An isoperimetric problem for leaky loops and related mean-chord inequalities

We consider a class of Hamiltonians in $L^2(\R^2)$ with attractive interaction supported by piecewise $C^2$ smooth loops $\Gamma$ of a fixed length $L$, formally given by $-\Delta-\alpha\delta(x-\Gamma)$ with $\alpha>0$. It is shown that the ground state of this operator is locally maximized by a circular $\Gamma$. We also conjecture that this property holds globally and show that the problem is related to an interesting family of geometric inequalities concerning mean values of chords of $\Gamma$.Comment: LaTeX, 16 page

Die behoefte aan ’n wyer artikel 2(3) van die Wet op Testamente 7 van 1953 (soos gewysig): ’n Kritiese beskouing

Uit teks: Die Hoogste Hof van Appél se uitspraak in Bekker v Naude en Andere 2003(5) SA 173 (HHA) het die posisie aangaande die toepassing van artikel 2(3) van die Wet op Testamente 7 van 1953 (soos gewysig) duidelik uiteengesit en alle onsekerheid uit die weg geruim

Electro-Magnetic Waves within a Model for Charged Solitons

We analyze the model of topological fermions (MTF), where charged fermions are treated as soliton solutions of the field equations. In the region far from the sources we find plane waves solutions with the properties of electro-magnetic waves.Comment: 4 pages, 2 figure

High-temperature hardness of Ga_(1−x)In_xAs

Substantial solid‐solution strengthening of GaAs by In acting as InAs_4 units has recently been predicted for an intermediate‐temperature plateau region. This strengthening could account, in part, for the reduction of dislocation density in GaAs single crystals grown from the melt. Hardness measurements at high temperatures up to 900 °C have been carried out on (100) GaAs, Ga_(0.9975)In_(0.0025)As, and Ga_(0.99)In_(0.01)As wafers, all of which contain small amounts of boron. Results show a significant strengthening effect in In‐doped GaAs. A nominally temperature‐independent flow‐stress region is observed for all three alloys. The In‐doped GaAs shows a higher plateau stress level with increasing In content. The results are consistent with the solid‐solution strengthening model. The magnitude of the solid‐solution hardening is sufficient to explain the reduction in dislocation density with In addition

Casimir Scaling from Center Vortices: Towards an Understanding of the Adjoint String Tension

We argue that the approximate ``Casimir scaling'' of the string tensions of higher-representation Wilson loops is an effect due to the finite thickness of center vortex configurations. It is shown, in the context of a simple model of the Z(2) vortex core, how vortex condensation in Yang-Mills theory can account for both Casimir scaling in intermediate size loops, and color-screening in larger loops. An implication of our model is that the deviations from exact Casimir scaling, which tend to grow with loop size, become much more pronounced as the dimensionality of the group representation increases.Comment: 13 pages, including 3 eps figures, Latex2e. Two references adde