Implementing Financial Equilibrium of Incomplete Markets: Bounded Portfolios and the Limiting Case

1998 ◽  
pp. 181-191 ◽  
Author(s):  
Monique Florenzano ◽  
Pascal Gourdel ◽  
Valeri Marakulin
Author(s):  
Joseph A. Zasadzinski

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.


Author(s):  
J. M. Walsh ◽  
J. C. Whittles ◽  
B. H. Kear ◽  
E. M. Breinan

Conventionally cast γ’ precipitation hardened nickel-base superalloys possess well-defined dendritic structures and normally exhibit pronounced segregation. Splat quenched, or rapidly solidified alloys, on the other hand, show little or no evidence for phase decomposition and markedly reduced segregation. In what follows, it is shown that comparable results have been obtained in superalloys processed by the LASERGLAZE™ method.In laser glazing, a sharply focused laser beam is traversed across the material surface at a rate that induces surface localized melting, while avoiding significant surface vaporization. Under these conditions, computations of the average cooling rate can be made with confidence, since intimate contact between the melt and the self-substrate ensures that the heat transfer coefficient is reproducibly constant (h=∞ for perfect contact) in contrast to the variable h characteristic of splat quenching. Results of such computations for pure nickel are presented in Fig. 1, which shows that there is a maximum cooling rate for a given absorbed power density, corresponding to the limiting case in which melt depth approaches zero.


2012 ◽  
Vol 21 (2) ◽  
pp. 223-243
Author(s):  
Irit Degani-Raz

The idea that Beckett investigates in his works the limits of the media he uses has been widely discussed. In this article I examine the fiction Imagination Dead Imagine as a limiting case in Beckett's exploration of limits at large and the limits of the media he uses in particular. Imagination Dead Imagine is shown to be the self-reflexive act of an artist who imaginatively explores the limits of that ultimate medium – the artist's imagination itself. My central aim is to show that various types of structural homologies (at several levels of abstraction) can be discerned between this poetic exploration of the limits of imagination and Cartesian thought. The homologies indicated here transcend what might be termed as ‘Cartesian typical topics’ (such as the mind-body dualism, the cogito, rationalism versus empiricism, etc.). The most important homologies that are indicated here are those existing between the role of imagination in Descartes' thought - an issue that until only a few decades ago was quite neglected, even by Cartesian scholars - and Beckett's perception of imagination. I suggest the use of these homologies as a tool for tracing possible sources of inspiration for Beckett's Imagination Dead Imagine.


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