For P a poset or lattice, let Id(P ) denote the poset, respectively, lattice, of upward directed downsets in P, including the empty set, and let id(P ) = Id(P )−{∅}. This note obtains various results to the effect that Id(P ) is always, and id(P ) often, “essentially larger” than P. In the first vein, we find that a poset P admits no <-respecting map (and so in particular, no one-to-one isotone...

This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is given. In the case of an ideal lattice of a lattice L, the decomposition into subdirectly irreducib...

The fundamental underpinnings of the well-known Bernoulli’s Equation, as used to describe steady state two-dimensional flow of an ideal incompressible irrotational flow, are typically described in terms of partial differential equations. However, it has been shown that the Cauchy Integral Theorem of standard complex variables also explain the Bernoulli’s Equation and, hence, can be directly use...

The effect of equilibrium velocity shear on the resistive tearing instability has been systematically studied, using the boundary layer approach. Both the "constant-f/!" tearing mode, which has a growth rate that scales as S -3/5, and the "nonconstant-f/!" tearing mode [a' (as) -1/3» 1], which has a growth rate that scales as S -1/3, are analyzed in the presence of flow. Here S is the usual rat...

  In this study, fluid flow and energy separation in a micro-scale Ranque-HilschVortex Tube are numerically investigated. The flow is assumed as 2D, steady,compressible ideal gas, and shear-stress-transport SST k-W is found to be a bestchoice for modeling of turbulence phenomena. The results are in a good agreementwith the experimental results reported in the literature. The results show that f...

Exploiting the analogy between exemplar models and population coding schemes, we characterize, by means of information theoretic tools, the efficiency of a large but finite population of cells coding for a discrete set of categories (e.g. vowels). The optimal code is shown to typically allocate more cells to class boundaries than to regions further apart. We then discuss the predicted perceptua...

We consider the problem of designing reliable and confidential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for finite lattice constellations a finite sum of inverse of algebraic norms, in fact the analogous for finite sums of the known criterion for infinite constellations, which motivates us to study totally real number fields w...