How Keynes's Mathematical Analysis in Chapters 20 and 21 of the General Theory of His Elasticity Ew, Which Could Take on Any Values between ew =0 (Rigid, Given, Fixed, Constant, or Inflexible Money Wages) and ew =1 (Flexible Money Wages) Completely Destroys F. Modigliani's 1944 Econometrica Conclusion that Keynes's General Theory Category of Involuntary Unemployment Required Rigid Money Wages

2018 ◽  
Author(s):  
Michael Emmett Brady
Keyword(s):  
General Theory ◽  
Mathematical Analysis ◽  
Involuntary Unemployment ◽  
Fixed Constant

scholarly journals XII. On the theory of probabilities

1862 ◽  
Vol 152 ◽  
pp. 225-252 ◽  
Keyword(s):  
General Theory ◽  
Mathematical Analysis ◽  
Royal Society ◽  
General Character ◽  
Algebraic Equations ◽  
Functional Determinant ◽  
Complete Development ◽  
A Value ◽  
Peculiar Form

This paper has for its object the investigation of the general analytical conditions of a Method for the solution of Questions in the Theory of Probabilities, which was proposed by me in a work entitled “An Investigation of the Laws of Thought” (London, Walton and Maberly, 1854). The application of this method to particular problems has been illustrated in the work referred to, and yet more fully in a ‘Memoir on the Combination of Testimonies and of Judgments’ published in the Transactions of the Royal Society of Edinburgh (vol. xxi. Part 4). Some observations, too, on the general character of the solutions to which the method leads, founded upon induction from particular cases, were contained in the original treatise, and the outlines, still in some measure conjectural, of their general theory were given in an Appendix to the Memoir. But the complete development of that theory was attended with analytical difficulties which I have only lately succeeded in overcoming. It involves discussions relating to the properties of a certain functional determinant, and to the possible solutions of a system of algebraic equations of peculiar form—discussions which will, I trust, be thought to possess a value, as contributions to Mathematical Analysis, independent of their present application.

Density waves in disk galaxies

1967 ◽  
Vol 31 ◽  
pp. 313-317 ◽  
Author(s):  
C. C. Lin ◽  
F. H. Shu
Keyword(s):  
Mathematical Analysis ◽  
Spiral Structure ◽  
Stellar System ◽  
Collective Modes ◽  
Disk Galaxies ◽  
Spiral Pattern ◽  
Density Waves ◽  
The Galaxy ◽  
Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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