972 research outputs found
Series expansion for L^p Hardy inequalities
We consider a general class of sharp Hardy inequalities in
involving distance from a surface of general codimension . We
show that we can succesively improve them by adding to the right hand side a
lower order term with optimal weight and best constant. This leads to an
infinite series improvement of Hardy inequalities.Comment: 16 pages, to appear in the Indiana Univ. Math.
Critical Hardy--Sobolev Inequalities
We consider Hardy inequalities in , , with best constant
that involve either distance to the boundary or distance to a surface of
co-dimension , and we show that they can still be improved by adding a
multiple of a whole range of critical norms that at the extreme case become
precisely the critical Sobolev norm.Comment: 22 page
PROPER 3C - A nucleon pion transport code
Computer programs to calculate and analyze pion and nucleon interaction within prescribed medium referred to as PROPER 3C Transport Cod
Sharp two-sided heat kernel estimates for critical Schr\"odinger operators on bounded domains
On a smooth bounded domain \Omega \subset R^N we consider the Schr\"odinger
operators -\Delta -V, with V being either the critical borderline potential
V(x)=(N-2)^2/4 |x|^{-2} or V(x)=(1/4) dist (x,\partial\Omega)^{-2}, under
Dirichlet boundary conditions. In this work we obtain sharp two-sided estimates
on the corresponding heat kernels. To this end we transform the Scr\"odinger
operators into suitable degenerate operators, for which we prove a new
parabolic Harnack inequality up to the boundary. To derive the Harnack
inequality we have established a serier of new inequalities such as improved
Hardy, logarithmic Hardy Sobolev, Hardy-Moser and weighted Poincar\'e. As a
byproduct of our technique we are able to answer positively to a conjecture of
E.B.Davies.Comment: 40 page
Universality in Blow-Up for Nonlinear Heat Equations
We consider the classical problem of the blowing-up of solutions of the
nonlinear heat equation. We show that there exist infinitely many profiles
around the blow-up point, and for each integer , we construct a set of
codimension in the space of initial data giving rise to solutions that
blow-up according to the given profile.Comment: 38 page
Hardy's inequality and curvature
A Hardy inequality of the form \int_{\tilde{\Omega}} |\nabla f({\bf{x}})|^p
d {\bf{x}} \ge (\frac{p-1}{p})^p \int_{\tilde{\Omega}} \{1 + a(\delta, \partial
\tilde{\Omega})(\x)\}\frac{|f({\bf{x}})|^p}{\delta({\bf{x}})^p} d{\bf{x}},
for all , is considered for , where can be either or with a domain in , , and
is the distance from to the
boundary The main emphasis is on determining the
dependance of on the geometric
properties of A Hardy inequality is also
established for any doubly connected domain in in terms
of a uniformisation of that is, any conformal univalent map of
onto an annulus
Experiment for Testing Special Relativity Theory
An experiment aimed at testing special relativity via a comparison of the
velocity of a non matter particle (annihilation photon) with the velocity of
the matter particle (Compton electron) produced by the second annihilation
photon from the decay Na-22(beta^+)Ne-22 is proposed.Comment: 7 pages, 1 figure, Report on the Conference of Nuclear Physics
Division of Russian Academy of Science "Physics of Fundamental Interactions",
ITEP, Moscow, November 26-30, 200
Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian
In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya
inequalities with best Hardy constants, for domains satisfying suitable
geometric assumptions such as mean convexity or convexity. We then use them to
produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants
for various fractional Laplacians. In the case where the domain is the half
space our results cover the full range of the exponent of the
fractional Laplacians. We answer in particular an open problem raised by Frank
and Seiringer \cite{FS}.Comment: 42 page
A Gas Leak Rate Measurement System for the ATLAS MUON BIS-Monitored Drift Tubes
A low-cost, reliable and precise system developed for the gas leak rate measurement of the BIS-Monitored Drift Tubes (MDTs) for the ATLAS Muon Spectrometer is presented. In order to meet the BIS-MDT mass production rate, a total number of 100 tubes are tested simultaneously in this setup. The pressure drop of each one of the MDT is measured, within a typical time interval of 48 hours, via a differential manometer comparing with the pressure of a gas tight reference tube. The precision of the method implemented is based on the system temperature homogeneity, with accuracy of ÄT = 0.3 oC. For this reason, two thermally isolated boxes are used testing 50 tubes each of them, to achieve high degree of temperature uniformity and stability. After measuring several thousands of the MDTs, the developed system is confirmed to be appropriate within the specifications for testing the MDTs during the mass production
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