CAUTIONARY NOTES ON THE RANK‐SIZE DISTRIBUTION

2019 ◽  
Vol 31 (3) ◽  
pp. 155-168
Author(s):  
John B. Parr
Keyword(s):  
Size Distribution

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Macrostructure and microphysics of Saturn's E-ring

1984 ◽  
Vol 75 ◽  
pp. 607-613 ◽  
Author(s):  
Kevin D. Pang ◽  
Charles C. Voge ◽  
Jack W. Rhoads
Keyword(s):  
Size Distribution ◽  
Spherical Shape ◽  
Mie Scattering ◽  
Narrow Size Distribution ◽  
Electrostatic Levitation ◽  
Volcanic Origin ◽  
Micron Diameter

Abstract.All observed optical and infrared properties of Saturn's E-ring can be explained in terms of Mie scattering by a narrow size distribution of ice spheres of 2 - 2.5 micron diameter. The spherical shape of the ring particles and their narrow size distribution imply a molten (possibly volcanic) origin on Enceladus. The E-ring consists of many layers, possibly stratified by electrostatic levitation.

Grain Refinement in Titanium-Erbium Alloys

1974 ◽  
Vol 32 ◽  
pp. 522-523
Author(s):  
B. B. Rath ◽  
J. E. O'Neal ◽  
R. J. Lederich
Keyword(s):  
Electron Microscopy ◽  
Size Distribution ◽  
Grain Refinement ◽  
Grain Growth ◽  
Volume Fraction ◽  
Pure Titanium ◽  
Systematic Investigation ◽  
Second Phase ◽  
Titanium Matrix ◽  
Average Size

Addition of small amounts of erbium has a profound effect on recrystallization and grain growth in titanium. Erbium, because of its negligible solubility in titanium, precipitates in the titanium matrix as a finely dispersed second phase. The presence of this phase, depending on its average size, distribution, and volume fraction in titanium, strongly inhibits the migration of grain boundaries during recrystallization and grain growth, and thus produces ultimate grains of sub-micrometer dimensions. A systematic investigation has been conducted to study the isothermal grain growth in electrolytically pure titanium and titanium-erbium alloys (Er concentration ranging from 0-0.3 at.%) over the temperature range of 450 to 850°C by electron microscopy.

Formation and Structure of Casein Micelles in Lactating Mammary Tissue

1970 ◽  
Vol 28 ◽  
pp. 150-151
Author(s):  
Robert J. Carroll ◽  
Marvin P. Thompson ◽  
Harold M. Farrell
Keyword(s):  
Size Distribution ◽  
G Protein ◽  
Milk Proteins ◽  
Mammary Tissue ◽  
Colloidal System ◽  
Casein Micelles ◽  
The Stability

Milk is an unusually stable colloidal system; the stability of this system is due primarily to the formation of micelles by the major milk proteins, the caseins. Numerous models for the structure of casein micelles have been proposed; these models have been formulated on the basis of in vitro studies. Synthetic casein micelles (i.e., those formed by mixing the purified αsl- and k-caseins with Ca2+ in appropriate ratios) are dissimilar to those from freshly-drawn milks in (i) size distribution, (ii) ratio of Ca/P, and (iii) solvation (g. water/g. protein). Evidently, in vivo organization of the caseins into the micellar form occurs in-a manner which is not identical to the in vitro mode of formation.

Crystallization of barium hexaferrite

1992 ◽  
Vol 50 (1) ◽  
pp. 362-363
Author(s):  
Chung-kook Lee ◽  
Yolande Berta ◽  
Robert F. Speyer
Keyword(s):  
Size Distribution ◽  
Raw Materials ◽  
Barium Hexaferrite ◽  
Recording Media ◽  
Magnetic Recording Media ◽  
Promising Candidate ◽  
Crystallization Method ◽  
Temperature Heat ◽  
High Density Magnetic Recording ◽  
Temperature Heat Treatment

Barium hexaferrite (BaFe12O19) is a promising candidate for high density magnetic recording media due to its superior magnetic properties. For particulate recording media, nano-sized single crystalline powders with a narrow size distribution are a primary application requirement. The glass-crystallization method is preferred because of the controllability of crystallization kinetics, hence, particle size and size distribution. A disadvantage of this method is the need to melt raw materials at high temperatures with non-reactive crucibles, e.g. platinum. However, in this work, we have shown that crystal growth of barium hexaferrite occurred during low temperature heat treatment of raw batches.

SIZE DISTRIBUTION AND ESR OF UNIFORM MICROCRYSTALS OF PLATINUM

1977 ◽  
Vol 38 (C2) ◽  
pp. C2-87-C2-91 ◽  
Author(s):  
D. A. GORDON ◽  
R. F. MARZKE ◽  
W. S. GLAUNSINGER
Keyword(s):  
Size Distribution

Effects of Particle Size Distribution on Corrosion Rate of Carbon Steel in Soil

2020 ◽  
Vol 69 (4) ◽  
pp. 102-106
Author(s):  
Shota Ohki ◽  
Shingo Mineta ◽  
Mamoru Mizunuma ◽  
Soichi Oka ◽  
Masayuki Tsuda
Keyword(s):  
Particle Size ◽  
Carbon Steel ◽  
Corrosion Rate ◽  
Particle Size Distribution ◽  
Size Distribution
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