110,041 research outputs found
Set-Rationalizable Choice and Self-Stability
A common assumption in modern microeconomic theory is that choice should be
rationalizable via a binary preference relation, which \citeauthor{Sen71a}
showed to be equivalent to two consistency conditions, namely
(contraction) and (expansion). Within the context of \emph{social}
choice, however, rationalizability and similar notions of consistency have
proved to be highly problematic, as witnessed by a range of impossibility
results, among which Arrow's is the most prominent. Since choice functions
select \emph{sets} of alternatives rather than single alternatives, we propose
to rationalize choice functions by preference relations over sets
(set-rationalizability). We also introduce two consistency conditions,
and , which are defined in analogy to and
, and find that a choice function is set-rationalizable if and only if
it satisfies . Moreover, a choice function satisfies
and if and only if it is \emph{self-stable}, a new concept based
on earlier work by \citeauthor{Dutt88a}. The class of self-stable social choice
functions contains a number of appealing Condorcet extensions such as the
minimal covering set and the essential set.Comment: 20 pages, 2 figure, changed conten
Investigation of the fine structure of antihydrogen.
At the historic Shelter Island Conference on the Foundations of Quantum Mechanics in 1947, Willis Lamb reported an unexpected feature in the fine structure of atomic hydrogen: a separation of the 2S1/2 and 2P1/2 states1. The observation of this separation, now known as the Lamb shift, marked an important event in the evolution of modern physics, inspiring others to develop the theory of quantum electrodynamics2-5. Quantum electrodynamics also describes antimatter, but it has only recently become possible to synthesize and trap atomic antimatter to probe its structure. Mirroring the historical development of quantum atomic physics in the twentieth century, modern measurements on anti-atoms represent a unique approach for testing quantum electrodynamics and the foundational symmetries of the standard model. Here we report measurements of the fine structure in the n = 2 states of antihydrogen, the antimatter counterpart of the hydrogen atom. Using optical excitation of the 1S-2P Lyman-α transitions in antihydrogen6, we determine their frequencies in a magnetic field of 1 tesla to a precision of 16 parts per billion. Assuming the standard Zeeman and hyperfine interactions, we infer the zero-field fine-structure splitting (2P1/2-2P3/2) in antihydrogen. The resulting value is consistent with the predictions of quantum electrodynamics to a precision of 2 per cent. Using our previously measured value of the 1S-2S transition frequency6,7, we find that the classic Lamb shift in antihydrogen (2S1/2-2P1/2 splitting at zero field) is consistent with theory at a level of 11 per cent. Our observations represent an important step towards precision measurements of the fine structure and the Lamb shift in the antihydrogen spectrum as tests of the charge-parity-time symmetry8 and towards the determination of other fundamental quantities, such as the antiproton charge radius9,10, in this antimatter system
Stability of Matter in Magnetic Fields
In the presence of arbitrarily large magnetic fields, matter composed of
electrons and nuclei was known to be unstable if or is too large.
Here we prove that matter {\it is stable\/} if and
.Comment: 10 pages, LaTe
Local stability implies global stability for the 2-dimensional Ricker map
Consider the difference equation where
is a positive parameter and d is a non-negative integer. The case d =
0 was introduced by W.E. Ricker in 1954. For the delayed version d >= 1 of the
equation S. Levin and R. May conjectured in 1976 that local stability of the
nontrivial equilibrium implies its global stability. Based on rigorous,
computer aided calculations and analytical tools, we prove the conjecture for d
= 1.Comment: for associated C++ program, mathematica worksheet and output, see
http://www.math.u-szeged.hu/~krisztin/ricke
Non-perturbative renormalization of the static axial current in two-flavour QCD
We perform the non-perturbative renormalization of matrix elements of the
static-light axial current by a computation of its scale dependence in lattice
QCD with two flavours of massless O(a) improved Wilson quarks. The
regularization independent factor that relates any running renormalized matrix
element of the axial current in the static effective theory to the
renormalization group invariant one is evaluated in the Schroedinger functional
scheme, where in this case we find a significant deviation of the
non-perturbative running from the perturbative prediction. An important
technical ingredient to improve the precision of the results consists in the
use of modified discretizations of the static quark action introduced earlier
by our collaboration. As an illustration how to apply the renormalization of
the static axial current presented here, we connect the bare matrix element of
the current to the B_s-meson decay constant in the static approximation for one
value of the lattice spacing, a ~ 0.08 fm, employing large-volume N_f=2 data at
beta=5.3.Comment: 33 pages including figures and tables, latex2e, uses JHEP3.cls;
version published in JHEP, small additions, results unchange
Search for long lived heaviest nuclei beyond the valley of stability
The existence of long lived superheavy nuclei (SHN) is controlled mainly by
spontaneous fission and -decay processes. According to microscopic
nuclear theory, spherical shell effects at Z=114, 120, 126 and N=184 provide
the extra stability to such SHN to have long enough lifetime to be observed. To
investigate whether the so-called "stability island" could really exist around
the above Z, N values, the -decay half lives along with the spontaneous
fission and -decay half lives of such nuclei are studied. The
-decay half lives of SHN with Z=102-120 are calculated in a quantum
tunneling model with DDM3Y effective nuclear interaction using
values from three different mass formulae prescribed by Koura, Uno, Tachibana,
Yamada (KUTY), Myers, Swiatecki (MS) and Muntian, Hofmann, Patyk, Sobiczewski
(MMM). Calculation of spontaneous fission (SF) half lives for the same SHN are
carried out using a phenomenological formula and compared with SF half lives
predicted by Smolanczuk {\it et al}. Possible source of discrepancy between the
calculated -decay half lives of some nuclei and the experimental data
of GSI, JINR-FLNR, RIKEN are discussed. In the region of Z=106-108 with N
160-164, the -stable SHN is predicted to have
highest -decay half life () using
value from MMM. Interestingly, it is much greater than the recently measured
() of deformed doubly magic
nucleus. A few fission-survived long-lived SHN which are either -stable
or having large -decay half lives are predicted to exist near
, , and .
These nuclei might decay predominantly through -particle emission.Comment: 14 pages, 6 figures, 1 tabl
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