19,256,523 research outputs found
A matrix subadditivity inequality for f(A+B) and f(A)+f(B)
Let f be a non-negative concave function on the positive half-line. Let A and
B be two positive matrices. Then, for all symmetric norms, || f(A+B) || is less
than || f(A)+f(B) ||. When f is operator concave, this was proved by Ando and
Zhan. Our method is simpler. Several related results are presented.Comment: accepted in LA
Axion decay in a strong magnetic field
The axion decay into charged fermion-antifermion pair is
studied in external crossed and magnetic fields. The result we have obtained
can be of use to re-examine the lower limit on the axion mass in case of
possible existence of strong magnetic fields at the early Universe stage.Comment: 6 pages, latex. Amended version, references added, to be published in
Phys.Lett.
A connected F-space
We present an example of a compact connected F-space with a continuous
real-valued function f for which the union of the interiors of its fibers is
not dense. This indirectly answers a question from Abramovich and Kitover in
the negative
Scale properties in data envelopment analysis
Recently there has been some discussion in the literature concerning the nature of scale properties in the Data Envelopment Model (DEA). It has been argued that DEA may not be able to provide reliable estimates of the optimal scale size. We argue in this paper that DEA is well suited to estimate optimal scale size, if DEA is augmented with two additional maintained hypotheses which imply that the DEA-frontier is consistent with smooth curves along rays in input and in output space that obey the Regular Ultra Passum (RUP) law (Frisch 1965). A necessary condition for a smooth curve passing through all vertices to obey the RUP-law is presented. If this condition is satisfied then upper and lower bounds for the marginal product at each vertex are presented. It is shown that any set of feasible marginal products will correspond to a smooth curve passing through all points with a monotonic decreasing scale elasticity. The proof is constructive in the sense that an estimator of the curve is provided with the desired properties. A typical DEA based return to scale analysis simply reports whether or not a DMU is at the optimal scale based on point estimates of scale efficiency. A contribution of this paper is that we provide a method which allows us to determine in what interval optimal scale is located.DEA; efficiency
Shot noise in a diffusive F-N-F spin valve
Fluctuations of electric current in a spin valve consisting of a diffusive
conductor connected to ferromagnetic leads and operated in the giant
magnetoresistance regime are studied. It is shown that a new source of
fluctuations due to spin-flip scattering enhances strongly shot noise up to a
point where the Fano factor approaches the full Poissonian value.Comment: 5 pages, 3 figure
F-Split and F-Regular Varieties with a Diagonalizable Group Action
Let be a diagonalizable group over an algebraically closed field of
positive characteristic, and a normal -variety with an -action. Under
a mild hypothesis, e.g. a torus or quasiprojective, we construct a
certain quotient log pair and show that is F-split (F-regular)
if and only if the pair if F-split (F-regular). We relate
splittings of compatible with -invariant subvarieties to compatible
splittings of , as well as discussing diagonal splittings of .
We apply this machinery to analyze the F-splitting and F-regularity of
complexity-one -varieties and toric vector bundles, among other examples.Comment: 40 page
(GL(n+1,F),GL(n,F)) is a Gelfand pair for any local field F
Let F be an arbitrary local field. Consider the standard embedding of GL(n,F)
into GL(n+1,F) and the two-sided action of GL(n,F) \times GL(n,F) on GL(n+1,F).
In this paper we show that any GL(n,F) \times GL(n,F)-invariant distribution
on GL(n+1,F) is invariant with respect to transposition.
We show that this implies that the pair (GL(n+1,F),GL(n,F)) is a Gelfand
pair. Namely, for any irreducible admissible representation of
(GL(n+1,F), dimHom_{GL(n,F)}(E,\cc) \leq 1.
For the proof in the archimedean case we develop several new tools to study
invariant distributions on smooth manifolds.Comment: v3: Archimedean Localization principle excluded due to a gap in its
proof. Another version of Localization principle can be found in
arXiv:0803.3395v2 [RT]. v4: an inaccuracy with Bruhat filtration fixed. See
Theorem 4.2.1 and Appendix
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