scholarly journals Geometric Compression Using Riemann Surface Structure

2003 ◽  
Vol 3 (3) ◽  
pp. 171-182 ◽  
Author(s):  
Xianfeng Gu ◽  
Yalin Wang ◽  
Shing-Tung Yau
2007 ◽  
Vol 26 (6) ◽  
pp. 853-865 ◽  
Author(s):  
Yalin Wang ◽  
Lok Ming Lui ◽  
Xianfeng Gu ◽  
Kiralee M. Hayashi ◽  
Tony F. Chan ◽  
...  

Author(s):  
Yalin Wang ◽  
Xianfeng Gu ◽  
Kiralee M. Hayashi ◽  
Tony F. Chan ◽  
Paul M. Thompson ◽  
...  

Author(s):  
Yalin Wang ◽  
Xianfeng Gu ◽  
K.M. Hayashi ◽  
T.F. Chan ◽  
P.M. Thompson ◽  
...  

2021 ◽  
Vol 2 (1) ◽  
pp. 7-16
Author(s):  
Ramya Deepak Shetty ◽  
Indira Narayana Swamy ◽  
Govind R Kadambi

In this paper, a generic procedure for the development and subsequent validation of the Riemann surface structure (RSS) for a punctured curved surface lying on a Riemann surface is discussed. The proposed procedure differs from the existing methods involving triangular meshes and rectangular grids that rely on induced patches on surfaces. This procedure can be applied to non-punctured surfaces as well as to surfaces with irregularly located punctures. Further, by defining appropriate transition functions, the proposed procedure eliminates the requirement for smooth transitions across the boundaries of adjacent patches. The analytic formulations of the RSS for an ellipsoid and a sphere are elaborated using the proposed procedure. Moreover, the RSS of a sphere defined through a family of conformal unit discs is proven equivalent to that defined by an existing method based on stereographic projection. This study proves that a smooth projection between the surface and (a subset of) the complex plane  , can be remapped to the original surface.


Author(s):  
Sanford H. Vernick ◽  
Anastasios Tousimis ◽  
Victor Sprague

Recent electron microscope studies have greatly expanded our knowledge of the structure of the Microsporida, particularly of the developing and mature spore. Since these studies involved mainly sectioned material, they have revealed much internal detail of the spores but relatively little surface detail. This report concerns observations on the spore surface by means of the transmission electron microscope.


Author(s):  
Robert M. Glaeser ◽  
Thea B. Scott

The carbon-replica technique can be used to obtain information about cell-surface structure that cannot ordinarily be obtained by thin-section techniques. Mammalian erythrocytes have been studied by the replica technique and they appear to be characterized by a pebbly or “plaqued“ surface texture. The characteristic “particle” diameter is about 200 Å to 400 Å. We have now extended our observations on cell-surface structure to chicken and frog erythrocytes, which possess a broad range of cellular functions, and to normal rat lymphocytes and mouse ascites tumor cells, which are capable of cell division. In these experiments fresh cells were washed in Eagle's Minimum Essential Medium Salt Solution (for suspension cultures) and one volume of a 10% cell suspension was added to one volume of 2% OsO4 or 5% gluteraldehyde in 0.067 M phosphate buffer, pH 7.3. Carbon replicas were obtained by a technique similar to that employed by Glaeser et al. Figure 1 shows an electron micrograph of a carbon replica made from a chicken erythrocyte, and Figure 2 shows an enlarged portion of the same cell.


Author(s):  
S. S. Breese ◽  
H. L. Bachrach

Models for the structure of foot-and-mouth disease virus (FMDV) have been proposed from chemical and physical measurements (Brown, et al., 1970; Talbot and Brown, 1972; Strohmaier and Adam, 1976) and from rotational image-enhancement electron microscopy (Breese, et al., 1965). In this report we examine the surface structure of FMDV particles by high resolution electron microscopy and compare it with that of particles in which the outermost capsid protein VP3 (ca. 30, 000 daltons) has been split into smaller segments, two of which VP3a and VP3b have molecular weights of about 15, 000 daltons (Bachrach, et al., 1975).Highly purified and concentrated type A12, strain 119 FMDV (5 mg/ml) was prepared as previously described (Bachrach, et al., 1964) and stored at 4°C in 0. 2 M KC1-0. 5 M potassium phosphate buffer at pH 7. 5. For electron microscopy, 1. 0 ml samples of purified virus and trypsin-treated virus were dialyzed at 4°C against 0. 2 M NH4OAC at pH 7. 3, deposited onto carbonized formvar-coated copper screens and stained with phosphotungstic acid, pH 7. 3.


Author(s):  
D. Johnson ◽  
P. Moriearty

Since several species of Schistosoma, or blood fluke, parasitize man, these trematodes have been subjected to extensive study. Light microscopy and conventional electron microscopy have yielded much information about the morphology of the various stages; however, scanning electron microscopy has been little utilized for this purpose. As the figures demonstrate, scanning microscopy is particularly helpful in studying at high resolution characteristics of surface structure, which are important in determining host-parasite relationships.


Author(s):  
O.L. Krivanek ◽  
G.J. Wood

Electron microscopy at 0.2nm point-to-point resolution, 10-10 torr specimei region vacuum and facilities for in-situ specimen cleaning presents intere; ing possibilities for surface structure determination. Three methods for examining the surfaces are available: reflection (REM), transmission (TEM) and profile imaging. Profile imaging is particularly useful because it giv good resolution perpendicular as well as parallel to the surface, and can therefore be used to determine the relationship between the surface and the bulk structure.


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