On the Fourier coefficients of Siegel–Eisenstein series of degree 2 for odd level

The Ramanujan Journal - We calculate the Fourier coefficients of the Siegel–Eisenstein series of degree 2, level $$p^n$$ with trivial character. The main result is to compute the Siegel...     

Recyclable carbon fiber‐reinforced plastics (CFRP) containing degradable acetal linkages: Synthesis,properties, and chemical recycling

Two epoxy resins containing degradable acetal linkages were synthesized by the reaction of cresol novolak‐type phenolic resin (CN) with vinyl ethers containing a glycidyl group [cyclohexane dimethanol vinyl glycidyl ether (CHDMVG) and 4‐vinyloxybutyl glycidyl ether (VBGE). Carbon fiber‐reinforced plastics (CFRPs) were prepared by heating laminated prepreg sheets with CN‐CHDMVG resin (derived from CN and CHDMVG) and CN‐VBGE resin (derived from CN and VBGE), in which carbon fibers are impregnated with epoxy resins containing curing agents [dicyandiamide (DICY)] and curing accelerator [3‐(3,4‐dichlorophenyl)‐1,1‐dimethylurea (DCMU)]. CN‐CHDMVG‐based CFRPs and CN‐VBGE‐based CFRPs exhibited almost the same tensile strength as the conventional bisphenol‐A‐based CFRPs. CN‐CHDMVG‐based CFRPs and CN‐VBGE‐based CFRPs underwent smooth breakdown with the treatment of hydrochloric acid in tetrahydrofuran at room temperature for 24 h to regenerate strands of carbon fibers. The surface conditions of the recovered carbon fibers had little changes during degradation and recovery processes on the basis of scanning electron microscopy (SEM) and X‐ray photoelectron spectroscopy (XPS). The recovered carbon fibers exhibited almost the same tensile strength as virgin carbon fibers and hence would be reused for the production of CFRPs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1052–1059     

Synthesis of C12-Keto Saxitoxin Derivatives with Unusual Inhibitory Activity Against Voltage-Gated Sodium Channels

A novel series of C12-keto-type saxitoxin (STX) derivatives bearing an unusual nonhydrated form of the ketone at C12 has been synthesized, and their Na_V-inhibitory activity has been evaluated in a cell-based assay as well as whole-cell patch-clamp recording. Among these compounds, 11-benzylidene STX ( 3 a ) showed potent inhibitory activity against neuroblastoma Neuro 2A in both cell-based and electrophysiological analyses, with EC₅₀ and IC₅₀ values of 8.5 and 30.7 nm , respectively. Interestingly, the compound showed potent inhibitory activity against tetrodotoxin-resistant subtype of Na_V1.5, with an IC₅₀ value of 94.1 nm . Derivatives 3 a – d and 3 f showed low recovery rates from Na_V1.2 subtype (ca 45–79 %) compared to natural dcSTX ( 2 ), strongly suggesting an irreversible mode of interaction. We propose an interaction model for the C12-keto derivatives with Na_V in which the enone moiety in the STX derivatives 3 works as Michael acceptor for the carboxylate of Asp¹⁷¹⁷.     

Coexistence of Spin–Lattice Relaxation and Phonon-Bottleneck Processes in GdIII–Phthlocyaninato Triple-Decker Complexes under Highly Diluted Conditions

Gd³⁺ complexes have been shown to undergo unusual slow magnetic relaxation processes similar to those of single-molecule magnets (SMMs), even though Gd³⁺ does not exhibit strong magnetic anisotropy. To reveal the origin of the slow magnetic relaxation of Gd³⁺ complexes, we have investigated the magnetic properties and heat capacities of two Gd³⁺-phthalocyaninato triple-decker complexes, one of which has intramolecular Gd³⁺–Gd³⁺ interactions and the other does not. It was found that the Gd³⁺–Gd³⁺ interactions accelerate the magnetic relaxation processes. In addition, magnetically diluted samples, prepared by doping a small amount of the Gd³⁺ complexes into a large amount of diamagnetic Y³⁺ complexes, underwent dual magnetic relaxation processes. A detailed dynamic magnetic analysis revealed that the coexistence of spin–lattice relaxation and phonon-bottleneck processes is the origin of the dual magnetic relaxation processes.     

Detailed Analysis of the Crystal Structures and Magnetic Properties of a Dysprosium(III) Phthalocyaninato Sextuple-Decker Complex: Weak f–f Interactions Suppress Magnetic Relaxation

In the research field of single-molecule magnets (SMMs), lanthanoid–lanthanoid interactions, so-called f–f interactions, are known to affect the SMM properties, although their magnitudes are small. In this article, an SMM with very weak f–f interactions is reported, and the effects of the interactions on the SMM properties are discussed. X-ray structural analysis of the Dy^III-Cd^II-phthalocyaninato sextuple-decker complex (Dy₂Cd₃) reveals that the intramolecular Dy−Dy length in Dy₂Cd₃ is more than 13 Å, which is longer than the intermolecular Dy−Dy length. Even though the two Dy^III ions are far apart, intermolecular ferromagnetic dipole–dipole interactions are observed in Dy₂Cd₃. From detailed analysis of ac magnetic susceptibilities, quantum tunneling of the magnetization (QTM) in Dy₂Cd₃ is partially suppressed owing to the existence of very weak Dy−Dy interactions. Our results show that even very weak Dy−Dy interactions act as a dipolar bias, suppressing QTM.     

Highly Chemoselective and Versatile Method for Direct Conversion of Carboxylic Acids to Ketones Utilizing Zinc Ate Complexes

Various carboxylic acids were directly transformed into the corresponding ketones by utilizing organozinc ate complexes, which provide high chemoselectivity without any overreaction to the undesired tertiary carbinol, owing to formation of a stable tetrahedral zincioketal intermediate. This method offers good overall atom/step/pot economy and operational simplicity.     

Development of variable‐magnification X‐ray Bragg optics

A novel X‐ray Bragg optics is proposed for variable‐magnification of an X‐ray beam. This X‐ray Bragg optics is composed of two magnifiers in a crossed arrangement, and the magnification factor, M, is controlled through the azimuth angle of each magnifier. The basic properties of the X‐ray optics such as the magnification factor, image transformation matrix and intrinsic acceptance angle are described based on the dynamical theory of X‐ray diffraction. The feasibility of the variable‐magnification X‐ray Bragg optics was verified at the vertical‐wiggler beamline BL‐14B of the Photon Factory. For X‐ray Bragg magnifiers, Si(220) crystals with an asymmetric angle of 14° were used. The magnification factor was calculated to be tunable between 0.1 and 10.0 at a wavelength of 0.112 nm. At various magnification factors (M≥ 1.0), X‐ray images of a nylon mesh were observed with an air‐cooled X‐ray CCD camera. Image deformation caused by the optics could be corrected by using a 2 × 2 transformation matrix and bilinear interpolation method. Not only absorption‐contrast but also edge‐contrast due to Fresnel diffraction was observed in the magnified images.     

Potassium-ion-selective sensing based on selective reflection of cholesteric liquid crystal membranes

It is well-known that cholesteric liquid crystals have an optical property, selective reflection, due to changes in the pitch of their helical structure. This unique property of cholesteric liquid crystals can be used to attain a visual sensing system showing color changes as the detection signal. In this paper, we report a visual sensing membrane comprising cholesteric liquid crystals, in which a 15-crown-5 derivative was incorporated as ion recognizing sites, for K⁺ in aqueous solution. The resulting CLC membrane showed a shift of the reflection peak sensitive to K⁺ in water. We have also designed polymer-dispersed liquid crystal membranes that showed ion-selective reflection peak shifts with improved response time.     

Effect of Static Magnetic Field on Photocatalytic Degradation of Methylene Blue over ZnO and TiO2 Powders

Magnetic field effects (MFEs) on photocatalytic degradation of methylene blue (MB) solution over ZnO and TiO₂ powders are investigated under static magnetic field up to 0.7 T with light irradiation by ultraviolet (UV) light emitting diode. The UV–visible-near-infrared spectrometer is used to monitor the MB concentrations. The positive MFE is observed for ZnO, while the negative MFE for TiO₂, and both MFEs are increased with the increase in the magnetic field applied. By increasing the settling time (the time interval between the preparation of MB solution and the powder dispersion into the MB solution), the photodegradation abilities under MFEs are decreased for both the catalysts. The cause of MFE is discussed in terms of dissolved oxygen in the MB solution and magnetic adsorption of the constituent molecules.