How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...     

Investigation of Relationships between Grain Structure and Inhomogeneous Deformation by Means of Laboratory-Based Multimodal X-Ray Tomography: Strain Accuracy Analysis

Experimental Mechanics - The internal strain distribution developing during plastic deformation is important for understanding the mechanical properties of polycrystalline materials. Such...     

One-sided invertibility of discrete operators with bounded coefficients

Aequationes mathematicae - For $$p\in (1,\infty )$$ , we establish several criteria of one-sided invertibility on spaces $$l^p=l^p(\mathbb {Z})$$ for discrete band-dominated operators being either...     

Direct Addition of Amides to Glycals Enabled by Solvation‐Insusceptible 2‐Haloazolium Salt Catalysis

The direct 2‐deoxyglycosylation of nucleophiles with glycals leads to biologically and pharmacologically important 2‐deoxysugar compounds. Although the direct addition of hydroxyl and sulfonamide groups have been well developed, the direct 2‐deoxyglycosylation of amide groups has not been reported to date. Herein, we show the first direct 2‐deoxyglycosylation of amide groups using a newly designed Brønsted acid catalyst under mild conditions. Through mechanistic investigations, we discovered that the amide group can inhibit acid catalysts, and the inhibition has made the 2‐deoxyglycosylation reaction difficult. Diffusion‐ordered two‐dimensional NMR spectroscopy analysis implied that the 2‐chloroazolium salt catalyst was less likely to form aggregates with amides in comparison to other acid catalysts. The chlorine atom and the extended π‐scaffold of the catalyst played a crucial role for this phenomenon. This relative insusceptibility to inhibition by amides is more responsible for the catalytic activity than the strength of the acidity.     

Ozonolysis of a Series of Methylated Alkenes: Reaction Rate Coefficients and Gas‐Phase Products

The gas‐phase ozonolysis of three methylated alkenes, i.e., trans‐2,2‐dimethyl‐3‐hexene (22dM3H), trans‐2,5‐dimethyl‐3‐hexene (25dM3H), and 4‐methyl‐1‐pentene (4M1P), has been investigated in the presence of sufficient hydroxyl radical scavenger in a laminar flow reactor at ambient temperature (296 ± 2 K) and P = 1 atm of dry air (RH ≤ 5%). Ozone levels in the reactor were monitored by an automatic analyzer. Alkene and gas‐phase product concentrations were determined via online sampling either on three‐bed adsorbent cartridges followed by thermodesorption and GC/FID‐MS analysis or on 2,4‐dinitrophenylhydrazine (DNPH) cartridges for subsequent HPLC/UV analysis. Reaction rate coefficients of (3.38 ± 0.12) × 10^?17 for 22dM3H and (2.71 ± 0.26) × 10^?17 for 25dM3H, both in cm³ molecule^?1 s^?1 units, have been obtained under pseudo–first‐order conditions. Primary carbonyl products have been identified for the three investigated alkenes, and branching ratios are reported. In the case of 4M1P ozonolysis, the yield of a Criegee intermediate was indirectly determined. Kinetics and product study results are compared to those of literature when available. This work represents the first investigation of reaction products in the ozonolysis of 22dM3H, 25dM3H, and 4M1P in a flow reactor.     

Rational Molecular Design towards Vis/NIR Absorption and Fluorescence by using Pyrrolopyrrole aza‐BODIPY and its Highly Conjugated Structures for Organic Photovoltaics

Pyrrolopyrrole aza‐BODIPY (PPAB) developed in our recent study from diketopyrrolopyrrole by titanium tetrachloride‐mediated Schiff‐base formation reaction with heteroaromatic amines is a highly potential chromophore due to its intense absorption and fluorescence in the visible region and high fluorescence quantum yield, which is greater than 0.8. To control the absorption and fluorescence of PPAB, particularly in the near‐infrared (NIR) region, further molecular design was performed using DFT calculations. This results in the postulation that the HOMO–LUMO gap of PPAB is perturbed by the heteroaromatic moieties and the aryl‐substituents. Based on this molecular design, a series of new PPAB molecules was synthesized, in which the largest redshifts of the absorption and fluorescence maxima up to 803 and 850 nm, respectively, were achieved for a PPAB consisting of benzothiazole rings and terthienyl substituents. In contrast to the sharp absorption of PPAB, a PPAB dimer, which was prepared by a cross‐coupling reaction of PPAB monomers, exhibited panchromatic absorption across the UV/Vis/NIR regions. With this series of PPAB chromophores in hand, a potential application of PPAB as an optoelectronic material was investigated. After identifying a suitable PPAB molecule for application in organic photovoltaic cells based on evaluation using time‐resolved microwave conductivity measurements, a maximized power conversion efficiency of 1.27 % was achieved.     

Stable all-optical formation of Bose–Einstein condensate using pointing-stabilized optical trapping beams

By stabilizing the beam pointing of optical trapping beams, we have succeeded in stable formation of Bose–Einstein condensate (BEC) of ⁸⁷Rb with all-optical method. The thermal effect of acousto-optic modulator (AOM) is usually one of the most serious problems to induce beam-pointing instability, especially for high power CO₂ laser. By passing the beam through AOM twice, we have improved the beam pointing from about 4.8 mrad to less than 0.4 mrad, which has been experimentally confirmed to be small enough to stably form BEC at the crossed region of CO₂ lasers as well as to perform experiments using an optical lattice which might have been affected by beam-pointing instability. PACS 32.80.Pj; 42.79.Jq; 03.75.Mn     

Rank one perturbations at infinite coupling in Pontryagin spaces

In this paper we relate the operators in the operator representations of a generalized Nevanlinna function N(z) and of the function −N(z)⁻¹ under the assumption that z=∞ is the only (generalized) pole of nonpositive type. The results are applied to the Q-function for S and H and the Q-function for S and H^∞, where H is a self-adjoint operator in a Pontryagin space with a cyclic element w, H^∞ is the self-adjoint relation obtained from H and w via a rank one perturbation at infinite coupling, and S is the symmetric operator given by S=H∩H^∞.