We compute the loss of power in likelihood ratio tests when we test the
original parameter of a probability density extended by the first Lehmann
alternative.

We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor
expansions of solutions of perturbed stochastic differential equations (SDEs).
In particular, we work out weight expressions for the Taylor coefficients of
the expansion. The results are applied to LIBOR market models in order to deal
with the typical stochastic drift and with stochastic volatility. In contrast
to other accurate methods like numerical schemes for the full SDE, we obtain
easily tractable expressions for accurate pricing. In particular, we present an
easily tractable alternative to “freezing the drift” in LIBOR market models,
which has an accuracy similar to the full numerical scheme. Numerical examples
underline the results.

We establish an unusual second-order almost sure limit theorem for the
minimal position in a one-dimensional super-critical branching random walk, and
also prove a martingale convergence theorem which answers a question of Biggins
and Kyprianou [7]. Our method applies furthermore to the study of directed
polymers on a disordered tree. In particular, we give a rigorous proof of a
phase transition phenomenon for the partition function (from the point of view
of convergence in probability), already described by Derrida and Spohn [14].
Surprisingly, this phase transition phenomenon disappears in the sense of upper
almost sure limits.

This paper is devoted to the analysis of a second order method for recovering
the \emph{a priori} unknown shape of an inclusion $\omega$ inside a body
$\Omega$ from boundary measurement. This inverse problem - known as electrical
impedance tomography - has many important practical applications and hence has
focussed much attention during the last years. However, to our best knowledge,
no work has yet considered a second order approach for this problem. This paper
aims to fill that void: we investigate the existence of second order derivative
of the state $u$ with respect to perturbations of the shape of the interface
$\partial\omega$, then we choose a cost function in order to recover the
geometry of $\partial \omega$ and derive the expression of the derivatives
needed to implement the corresponding Newton method. We then investigate the
stability of the process and explain why this inverse problem is severely
ill-posed by proving the compactness of the Hessian at the global minimizer.

Let s_v denote the pure power sum \sum_{k=1}^n z_k^v. In a previous paper we
proved that \sqrt n <= \inf_{|z_k| => 1} \max_{v=1,…,n^2} |s_v| <= \sqrt{n+1}
when n+1 is prime. In this paper we prove that \inf_{|z_k| = 1}
\max_{v=1,…,n^2-n} |s_v| = \sqrt{n-1} when n-1 is a prime power, and if 2 <=
i <= n-1 and n => 3 is a prime power then \inf_{|z_k| => 1}
\max_{v=1,…,n^2-i} |s_v| =\sqrt n. We give explicit constructions of n-tuples
(z_1,…,z_n) which we prove are global minima for these problems. These are
two of the few times in Turan power sum theory where solutions in the inf max
problem can be explicitly calculated.

The notion of topological free entropy dimension of $n-$tuples of elements in
a C$^*$ algebra was introduced by Voiculescu. In the paper, we compute
topological free entropy dimension of one self-adjoint element and topological
orbit dimension of one self-adjoint element in a C$^*$ algebra.

We prove that the Pauli representation of the quantum permutation algebra
$A(S_4)$ is faithful. This provides the second known model for a free quantum
algebra. We use this model for performing some computations, with the result
that at level of laws of diagonal coordinates, the Lebesgue measure appears
between the Dirac mass and the free Poisson law.

Let $\Goo$ be a semisimple real Lie group with unitary dual $\Ghat$. The goal
of this note is to produce new upper bounds for the multiplicities with which
representations $\pi \in \Ghat$ of cohomological type appear in certain spaces
of cusp forms on $\Goo$.

Let $F$ be a global function field of characteristic $p>0$, $\mathcal F/F$ a
Galois extension with $Gal(\tilde F/F)\simeq \mathbb{Z}_p^{\mathbb N}$ and
$E/F$ a non-isotrivial elliptic curve. We study the behaviour of Selmer groups
$Sel_E(L)_l$ ($l$ any prime) as $L$ varies through the subextensions of
$\mathcal F$ via appropriate versions of Mazur’s Control Theorem. In the case
$l=p$ we let $\mathcal F=\bigcup \mathcal F_d$ where $\mathcal F_d/F$ is a
$\mathbb{Z}_p^d$-extension. With a mild hypothesis on $Sel_E(F)_p$ (essentially
a consequence of the Birch and Swinnerton-Dyer conjecture) we prove that
$Sel_E(\mathcal F_d)_p$ is a cofinitely generated (in some cases cotorsion)
$\mathbb{Z}_p[[Gal(\mathcal F_d/F)]]$-module and we associate to its Pontrjagin
dual a Fitting ideal. This allows to define an algebraic $L$-function
associated to $E$ in $\mathbb{Z}_p[[Gal(\mathcal F/F)]]$, providing an
ingredient for a function field analogue of Iwasawa’s Main Conjecture for
elliptic curves.

We introduce a finite volume scheme for the two-dimensional incompressible
Navier-Stokes equations. We use a triangular mesh. The unknowns for the
velocity and pressure are respectively piecewise constant and affine. We use a
projection method to deal with the incompressibility constraint. We show that
the differential operators in the Navier-Stokes equations and their discrete
counterparts share similar properties. In particular we state an inf-sup
(Babuska-Brezzi) condition. Using these properties we infer the stability of
the scheme.

We consider a finite volume scheme for the two-dimensional incompressible
Navier-Stokes equations. We use a triangular mesh. The unknowns for the
velocity and pressure are respectively piecewise constant and affine. We use a
projection method to deal with the incompressibility constraint. In a former
paper, the stability of the scheme has been proven. We infer from it its
convergence.

Given a remarkable representation of the generalized Pauli operators of
two-qubits in terms of the points of the generalized quadrangle of order two,
W(2), it is shown that specific subsets of these operators can also be
associated with the points and lines of the four-dimensional projective space
over the Galois field with two elements - the so-called Veldkamp space of W(2).
An intriguing novelty is the recognition of (uni- and tri-centric) triads and
specific pentads of the Pauli operators in addition to the “classical” subsets
answering to geometric hyperplanes of W(2).

The spectral action on noncommutative torus is obtained, using a
Chamseddine–Connes formula via computations of zeta functions. The importance
of a Diophantine condition is outlined. Several results on holomorphic
continuation of series of holomorphic functions are obtained in this context.

The Faddeev-Volkov solution of the star-triangle relation is connected with
the modular double of the quantum group U_q(sl_2). It defines an Ising-type
lattice model with positive Boltzmann weights where the spin variables take
continuous values on the real line. The free energy of the model is exactly
calculated in the thermodynamic limit. The model describes quantum fluctuations
of circle patterns and the associated discrete conformal transformations
connected with the Thurston’s discrete analogue of the Riemann mappings
theorem. In particular, in the quasi-classical limit the model precisely
describe the geometry of integrable circle patterns with prescribed
intersection angles.

We introduce a finite volume scheme for the two-dimensional incompressible
Navier-Stokes equations. We use a triangular mesh. The unknowns for the
velocity and pressure are both piecewise constant (colocated scheme). We use a
projection (fractional-step) method to deal with the incompressibility
constraint. We prove that the differential operators in the Navier-Stokes
equations and their discrete counterparts share similar properties. In
particular, we state an inf-sup (Babuska-Brezzi) condition. We infer from it
the stability of the scheme.