In situ broadband pulse compression for multiphoton microscopy using a shaper-assisted collinear SPIDER

The characterization and control of the phase of broadband femtosecond pulses in nonlinear microscopy are successfully demonstrated with a collinear configuration of spectral shear interferometry for direct electric field reconstruction (SPIDER). A femtosecond-pulse shaper is used as a dispersionless interferometer for the measurement of the spectral phase and to actively compress a broadband supercontinuum from a photonic crystal fiber. This allows in situ online phase management and enables the application of quantum control spectroscopy in microenvironments.     

Search for associated higgs boson production WH-->WWW*-->l+/-nul'+/-nu'+X in pp collisions at square root s=1.96 Te V

We present a search for associated Higgs boson production in the process pp-->WH-->WWW*-->l;+/-nul'+/-nu'+X in final states containing two like-sign isolated electrons or muons (e+/-e;+/-, e+/-micro+/-, or micro+/-micro+/-). The search is based on D0 run II data samples corresponding to integrated luminosities of 360-380 pb-1. No excess is observed over the predicted standard model background. We set 95% C.L. upper limits on sigma(pp-->WH)xBr(H-->WW*) between 3.2 and 2.8 pb for Higgs boson masses from 115 to 175 GeV.     

Symmetric square L-values and dihedral congruences for cusp forms

Let be a prime, and k=(p+1)/2. In this paper we prove that two things happen if and only if the class number . One is the non-integrality at p of a certain trace of normalised critical values of symmetric square L-functions, of cuspidal Hecke eigenforms of level one and weight k. The other is the existence of such a form g whose Hecke eigenvalues satisfy “dihedral” congruences modulo a divisor of p (e.g. p=23, k=12, g=Δ). We use the Bloch-Kato conjecture to link these two phenomena, using the Galois interpretation of the congruences to produce global torsion elements which contribute to the denominator of the conjectural formula for an L-value. When , the trace turns out always to be a p-adic unit.     

Extension of results of Kostant and Han

The Ramanujan Journal - Kostant proved that the mth coefficient of the $$(r^2-1)$$ th power of the Dedekind eta function is non-vanishing for $$r \ge \mathsf {max} \{4,m \}$$ and r an...     

On the shape of random Pólya structures

Panagiotou and Stufler recently proved an important fact on their way to establish the scaling limits of random Pólya trees: a uniform random Pólya tree of size $n$ consists of a conditioned critical Galton–Watson tree $C_n$ and many small forests, where with probability tending to one, as $n$ tends to infinity, any forest $F_n\left(v\right)$, that is attached to a node $v$ in $C_n$, is maximally of size $\left|F_n\left(v\right)\right|=O(logn)$. Their proof used the framework of a Boltzmann sampler and deviation inequalities.In this paper, first, we employ a unified framework in analytic combinatorics to prove this fact with additional improvements for $\left|F_n\left(v\right)\right|$, namely $\left|F_n\left(v\right)\right|=\Theta (logn)$. Second, we give a combinatorial interpretation of the rational weights of these forests and the defining substitution process in terms of automorphisms associated to a given Pólya tree. Third, we derive the limit probability that for a random node $v$ the attached forest $F_n\left(v\right)$ is of a given size. Moreover, structural properties of those forests like the number of their components are studied. Finally, we extend all results to other Pólya structures.     

Zero Leakage Sealings for Reciprocating Compressors

The piston rod of a reciprocating compressor is sealed with elastic cylindrical sealing elements. Across the sealings the pressure drops from the operating pressure to the ambient pressure. The lubrication gap between the elastic sealing and reciprocating piston rod is studied with the aim to find conditions of a leakage free sealing. The flow in the lubrication gap and the elastic deformation of the sealing are determined simultaneously. The netflow during one cycle of the reciprocating piston rod is calculated. It turns out that maintaining zero leakage is very sensible. Indeed the outbound flow during out-stroke has to be equal the inbound flow during the instroke. By prescribing a special shape of the undeformed sealing zero leakage can be attained — at least theoretically for certain operating conditions. It turns out that temperature dependent material data and a model for cavitation is necessary. The model, its numerical implementation and results will be discussed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Carleson Measure Criterion in Linear Systems Theory

In Ho and Russell (SIAM J Control Optim 21(4):614–640, 1983), and Weiss (Syst Control Lett 10(1): 79–82, 1988), a Carleson measure criterion for admissibility of one-dimensional input elements with respect to diagonal semigroups is given. We extend their results from the Hilbert space situation (L ²-admissibility on the state space ℓ ₂) to the more general situation of L ^p -admissibility on the state space ℓ _q . For analytic diagonal semigroups we present a new result that does not rely on Laplace transform methods. A comparison of both criteria leads to a result on L ^p -admissibility for reciprocal systems in the sense of Curtain (Syst Control Lett 49(2):81–89, 2003).     

Best constants in a borderline case of second-order Moser type inequalities

We study optimal embeddings for the space of functions whose Laplacian Δu   belongs to L¹(Ω)$L^1(\Omega )$, where Ω⊂RN$\Omega \subset {\mathbb{R}}^N$ is a bounded domain. This function space turns out to be strictly larger than the Sobolev space W2,1(Ω)$W^{2,1}(\Omega )$ in which the whole set of second-order derivatives is considered. In particular, in the limiting Sobolev case, when N=2$N=2$, we establish a sharp embedding inequality into the Zygmund space Lexp(Ω)$L_{\mathit{exp}}(\Omega )$. On one hand, this result enables us to improve the Brezis–Merle (Brezis and Merle (1991) [13]) regularity estimate for the Dirichlet problem Δu=f(x)∈L¹(Ω)$\mathrm{\Delta }u=f(x)\in L^1(\Omega )$, u=0$u=0$ on ∂Ω; on the other hand, it represents a borderline case of D.R. Adams' (1988) [1] generalization of Trudinger–Moser type inequalities to the case of higher-order derivatives. Extensions to dimension N?3$N?3$ are also given. Besides, we show how the best constants in the embedding inequalities change under different boundary conditions.     

An Interpolating Distance Between Optimal Transport and Fisher–Rao Metrics

This paper defines a new transport metric over the space of nonnegative measures. This metric interpolates between the quadratic Wasserstein and the Fisher–Rao metrics and generalizes optimal transport to measures with different masses. It is defined as a generalization of the dynamical formulation of optimal transport of Benamou and Brenier, by introducing a source term in the continuity equation. The influence of this source term is measured using the Fisher–Rao metric and is averaged with the transportation term. This gives rise to a convex variational problem defining the new metric. Our first contribution is a proof of the existence of geodesics (i.e., solutions to this variational problem). We then show that (generalized) optimal transport and Hellinger metrics are obtained as limiting cases of our metric. Our last theoretical contribution is a proof that geodesics between mixtures of sufficiently close Dirac measures are made of translating mixtures of Dirac masses. Lastly, we propose a numerical scheme making use of first-order proximal splitting methods and we show an application of this new distance to image interpolation.     

Harmonic Analysis for Real Spherical Spaces

We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces Z = G/H attached to a real reductive Lie group G. A special emphasis is made to the case where Z is real spherical.