Lagrangian submanifolds and moment convexity

We consider a Hamiltonian torus action on a compact connected symplectic manifold and its associated momentum map . For certain Lagrangian submanifolds we show that is convex. The submanifolds arise as the fixed point set of an involutive diffeomorphism which satisfies several compatibility conditions with the torus action, but which is in general not anti-symplectic. As an application we complete a symplectic proof of Kostant's non-linear convexity theorem.

     

Moufang sets from groups of mixed type

We consider the existence of Moufang sets related to certain groups of mixed type. This way, we obtain new examples of Moufang sets and new constructions of known classes. The most interesting class of new examples is related to the Moufang quadrangles of type and to the Ree–Tits octagon over a nonperfect field, and the root groups of each member have nilpotency class three.     

Synthesis of 1,2-dihydropyridines using vinyloxiranes as masked dienolates in imino-aldol reactions

[reaction: see text] The application of vinyloxiranes, substituted with an electron-withdrawing group, as masked dienolates in vinylogous imino-aldol reactions was achieved. Under the reaction conditions highly substituted 1,2-dihydropyridines were obtained in moderate to good yields. Mechanistic studies indicate that the reaction proceeds via the formation of an (E)-amino-alpha,beta-unsaturated aldehyde, followed by isomerization to the (Z)-isomer, cyclization, and elimination of a water molecule, leading to the formation of the 1,2-dihydropyridine.     

Sequential kinetic resolution catalyzed by halohydrin dehalogenase

A sequential kinetic resolution catalyzed by halohydrin dehalogenase was employed for the synthesis of two valuable enantiopure building blocks. Resolution of methyl 4-chloro-3-hydroxybutanoate methylester ((R,S)-2) with use of a Trp249Phe mutant of halohydrin dehalogenase yielded methyl 4-cyano-3-hydroxybutanoate methylester ((S)-4) with 96.8% ee (40% yield) and (S)-2 with 95.2% ee (41% yield). This reaction is carried out in aqueous solution under mild conditions and provides access to a useful statin side-chain building block.     

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)