scholarly journals Codensity and stone spaces

2018 ◽  
Vol 68 (1) ◽  
pp. 57-70
Author(s):  
Andrei Sipoş
Keyword(s):  
Stone Spaces ◽  
Detailed Computation

AbstractWe present a detailed computation of two codensity monads associated to two canonical functors – the inclusion functor ofFinSetintoTopand the inclusion functor of the category of the powers of the Sierpiński space intoTop. We show that the categories of algebras of the two monads are the categories of Stone spaces and of sober spaces, respectively. A new motivation for defining these classes of spaces is therefore obtained.

QUASI-TOPOLOGICAL STONE SPACES

1994 ◽  
Vol 27 (3-4) ◽  
Author(s):  
Bronislaw Tembrowski
Keyword(s):  
Stone Spaces

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

scholarly journals A category of compositional domain-models for separable Stone spaces

2003 ◽  
Vol 290 (1) ◽  
pp. 599-635 ◽  
Author(s):  
Fabio Alessi ◽  
Paolo Baldan ◽  
Furio Honsell
Keyword(s):  
Domain Models ◽  
Stone Spaces

scholarly journals Bitopological duality for distributive lattices and Heyting algebras

2010 ◽  
Vol 20 (3) ◽  
pp. 359-393 ◽  
Author(s):  
GURAM BEZHANISHVILI ◽  
NICK BEZHANISHVILI ◽  
DAVID GABELAIA ◽  
ALEXANDER KURZ
Keyword(s):  
Boolean Algebras ◽  
Distributive Lattices ◽  
Heyting Algebras ◽  
Priestley Spaces ◽  
Spectral Spaces ◽  
Algebraic Concepts ◽  
Stone Spaces

We introduce pairwise Stone spaces as a bitopological generalisation of Stone spaces – the duals of Boolean algebras – and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important in the study of distributive lattices. We also give new bitopological and spectral dualities for Heyting algebras, thereby providing two new alternatives to Esakia's duality.

scholarly journals White Dwarf Crystallization

1994 ◽  
Vol 147 ◽  
pp. 161-185
Author(s):  
Enrique Garcia-Berro ◽  
Margarida Hernanz
Keyword(s):  
White Dwarf ◽  
Luminosity Function ◽  
Crystallization Process ◽  
Galactic Disk ◽  
Chemical Species ◽  
Galactic Chemical Evolution ◽  
Crucial Importance ◽  
Solidification Processes ◽  
Detailed Computation

AbstractThe inclusion of a detailed treatment of solidification processes in the cooling theory of carbon–oxygen white dwarfs is of crucial importance for the determination of their luminosity function. Carbon–oxygen separation at crystallization yields delays larger than 2 Gyr to cool down to luminosities corresponding to the observed cut–off. This leads to estimates of the age of the galactic disk 1.5 to 2 Gyr older than the ones obtained in previous studies (about 9 Gyr). Furthermore, the presence of minor chemical species, in particular 22Ne, alters significantly the crystallization process, and produces extra delays of 2 to 3 gigayears. However, the detailed computation of the theoretical white dwarf luminosity function, taking into account a reasonable model of galactic chemical evolution, and including the effect of these species, shows that the location of the cut–off, and then the estimated age of the disk, is not modified significantly.

scholarly journals Transient fields produced by a cylindrical electron beam flowing through a plasma

2012 ◽  
Vol 30 (3) ◽  
pp. 497-507
Author(s):  
Marie-Christine Firpo
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Laplace Transform ◽  
Control Parameter ◽  
Bessel Functions ◽  
Skin Depth ◽  
The Other ◽  
Beam Radius ◽  
Equilibrium Situation ◽  
Detailed Computation

AbstractThe out-of-equilibrium situation in which an initially sharp-edged cylindrical electron beam, that could, e.g., model electrons flowing within a wire, is injected into a plasma is considered. A detailed computation of the subsequently produced magnetic field is presented. The control parameter of the problem is shown to be the ratio of the beam radius to the electron skin depth. Two alternative ways to address analytically the problem are considered: one uses the usual Laplace transform approach, the other one involves Riemann's method in which causality conditions manifest through some integrals of triple products of Bessel functions.

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