaka Kanai
Keyword(s):  
Impact Strength ◽  
Physical Properties ◽  
Physical Property ◽  
High Impact ◽  
Thermal Shrinkage ◽  
Double Bubble ◽  
Biaxial Stretching ◽  
High Impact Strength ◽  
The Difference ◽  
Stretching Process

Abstract There are two different stretching processes that produce the biaxially oriented film, namely the tenter process and double bubble tubular film process. Furthermore, there are two tenter processes, i.e., the sequential biaxial stretching process and simultaneous biaxial stretching process. There is no report describing the difference among film physical properties of the three different processes. The biaxially oriented polyamide film using the double bubble tubular process has good balanced physical property and high impact strength, thus it is used for proper applications utilizing their advantage properties. In this report, the influence of each biaxial stretching process on film physical properties of polyamide, which has hydrogen bond, was studied in detail. As a result, the tentering process film has anisotropic tensile properties between machine direction (MD) and transverse direction (TD). This result was influenced by a later stretching process, namely TD stretching. On the contrary, the double bubble tubular film has good balanced properties, especially thermal shrinkage and impact strength. Tentering simultaneous stretching film has much larger shrinkage in MD than in TD. The sequential stretching film has larger shrinkage in TD than in MD. The double bubble tubular film has high impact strength, because it corresponds to the balanced molecular orientation.

scholarly journals Symmetric double bubbles in the Grushin plane

2019 ◽  
Vol 25 ◽  
pp. 77
Author(s):  
Valentina Franceschi ◽  
Giorgio Stefani
Keyword(s):  
Direct Method ◽  
Regularity Theory ◽  
Contact Interface ◽  
Double Bubble ◽  
Grushin Plane ◽  
Existence Of Minimizers ◽  
Double Bubbles ◽  
The Given ◽  
Suitable Change ◽  
Horizontal Interface

We address the double bubble problem for the anisotropic Grushin perimeter Pα, α ≥ 0, and the Lebesgue measure in ℝ2, in the case of two equal volumes. We assume that the contact interface between the bubbles lies on either the vertical or the horizontal axis. We first prove existence of minimizers via the direct method by symmetrization arguments and then characterize them in terms of the given area by first variation techniques. Even though no regularity theory is available in this setting, we prove that angles at which minimal boundaries intersect satisfy the standard 120-degree rule up to a suitable change of coordinates. While for α = 0 the Grushin perimeter reduces to the Euclidean one and both minimizers coincide with the symmetric double bubble found in Foisy et al. [Pacific J. Math. 159 (1993) 47–59], for α = 1 vertical interface minimizers have Grushin perimeter strictly greater than horizontal interface minimizers. As the latter ones are obtained by translating and dilating the Grushin isoperimetric set found in Monti and Morbidelli [J. Geom. Anal. 14 (2004) 355–368], we conjecture that they solve the double bubble problem with no assumptions on the contact interface.

Case 26: Left Double Bubble

2016 ◽  
pp. 277-280
Author(s):  
Michael J. Higgs ◽  
John Flynn ◽  
Robert Yoho ◽  
David Topchian ◽  
Melvin A. Shiffman
Keyword(s):  
Double Bubble
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