Range of the first two eigenvalues of the laplacian

1994 ◽  
Vol 447 (1930) ◽  
pp. 397-412 ◽  
Keyword(s):  
Local Minimum ◽  
Unit Area ◽  
Circular Disc ◽  
Planar Domain ◽  
Dirichlet Eigenvalues ◽  
Eigenvalues Of The Laplacian ◽  
Straight Lines

For each planar domain D of unit area, the first two Dirichlet eigenvalues of —∆ on D determine a point (λ 1 ( D ), λ 2 ( D ) in the (λ 1 , λ 2 ) plane. As D varies over all such domains, this point varies over a set R which we determine. Its boundary consists of two semi-infinite straight lines and a curve connecting their endpoints. This curve is found numerially. We also show how to minimize the n th eigenvalue when the minimizing domain is diconnected. For n = 3 we show that the minimizing domain is connected and that λ 3 is a local minimum for D a circular disc.

scholarly journals On the ‘Mean Flow’ Pore Size Distribution of Microfiber and Nanofiber Webs

2005 ◽  
Vol os-14 (1) ◽  
pp. 1558925005os-14 ◽  
Author(s):  
Norman Lifshutz
Keyword(s):  
Pore Diameter ◽  
Unit Area ◽  
Fiber Diameter ◽  
Cumulative Distribution ◽  
Mean Flow ◽  
Fibrous Filter ◽  
Fibrous Filter Media ◽  
The Mean ◽  
Two Layer Model ◽  
Straight Lines

A nonwoven fibrous filter media is modeled as a planar stochastic array of straight lines defining multiple polygons. The cumulative distribution and mean of the hydraulic diameter of these polygons is determined, and related theoretically to the “mean flow” pore diameter commonly measured by commercial partial flow testers. This model is tested against data obtained for a range of wetlaid glass microfiber handsheets and electrospun polymeric nanofiber webs. The results indicate that the simple two-layer model is inadequate. However, a statistically powerful correlation between “mean flow” pore diameter, total fiber length per unit area, and fiber diameter, is demonstrated to hold.

Radiation Damage, Contrast and Statistics in High Resolution Biological Electron Microscopy

1970 ◽  
Vol 28 ◽  
pp. 260-261
Author(s):  
Robert M. Glaeser
Keyword(s):  
High Resolution ◽  
Particle Flux ◽  
Unit Area ◽  
Signal To Noise ◽  
Resolution Image ◽  
High Resolution Image ◽  
Pass Through ◽  
Counting Statistics ◽  
The Relationship ◽  
Picture Element

It is well known that a large flux of electrons must pass through a specimen in order to obtain a high resolution image while a smaller particle flux is satisfactory for a low resolution image. The minimum particle flux that is required depends upon the contrast in the image and the signal-to-noise (S/N) ratio at which the data are considered acceptable. For a given S/N associated with statistical fluxtuations, the relationship between contrast and “counting statistics” is s131_eqn1, where C = contrast; r2 is the area of a picture element corresponding to the resolution, r; N is the number of electrons incident per unit area of the specimen; f is the fraction of electrons that contribute to formation of the image, relative to the total number of electrons incident upon the object.

Domain Formation in Synthetic Quartz

1971 ◽  
Vol 29 ◽  
pp. 156-157
Author(s):  
Joseph J. Comer
Keyword(s):  
Electron Beam ◽  
Room Temperature ◽  
Domain Formation ◽  
Synthetic Quartz ◽  
Transmission Electron ◽  
Black Spots ◽  
Diffraction Mode ◽  
Domain Boundaries ◽  
Kikuchi Lines ◽  
Straight Lines

Domains visible by transmission electron microscopy, believed to be Dauphiné inversion twins, were found in some specimens of synthetic quartz heated to 680°C and cooled to room temperature. With the electron beam close to parallel to the [0001] direction the domain boundaries appeared as straight lines normal to <100> and <410> or <510> directions. In the selected area diffraction mode, a shift of the Kikuchi lines was observed when the electron beam was made to traverse the specimen across a boundary. This shift indicates a change in orientation which accounts for the visibility of the domain by diffraction contrast when the specimen is tilted. Upon exposure to a 100 KV electron beam with a flux of 5x 1018 electrons/cm2sec the boundaries are rapidly decorated by radiation damage centers appearing as black spots. Similar crystallographio boundaries were sometimes found in unannealed (0001) quartz damaged by electrons.

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

Morphometric SEM study of the effects of ACTH on endothelial fenestrae in the rat adrenal cortex

1984 ◽  
Vol 42 ◽  
pp. 234-235
Author(s):  
J. Curtis ◽  
K. S. Schwartz ◽  
R. P. Apkarian
Keyword(s):  
Anterior Pituitary ◽  
Lipid Droplets ◽  
Adrenocorticotropic Hormone ◽  
Unit Area ◽  
High Density Lipoproteins ◽  
Capillary Endothelium ◽  
Zona Fasciculata ◽  
Sem Study ◽  
Saline Vehicle ◽  
Scanning Electron

A scanning electron microscope (SEM) study was made of the effect of adrenocorticotropic hormone (ACTH) on the size and numbers of fenestrae/unit area in the capillary endothelium of the zona fasciculata (ZF) of the rat adrenal. The stimulatory effect of ACTH on cholesterol uptake via high density lipoproteins in the rat and evidence for the secretion of glucocorticoids by exocytosis of lipid droplets described by Rhodin suggest that endothelial change may accompany these transport phenomena.Twelve rats received two Dexamethasone (DEX) ip injections (25 μg DEX/100 g body wt.), the first at 8 PM and the second at 8 AM the next day, to inhibit the release of endogenous ACTH by the anterior pituitary. The animals were then divided into two groups. Six animals received only saline vehicle and six rats received ACTH (100 ng/100 g body wt.).

Dissociated Σ=27 boundaries in silicon

1988 ◽  
Vol 46 ◽  
pp. 624-625
Author(s):  
A. Garg ◽  
W.A.T. Clark ◽  
J.P. Hirth
Keyword(s):  
Electron Diffraction ◽  
Local Minimum ◽  
Boundary Energy ◽  
Coincidence Site Lattice ◽  
Boundary Plane ◽  
Low Energy ◽  
Theoretical Understanding ◽  
Site Lattice ◽  
Kikuchi Pattern ◽  
Analysis Techniques

In the last twenty years, a significant amount of work has been done in the theoretical understanding of grain boundaries. The various proposed grain boundary models suggest the existence of coincidence site lattice (CSL) boundaries at specific misorientations where a periodic structure representing a local minimum of energy exists between the two crystals. In general, the boundary energy depends not only upon the density of CSL sites but also upon the boundary plane, so that different facets of the same boundary have different energy. Here we describe TEM observations of the dissociation of a Σ=27 boundary in silicon in order to reduce its surface energy and attain a low energy configuration.The boundary was identified as near CSL Σ=27 {255} having a misorientation of (38.7±0.2)°/[011] by standard Kikuchi pattern, electron diffraction and trace analysis techniques. Although the boundary appeared planar, in the TEM it was found to be dissociated in some regions into a Σ=3 {111} and a Σ=9 {122} boundary, as shown in Fig. 1.

The Application of Protein A-Gold Immunocytochemistry to Studies of Protein Secretion

1985 ◽  
Vol 43 ◽  
pp. 426-429
Author(s):  
George H. Herbener ◽  
Antonio Nanci ◽  
Moise Bendayan
Keyword(s):  
Tissue Section ◽  
Colloidal Gold ◽  
Unit Area ◽  
Protein A ◽  
Extracellular Proteins ◽  
Gold Complex ◽  
Second Step ◽  
Igg Antibodies ◽  
Tissue Sections ◽  
Antigenic Sites

Protein A-gold immunocytochemistry is a two-step, post-embedding labeling procedure which may be applied to tissue sections to localize intra- and extracellular proteins. The key requisite for immunocytochemistry is the availability of the appropriate antibody to react in an immune response with the antigenic sites on the protein of interest. During the second step, protein A-gold complex is reacted with the antibody. This is a non- specific reaction in that protein A will combine with most IgG antibodies. The ‘label’ visualized in the electron microscope is colloidal gold. Since labeling is restricted to the surface of the tissue section and since colloidal gold is particulate, labeling density, i.e., the number of gold particles per unit area of tissue section, may be quantitated with ease and accuracy.

Maximum Interlabial Pressures in Normal Speakers

1997 ◽  
Vol 40 (2) ◽  
pp. 400-404 ◽  
Author(s):  
Virginia A. Hinton ◽  
Winston M. C. Arokiasamy
Keyword(s):  
Speech Production ◽  
Contact Pressure ◽  
Direct Evidence ◽  
Unit Area ◽  
Jaw Movement ◽  
Contractile Forces ◽  
Contact Pressures ◽  
Muscle Contractile

It has been hypothesized that typical speech movements do not involve large muscular forces and that normal speakers use less than 20% of the maximum orofacial muscle contractile forces that are available (e.g., Amerman, 1993; Barlow & Abbs, 1984; Barlow & Netsell, 1986; DePaul & Brooks, 1993). However, no direct evidence for this hypothesis has been provided. This study investigated the percentage of maximum interlabial contact pressures (force per unit area) typically used during speech production. The primary conclusion of this study is that normal speakers typically use less than 20% of the available interlabial contact pressure, whether or not the jaw contributes to bilabial closure. Production of the phone [p] at conversational rate and intensity generated an average of 10.56% of maximum available interlabial pressure (MILP) when jaw movement was not restricted and 14.62% when jaw movement was eliminated.

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