scholarly journals On the stable size distribution of populations reproducing by fission into two unequal parts

1984 ◽  
Vol 72 (1) ◽  
pp. 19-50 ◽  
Author(s):  
H.J.A.M. Heijmans
2018 ◽  
Vol 41 (8) ◽  
pp. 2894-2905 ◽  
Author(s):  
Luis M. Abia ◽  
Óscar Angulo ◽  
Juan Carlos López-Marcos ◽  
Miguel Ángel López-Marcos

1999 ◽  
Vol 07 (03) ◽  
pp. 285-306
Author(s):  
HAMILTON F. LECKAR ◽  
LAÉRCIO L. VENDITE

A size-structured model is developed to study the growth of tumor cell populations during chemotherapeutic treatment with two non-cross resistant drugs, [Formula: see text] and [Formula: see text]. The cells reproduce by fission. Four types of cells are considered: sensitive cells to both [Formula: see text] and [Formula: see text], cells that are resistant to [Formula: see text] only, cells that are resistant to [Formula: see text] only, and cells that are resistant to both [Formula: see text] and [Formula: see text]. Resistant cells arise by spontaneous genetic mutation from sensitive cells and are selected during the growth of the mixed population. The model consists on a system of linear partial differential equations describing the size-density of each type of cells. That corresponds to chemotherapeutic treatment on a given time sequence intervals such that, we continuously apply [Formula: see text] at a first interval and next we apply [Formula: see text] at a second interval, and so forth. We obtain a stable size-distribution theorem for this case.


2012 ◽  
Vol 71 (8) ◽  
pp. 694-701 ◽  
Author(s):  
Alberto Serrano-Pozo ◽  
Matthew L. Mielke ◽  
Alona Muzitansky ◽  
Teresa Gómez-Isla ◽  
John H. Growdon ◽  
...  

1983 ◽  
Vol 18 (2) ◽  
pp. 135-148 ◽  
Author(s):  
O. Diekmann ◽  
H. A. Lauwerier ◽  
T. Aldenberg ◽  
J. A. J. Metz

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell

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.


1984 ◽  
Vol 75 ◽  
pp. 607-613 ◽  
Author(s):  
Kevin D. Pang ◽  
Charles C. Voge ◽  
Jack W. Rhoads

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.


Author(s):  
B. B. Rath ◽  
J. E. O'Neal ◽  
R. J. Lederich

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.


Author(s):  
Robert J. Carroll ◽  
Marvin P. Thompson ◽  
Harold M. Farrell

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.


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