1,890 research outputs found
Integral geometry, hypergroups, and I.M. Gelfand's question
This note is an attempt to give an answer for the following old I.M.
Gelfand's question: why some important problems of integral geometry (e.g., the
Radon transform and others) are related to harmonic analysis on groups, but for
other quite similar problems such relations are not clear? In the note we
examine standard problems of integral geometry generating harmonic analysis
(the Plancherel theorem etc.) on pairs of commutative hypergroups that are in a
duality of Pontryagin's type. As a result new meaningful examples of
hypergroups are constructed.Comment: 10 pages, to be published in Doklady Mathematics, 201
Indirect coupling between spins in semiconductor quantum dots
The optically induced indirect exchange interaction between spins in two
quantum dots is investigated theoretically. We present a microscopic
formulation of the interaction between the localized spin and the itinerant
carriers including the effects of correlation, using a set of canonical
transformations. Correlation effects are found to be of comparable magnitude as
the direct exchange. We give quantitative results for realistic quantum dot
geometries and find the largest couplings for one dimensional systems.Comment: 4 pages, 3 figure
Beyond Wigner's isobaric multiplet mass equation: Effect of charge-symmetry-breaking interaction and Coulomb polarization
The quadratic form of the isobaric multiplet mass equation (IMME), which was
originally suggested by Wigner and has been generally regarded as valid, is
seriously questioned by recent high-precision nuclear mass measurements. The
usual resolution to this problem is to add empirically the cubic and quartic
-terms to characterize the deviations from the IMME, but finding the
origin of these terms remains an unsolved difficulty. Based on a strategy
beyond the Wigner's first-order perturbation, we derive explicitly the cubic
and quartic -terms. These terms are shown to be generated by the effective
charge-symmetry breaking and charge-independent breaking interactions in
nuclear medium combined with the Coulomb polarization effect. Calculations for
the - and lower -shells explore a systematical emergence of the cubic
-term, suggesting a general deviation from the original IMME.
Intriguingly, the magnitude of the deviation exhibits an oscillation-like
behavior with mass number, modulated by the shell effect.Comment: 13 pages, 4 figure
Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like Pr and Pm Ions
We report on time-modulated two-body weak decays observed in the orbital
electron capture of hydrogen-like Pr and Pm
ions coasting in an ion storage ring. Using non-destructive single ion,
time-resolved Schottky mass spectrometry we found that the expected exponential
decay is modulated in time with a modulation period of about 7 seconds for both
systems. Tentatively this observation is attributed to the coherent
superposition of finite mass eigenstates of the electron neutrinos from the
weak decay into a two-body final state.Comment: 12 pages, 5 figure
The choice of the reliability model of technical systems in the Mathcad package based on operational data
The subject of the research includes selection procedures, which allows determining the most adequate reliability model. Various goodness-of-fit tests and information criteria are objects of the research. Work objective is to select from predefined set the reliability model which represents given failure data sample best, by application of various statistical and information criteria
Toward CP-even Neutrino Beam
The best method of measuring CP violating effect in neutrino oscillation
experiments is to construct and use a neutrino beam made of an ideal mixture of
and of monochromatic lines. The conceptual design of such
a beam is described, together with how to measure the CP-odd quantity. We
propose to exploit an accelerated unstable hydrogen-like heavy ion in a storage
ring, whose decay has both electron capture and bound beta decay with a
comparable fraction.Comment: 6 pages, 2 figures, Published versio
Semiring and semimodule issues in MV-algebras
In this paper we propose a semiring-theoretic approach to MV-algebras based
on the connection between such algebras and idempotent semirings - such an
approach naturally imposing the introduction and study of a suitable
corresponding class of semimodules, called MV-semimodules.
We present several results addressed toward a semiring theory for
MV-algebras. In particular we show a representation of MV-algebras as a
subsemiring of the endomorphism semiring of a semilattice, the construction of
the Grothendieck group of a semiring and its functorial nature, and the effect
of Mundici categorical equivalence between MV-algebras and lattice-ordered
Abelian groups with a distinguished strong order unit upon the relationship
between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of
Section
Cyclic projectors and separation theorems in idempotent convex geometry
Semimodules over idempotent semirings like the max-plus or tropical semiring
have much in common with convex cones. This analogy is particularly apparent in
the case of subsemimodules of the n-fold cartesian product of the max-plus
semiring it is known that one can separate a vector from a closed subsemimodule
that does not contain it. We establish here a more general separation theorem,
which applies to any finite collection of closed semimodules with a trivial
intersection. In order to prove this theorem, we investigate the spectral
properties of certain nonlinear operators called here idempotent cyclic
projectors. These are idempotent analogues of the cyclic nearest-point
projections known in convex analysis. The spectrum of idempotent cyclic
projectors is characterized in terms of a suitable extension of Hilbert's
projective metric. We deduce as a corollary of our main results the idempotent
analogue of Helly's theorem.Comment: 20 pages, 1 figur
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