Parking spaces

Let W be a Weyl group with root lattice Q and Coxeter number h  . The elements of the finite torus Q/(h+1)Q$Q/(h+1)Q$ are called the W-parking functions, and we call the permutation representation of W on the set of W-parking functions the (standard) W-parking space. Parking spaces have interesting connections to enumerative combinatorics, diagonal harmonics, and rational Cherednik algebras. In this paper we define two new W-parking spaces, called the noncrossing parking space and the algebraic parking space, with the following features:

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They are defined more generally for real reflection groups.     

Organocatalytic Cascade Reactions: Towards the Diversification of Hydroisochromenes and Chromenes through Two Different Activation Modes

The organocatalytic enantioselective syntheses of functionalized hydroisochromenes and chromenes by trienamine‐mediated [4+2]‐cycloaddition/nucleophilic ring‐closing and iminium‐ion/aminal‐mediated oxa‐Michael/Michael/nucleophilic ring‐closing with 2‐nitroallylic alcohols are presented. The corresponding cycloadducts, with up to five stereocenters, are formed in good yield and excellent enantioselectivities. The synthetic applications of the obtained products have been demonstrated.     

Routine Method for Quantification of Starch by Planar Chromatography (HPTLC)

JPC – Journal of Planar Chromatography – Modern TLC - Starch is widely distributed in diverse plant organs as a reserve carbohydrate; it is also a major source of carbohydrates in human...     

A gap 1 cardinal transfer theorem

We extend the gap 1 cardinal transfer theorem (κ ⁺, κ ) → (λ ⁺, λ ) to any language of cardinality ≤λ, where λ is a regular cardinal. This transfer theorem has been proved by Chang under GCH for countable languages and by Silver in some cases for bigger languages (also under GCH). We assume the existence of a coarse (λ, 1)‐morass instead of GCH. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental adiabatic vortex ratchet effect in Nb films with asymmetric pinning trap

Nb films grown on top of an array of asymmetric pinning centers show a vortex ratchet effect. A net flow of vortices is induced when the vortex lattice is driven by fluctuating forces on an array of pinning centers without reflection symmetry. This effect occurs in the adiabatic regime and it could be mimiced only by reversible DC driven forces.     

Comments on the Paper astro-ph/0103335 by C. Rubano and P. Scudellaro

We briefly comment on a paper by Rubano and Scudellaro [Gen. Rel. Grav. 34 (2002) 307, astro-ph/0103335] where they found general exact solutions for two classes of exponential potentials in a scalar field model for quintessence. In that paper the authors were led to some interesting conclusions after a proper choice of the integration constants. By using dimensionless variables we show that the integration constants can be found explicitly without additional assumptions. In consequence we revise some results and conclusions in that paper. We also reproduce observations for Type-Ia supernovae with good accuracy.     

Switch in regioselectivity of epoxide ring-opening by changing the organometallic reagent

The regio- and stereoselective ring-opening of a 2-(2'-oxiranyl)-1,2,3,6-tetrahydropyridine using organometallic reagents is reported. The choice of the organometallic reagent determines the formation of either 2-[(R)-1-hydroxyalkyl]- or 2-[(S)-2-hydroxy-1-alkyl]-1,2,3,6-tetrahydropyridines. The formation of 2-[(S)-2-hydroxy-1-alkyl]-1,2,3,6-tetrahydropyridines is a rare example of epoxide ring-opening with retention of configuration. The process has been applied to the asymmetric synthesis of β-(+)-conhydrine and to the formal synthesis of (2S,2'R)-erythro-methylphenidate from a common precursor. Extension of the structural diversity of the process has allowed the synthesis of several β-(+)-conhydrine analogs.     

Coherent state transfer between an electron and nuclear spin in (15)N@C(60)

Electron spin qubits in molecular systems offer high reproducibility and the ability to self-assemble into larger architectures. However, interactions between neighboring qubits are "always on," and although the electron spin coherence times can be several hundred microseconds, these are still much shorter than typical times for nuclear spins. Here we implement an electron-nuclear hybrid scheme which uses coherent transfer between electron and nuclear spin degrees of freedom in order to both effectively turn on or off interqubit coupling mediated by dipolar interactions and benefit from the long nuclear spin decoherence times (T(2n)). We transfer qubit states between the electron and (15)N nuclear spin in (15)N@C(60) with a two-way process fidelity of 88%, using a series of tuned microwave and radio frequency pulses and measure a nuclear spin coherence lifetime of over 100 ms.     

Study of Polymer-Solvent Interactions of Complex Polysiloxanes Using Dissipative Particle Dynamics

The mesoscopic modeling of three polysiloxanes in solution is reported in this work, with the purpose of predicting their physicochemical properties as functions of the quality of the solvent, so that a judicious choice of polymer/solvent can be made for various applications. The polymers studied were the following polysiloxanes: polydimethylsiloxane (PDMS), polysiloxane with a bulky alkyl side group (PMHS) and a siloxane copolymer with a hydrophilic polar side group (P2DMPAS). The model used and solved through numerical simulations is the one known as dissipative particle dynamics. Density profiles and radial distribution functions were calculated for each system. We analyzed how the polymers behave in the presence of solvents of varying quality and compared their behavior with experimental data. We observed that we could replicate the behavior in good solvents for PDMS and PMHS. We also observed in the simulation box the formation of pseudo-micelles for P2DMPAS.     

Optimización de forma de modelos paramétricos bidimensionales basada en ponderación geométrica y reglas evolutivas

This paper presents a method for shape optimization of two-dimensional models subjected to simple or multiple load cases. The optimization is performed iteratively using evolutionary rules, based on the stress level. These rules determine regions on the boundary where the material is underused or overused; the objective is that the model evolves to a minimum weight model with a high and homogeneous stress level. The evolution is performed by modifying the boundary of the model slowly. Since the boundary is defined by parametric B-spline curves, generated changes result in a smooth boundary. The main proposal of the method is that boundary modifications are given by a set of displacements that, its magnitude and direction, take into account the geometrical information of the neighborhood, unlike other methods that simply generate displacement perpendicular to the boundary. Finally, the paper presents the design of a frame bike in order to show the good performance of the method.