39,613 research outputs found
Correlating and Decays with Four Generations
The long-awaited mode has finally been observed at rate
consistent with Standard Model, albeit lower by 1.2. There is some hint
for New Physics in the rarer decay, especially if the
currently 2.2-enhanced central value persists with more data. The
measurement of violating phase , via both
and modes, has reached Standard Model sensitivity. These
measurements stand major improvement when LHC enters Run 2. Concurrently, the
and modes are being pursued in
a similar time frame. We illustrate the possible correlations between New
Physics effects in these four modes, using the fourth generation as example.
While correlations may or may not exist in other New Physics models, the four
generation model can accommodate enhancements in both
and .Comment: 9 pages, 5 figures for V1; for V2 title modified, minor changes
performed to figures, part of contents revised to 7 pages, note added, one of
the authors' affiliation changed, accepted for the publication of PL
A M\"untz-Collocation spectral method for weakly singular volterra integral equations
In this paper we propose and analyze a fractional Jacobi-collocation spectral
method for the second kind Volterra integral equations (VIEs) with weakly
singular kernel . First we develop a family of fractional
Jacobi polynomials, along with basic approximation results for some weighted
projection and interpolation operators defined in suitable weighted Sobolev
spaces. Then we construct an efficient fractional Jacobi-collocation spectral
method for the VIEs using the zeros of the new developed fractional Jacobi
polynomial. A detailed convergence analysis is carried out to derive error
estimates of the numerical solution in both - and weighted
-norms. The main novelty of the paper is that the proposed method is
highly efficient for typical solutions that VIEs usually possess. Precisely, it
is proved that the exponential convergence rate can be achieved for solutions
which are smooth after the variable change for a
suitable real number . Finally a series of numerical examples are
presented to demonstrate the efficiency of the method
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