Chapter III. Elementary Theory of 𝑙-adic Integration

The purpose of this paper is to develop and to consider in detail some of the expressions which may be applied to reactions involving simple hæmolytic systems. In doing so, a number of rather unusual conditions have to be considered; these may first be set down. 1. It has been shown (1) that the curves obtained by plotting the amount of hæmolysis, expressed as a percentage of the total, against time, are sigmoid in form, the sigmoid curve often presenting a considerable degree of skewness in one or the other direction. In explanation of this form, it was suggested that the cells of the system present different degrees of resistance to the action of the lysin, these resistances being distributed according to a symmetrical frequency curve, and that the skewness encountered is due to the presence of secondary reactions, principally the reaction of the liberated cell-contents with the lysin. Such suggestions are, in general, in agreement with the findings of Brooks (2), of Fulmer and Buchanan (3), and of other workers on hæmolysis and the allied problem of bacteriolysis. To the two papers mentioned the reader is referred for excellent discussions of both facts and elementary theory, as well as for reviews of the literature. It appears that the bulk of the recent investigation has shown that these variations in cell resistance, and the distribution of these resistances, are of fundamental importance in problems of this kind, and that it is completely fallacious to deal with such problems without allowing for the heterogeneity of the material involved.

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Elementary theory of molecular beam scattering

Journal of Chemical Education ◽

10.1021/ed043p480 ◽

1966 ◽

Vol 43 (9) ◽

pp. 480

Author(s):

C. J. G. Raw

Keyword(s):

Molecular Beam ◽

Elementary Theory ◽

Molecular Beam Scattering ◽

Beam Scattering

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Bending of an Infinite Beam on an Elastic Foundation

Journal of Applied Mechanics ◽

10.1115/1.4008739 ◽

1937 ◽

Vol 4 (1) ◽

pp. A1-A7 ◽

Cited By ~ 18

Author(s):

M. A. Biot

Keyword(s):

Elastic Foundation ◽

Poisson Ratio ◽

Elementary Theory ◽

Three Dimensional ◽

Bending Moment ◽

Two Dimensional ◽

Concentrated Load ◽

Elastic Continuum ◽

Infinite Beam ◽

A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

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Social Structures in Transition: Applications of Two Theories to Chiefdoms

Socius Sociological Research for a Dynamic World ◽

10.1177/2378023118771758 ◽

2018 ◽

Vol 4 ◽

pp. 237802311877175 ◽

Cited By ~ 1

Author(s):

Pamela Emanuelson ◽

David Willer

Keyword(s):

Elementary Theory ◽

Social Structures ◽

High Status ◽

Structural Form ◽

Downward Mobility ◽

Status Characteristics Theory ◽

The Third ◽

Status Characteristics ◽

The Status ◽

Lineage Structure

Status characteristics theory and elementary theory are applied to explain developments through three structural forms that chiefdoms are known to take. Theoretic models find that downward mobility inherent in the first form, the status-lineage structure, destabilizes its system of privilege. As a consequence, high-status actors are motivated to find mechanisms to preserve and enhance privilege. By engaging in hostile relations with other chiefdoms, high-status actors offer protection to low-status others from real or imagined threats. Through that protection, they gain tribute and support. The result is structural change from influence based on status to power exercised through indirect coercion, the second structural form. In settled societies, accumulation through war and selective redistribution contribute to separation of warrior and commoner rankings. That separation leads to the third structural form, direct coercive chiefdom.

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