Tensor product surfaces guided by minimal surface area triangulations

2002 ◽  
Author(s):  
J.K. Johnstone ◽  
K.R. Sloan
Keyword(s):  
Tensor Product ◽  
Minimal Surface ◽  
Surface Area ◽  
Minimal Surface Area

Application of Raman Spectroscopy to the Study of Adsorption Effects at Liquid-Solid Interfaces

1982 ◽  
Vol 36 (4) ◽  
pp. 471-473 ◽  
Author(s):  
Klaus Witke
Keyword(s):  
Raman Spectroscopy ◽  
Carbon Tetrachloride ◽  
Adsorption Isotherm ◽  
Minimal Surface ◽  
Linear Relationship ◽  
Surface Area ◽  
Long Range ◽  
Raman Spectra ◽  
Sample Cell ◽  
Minimal Surface Area

A sample cell for investigating suspensions or emulsions by Raman spectroscopy in the optically favorable 90° scattering arrangement is described. The Raman spectra of pyridine in a suspension of Aerosil 200 in carbon tetrachloride are recorded. The adsorption isotherm of pyridine is determined from the intensities of the Raman lines at 1008 and 990 cm−1. Over a long range of coverage a linear relationship exists between reciprocal concentrations of chemisorbed and dissolved molecules. The minimal surface area that is occupied by a chemisorbed molecule is determined to be approximately 0.75 nm2.

scholarly journals Origin and structure of Ubisch bodies in Pinus sylvestris

2014 ◽  
Vol 56 (2) ◽  
pp. 215-227 ◽  
Author(s):  
John R. Rowley ◽  
Björn Walles
Keyword(s):  
Plasma Membrane ◽  
Pinus Sylvestris ◽  
Minimal Surface ◽  
Surface Area ◽  
Body Wall ◽  
Current State ◽  
Ubisch Bodies ◽  
Ubisch Body ◽  
Tapetal Cells ◽  
Minimal Surface Area

In <em>Pinus sylvestris</em> Ubisch bodies are produced repeatedly, and each crop is formed at a distinct phase in the secretory cycles of tapetal cells. While each production has a Ubisch body wall similar to the then current state of the exine with regard to thickening and ornamentation, the survivers of previous productions do not change. Examples of all the structurally different Ubisch body wall forms can be seen when terminally, at the time of pollen shedding, the relict Ubisch bodies become spatially concentrated on the minimal surface area of the senescent cells of the tapetum. In angiosperms after one or a few periods of initiation Ubisch bodies may remain in association with the surface of tapetal cells where the Ubisch body wall undergoes changes like those of the maturing pollen exine. We conclude that as a consequence of Ubisch body detachment from the plasma membrane of tapetal cells there is in <em>Pinus sylvestris</em> no updated information for modification of the wall and the Ubisch body wall remains static.

Comparing the M-position with some classical positions of convex bodies

2011 ◽  
Vol 152 (1) ◽  
pp. 131-152 ◽  
Author(s):  
E. MARKESSINIS ◽  
G. PAOURIS ◽  
CH. SAROGLOU
Keyword(s):  
Minimal Surface ◽  
Surface Area ◽  
Convex Bodies ◽  
Mean Width ◽  
Quantitative Results ◽  
Minimal Surface Area

AbstractThe purpose of this paper is to compare some classical positions of convex bodies. We provide exact quantitative results which show that the minimal surface area position and the minimal mean width position are not necessarily M-positions. We also construct examples of unconditional convex bodies of minimal surface area that exhibit the worst possible behavior with respect to their mean width or their minimal hyperplane projection.

scholarly journals Sections of Convex Bodies in John’s and Minimal Surface Area Position

2021 ◽  
Author(s):  
David Alonso-Gutiérrez ◽  
Silouanos Brazitikos
Keyword(s):  
Minimal Surface ◽  
Surface Area ◽  
Convex Bodies ◽  
Regular Simplex ◽  
Symmetric Convex ◽  
Polar Bodies ◽  
Mean Width ◽  
Centrally Symmetric ◽  
The Mean ◽  
Minimal Surface Area

Abstract We prove several estimates for the volume, the mean width, and the value of the Wills functional of sections of convex bodies in John’s position, as well as for their polar bodies. These estimates extend some well-known results for convex bodies in John’s position to the case of lower-dimensional sections, which had mainly been studied for the cube and the regular simplex. Some estimates for centrally symmetric convex bodies in minimal surface area position are also obtained.

Evaluation and Comparison of the Surface Roughness and Porosity of Different Provisional Restorative Materials: An in vitro Study

2016 ◽  
Vol 8 (1) ◽  
pp. 39-45
Author(s):  
G Vinaya Kumar ◽  
Renuka Devi ◽  
Nimmy Anto
Keyword(s):  
Surface Roughness ◽  
Statistical Analysis ◽  
Minimal Surface ◽  
Surface Area ◽  
In Vitro Study ◽  
Acrylic Resin ◽  
Anova Test ◽  
Restorative Materials ◽  
Dial Indicator

ABSTRACT Aim The purpose of this study was to evaluate and compare the surface roughness and porosity of different provisional restorative materials. Materials and methods Provisional restorative materials were divided into following three groups: Dental products of india (DPI), Protemp, Tempofit. For each group, wax block with 20 × 10 × 3 mm was made for making vinyl polysiloxane impression material to give 12 samples in each group of three different provisional restorative materials. The acrylic resin was inserted into the silicon impression mold. A total of 12 specimens of one material were obtained. The specimens were finished with the help of lathe using a sequence of grit sand paper. The surface roughness was verified with the help of a micron dial indicator. To facilitate the porosity readings, the specimens were immersed in dye for 2 hours. The number of pores in each area was determined with a stereomicroscope with magnification 1× 50× to check the porosity of three different provisional restorative materials. Values were subjected to statistical analysis. Results Analysis of variance (ANOVA) test was used to compare between Tempofit, Protemp, and DPI. The results obtained indicated that surface roughness of Protemp was least compared with Tempofit and DPI. The ANOVA test was used to check surface area of porosities in each provisional material, followed by Kruskal–Wallis test and Mann–Whitney test (highly significant) (p < 0.001). The results obtained indicate that Protemp material showed the least number of porosities and minimal surface roughness followed by Tempofit and DPI. Henceforth, it can be concluded that among the three tested materials, Protemp was the best material which can be used for provisional restorations. Conclusion Surface roughness and porosity were compared among Protemp, Tempofit, and DPI material; the best results were obtained with the use of Protemp material which had shown the least number of porosities and minimal surface roughness. How to cite this article Kumar GV, Devi R, Anto N. Evaluation and Comparison of the Surface Roughness and Porosity of Different Provisional Restorative Materials: An in vitro Study. CODS J Dent 2016;8(1):39-45.

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