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Under Martin’s Axiom a c.c.c. nonseparable compact space is constructed which maps continuously into [0, 1] with linear fibers. Such a space can not, for instance, map onto [0, 1]ℵ1.
The order of a linearly invariant familiy in C^n
Schwarzian derivative homeomorphic extension ball univalence convexity Bergman metric weakly linearly convex projective dual space
2012/6/19
We study the (trace) norm of a linearly invariant family in the ball in $\C$. By adapting an approach that in one variable yields optimal results, we are able to derive an upper bound for the norm of ...
Spontaneous symmetry breaking in linearly coupled disk-shaped Bose-Einstein condensates
linearly coupled disk-shaped Bose-Einstein condensates Spontaneous symmetry breaking
2011/7/7
We study effects of tunnel coupling on a pair of parallel disk-shaped Bose-Einstein condensates with the self-attractive intrinsic nonlinearity. Each condensate is trapped in a combination of in-plane...
Reynolds number dependence of kinetic helicity decay in linearly forced turbulence
Reynolds number dependence linearly forced turbulence
2010/12/28
The decay of kinetic helicity is studied in numerical models of forced turbulence using either an externally imposed forcing function as an inhomogeneous term in the equations or, lternatively, a term...
On Archimedean Decompositions of Linearly Ordered Fields
On Archimedean Decompositions Linearly Ordered Fields
2010/11/22
In 1907, Hans Hahn proved the remarkable fact that any ordered group can be embedded in an ordered real function space. This set the stage for work on ordered groups and fields, and this area receive...
Note on a Differential-Geometrical Construction of Optimal Directions in Linearly-Constrained Systems
Linear programming Linear algebra Differential forms
2010/11/30
This note presents an analytic construction of the optimal unit-norm direction bx = x/||x|| that maximizes or minimizes the objective linear expression, B · bx, subject to a system of linear constrain...
Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations
Nonlinear instability linearly unstable standing waves nonlinear Schrö dinger equations
2010/12/13
We study the instability of standing waves for nonlinear Schr¨odinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimensi...
We prove that a C1,1-smooth bounded domain D in Cn is linearly convex if and only if the convex hull of any two discs in D with common center lies in D.