Gold(I)‐Catalyzed Cyclodehydration Enabled by the Triisopropylsilyl Group: A Synthetically Versatile Methodology

Introduction of a triisopropylsilyl group into allyl and allenyl carbinols greatly enhances the efficiency of gold(I)‐catalyzed cyclodehydration, which can provide rapid access to a library of various compounds including 1H‐indenes (Table 2 and Scheme 5), benzofulvenes (Table 3), indan‐2‐ones (Scheme 2), fulvenes (Table 4), cyclopentadienes (Table 4), 5H‐dibenzo[a,c][7]annulenes (Scheme 6) and dibenzosuberones (Scheme 6). The developed method enables unprecedented product generality for several classes of cyclodehydration reactions, which is particularly notable for the preparation of 1H‐indenes. The first synthesis of non‐benzo‐fused fulvenes via cyclodehydration of allenyl vinyl carbinols could be accomplished. The protocol is remarkable for mild conditions, operational convenience, and easy access to starting materials.     

Shape-Wilf-equivalences for vincular patterns

We extend the notion of shape-Wilf-equivalence to vincular patterns (also known as “generalized patterns” or “dashed patterns”). First we introduce a stronger equivalence on patterns which we call filling-shape-Wilf-equivalence. When vincular patterns α and β   are filling-shape-Wilf-equivalent, we prove that α⊕σ$\alpha \oplus \sigma$ and β⊕σ$\beta \oplus \sigma$ must also be filling-shape-Wilf-equivalent. We also discover two new pairs of patterns which are filling-shape-Wilf-equivalent: when α, β, and σ   are nonempty consecutive patterns which are Wilf-equivalent, α⊕σ$\alpha \oplus \sigma$ is filling-shape-Wilf-equivalent to β⊕σ$\beta \oplus \sigma$; and for any consecutive pattern α  , 1⊕α$1\oplus \alpha$ is filling-shape-Wilf-equivalent to 1?α$1?\alpha$. These new equivalences imply many new Wilf-equivalences for vincular patterns.     

Annihilator varieties, adduced representations, Whittaker functionals, and rank for unitary representations of GL(n)

In this paper, we study irreducible unitary representations of ${GL_{n}(\mathbb{R})}$ and prove a number of results. Our first result establishes a precise connection between the annihilator of a representation and the existence of degenerate Whittaker functionals, thereby generalizing results of Kostant, Matumoto and others. Our second result relates the annihilator to the sequence of adduced representations, as defined in this setting by one of the authors. Based on those results, we suggest a new notion of rank of a smooth admissible representation of ${GL_{n}(\mathbb{R})}$ , which for unitarizable representations refines Howe’s notion of rank. Our third result computes the adduced representations for (almost) all irreducible unitary representations in terms of the Vogan classification. We also indicate briefly the analogous results over complex and p-adic fields.     

A Unified Stability Property in Spin Glasses

Gibbs’ measures in the Sherrington-Kirkpatrick type models satisfy two asymptotic stability properties, the Aizenman-Contucci stochastic stability and the Ghirlanda-Guerra identities, which play a fundamental role in our current understanding of these models. In this paper we show that one can combine these two properties very naturally into one unified stability property.     

Double‐shell metamaterial coatings for plasmonic cloaking

We study a double‐shell cloak for hiding objects with the dimensions comparable with the radiation wavelength. We demonstrate that the structure consisting of a dielectric layer and a layer of an epsilon‐near‐zero material can suppress sub‐ stantially the scattering from a sphere and at the same time shield its interiors. The double‐layer coating allows to cloak different objects with various material and geometrical parameters. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Fiber Bundle Approach to the Transpositional Relations in Nonholonomic Mechanics

The equations of nonholonomic mechanics may be derived using a number of variational principles. This paper studies some of these principles from the contemporary geometric point of view, taking into account various bundle structures that are intrinsically present in the nonholonomic setting.     

Two-dye and one- or two-quencher DNA probes for real-time PCR assay: synthesis and comparison with a TaqMan? probe

A typical TaqMan? real-time PCR probe contains a 5'-fluorescent dye and a 3'-quencher. In the course of the amplification, the probe is degraded starting from the 5'-end, thus releasing fluorescent dye. Some fluorophores (including fluorescein) are known to be prone to self-quenching when located near each other. This work is aimed at studying dye-dye and dye-quencher interactions in multiply modified DNA probes. Twenty-one fluorogenic probes containing one and two fluoresceins (FAM), or a FAM-JOE pair, and one or two BHQ1 quenchers were synthesized using non-nucleoside reagents and "click chemistry" post-modification on solid phase and in solution. The probes were tested in real-time PCR using an ~300-bp-long natural DNA fragment as a template. The structural prerequisites for lowering the probe background fluorescence and increasing the end-plateau fluorescence intensity were evaluated and discussed.     

1,4-bis-(3-hydroxy-4-oxo-4H-chromen-2-yl)-benzene (bis-flavonol): synthesis, spectral properties and principle possibility of the excited state double proton transfer reaction

Synthesis and systematic investigation of the spectral-luminescent properties of “bis-flavonol” {1,4-bis-(3-hydroxy-4-oxo-4H-chromen-2-yl)-benzene} were performed. Hypothetical possibility for the double excited-state proton transfer reaction in bis-flavonol is discussed based on both quantum-chemical modeling and experimental data. Consecutive S₁*-state transfer of the two protons of the title molecule is shown to be energetically unfavorable, however, still preserving a possibility for the concerted double proton transfer in the excited dienol form.