18,316 research outputs found
On -extensions of the Hankel determinants of certain automatic sequences
In 1998, Allouche, Peyri\`ere, Wen and Wen considered the Thue--Morse
sequence, and proved that all the Hankel determinants of the period-doubling
sequence are odd integral numbers. We speak of -extension when the entries
along the diagonal in the Hankel determinant are all multiplied by~. Then we
prove that the -extension of each Hankel determinant of the period-doubling
sequence is a polynomial in , whose leading coefficient is the {\it only
one} to be an odd integral number. Our proof makes use of the combinatorial
set-up developed by Bugeaud and Han, which appears to be very suitable for this
study, as the parameter counts the number of fixed points of a permutation.
Finally, we prove that all the -extensions of the Hankel determinants of the
regular paperfolding sequence are polynomials in of degree less than or
equal to
Existence and uniqueness of global weak solutions to a Cahn-Hilliard-Stokes-Darcy system for two phase incompressible flows in karstic geometry
We study the well-posedness of a coupled Cahn-Hilliard-Stokes-Darcy system
which is a diffuse-interface model for essentially immiscible two phase
incompressible flows with matched density in a karstic geometry. Existence of
finite energy weak solution that is global in time is established in both 2D
and 3D. Weak-strong uniqueness property of the weak solutions is provided as
well
When bigger isn’t better : bailouts and bank behaviour
Lending retail deposits to SMEs and household borrowers may be the traditional role of
commercial banks: but banking in Britain has been transformed by increasing consolidation
and by the lure of high returns available from wholesale Investment activities. With
appropriate changes to the baseline model of commercial banking in Allen and Gale (2007),
we show how market power enables banks to collect „seigniorage‟; and how „tail risk‟
investment allows losses to be shifted onto the taxpayer.
In principle, the high franchise values associated with market power assist regulatory capital
requirements to check risk-taking. But when big banks act strategically, bailout expectations
can undermine these disciplining devices: and the taxpayer ends up „on the hook‟- as in the
recent crisis. That structural change is needed to prevent a repeat seems clear from the
Vickers report, which proposes to protect the taxpayer by a „ring fence‟separating
commercial and investment banking
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