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Absolute continuity of the spectrum of the periodic Schrödinger operator in a layer and in a smooth cylinder
spectrum the periodic Schrö dinger operator layer smooth cylinder
2010/11/11
We consider the Schr\"odinger operator $H = -\Delta + V$ in a layer or in a $d$-dimensional cylinder. The potential $V$ is assumed to be periodic with respect to some lattice. We establish the absolu...
On the continuity of functions
nonstandard Analysis convex functions continuity compact set convex set
2009/3/3
Some theorems on continuity are presented. First we will prove
that every convex function f : Rn ! R is continuous using nonstandard
analysis methods. Then we prove that if the image of every compac...
On the continuity of functions
nonstandard Analysis convex functions continuity compact set convex set
2009/1/6
Some theorems on continuity are presented. First we will prove
that every convex function f : Rn ! R is continuous using nonstandard
analysis methods. Then we prove that if the image of every compac...
Some results concerning quasi-continuity and fragmentability
Quasi-open sets Quasi-continuity Fragmentability
2010/9/10
We shall show that every quasi-continuous mapping g : Z −→ X of a topological space Z into a topological space X which has countable base can be discontinuous only on a set of first category. Al...
Continuity Properties of Convex-type Set-Valued Maps
Convex functions set--valued maps $K$-midconvex set-valued maps $K$-continuity
2008/7/1
Continuity Properties of Convex-type Set-Valued Maps.
A unified approach is proposed for making a continuity adjustment on some control charts for attributes, e.g., np-chart and c-chart, through adding a uniform (0, 1) random observation to the conventio...