On magnetoelastic problems of a plane with an arbitrarily shaped hole under stress and displacement boundary conditions

An analytical method for the static plane problem of magnetoelasticityis developed for an infinite plane containing a hole of arbitraryshape under stress and displacement boundary conditions in aprimary uniform magnetic field. The magnetic field influencesthe elastic field by introducing a body force called the Lorentzponderomotive force in the equilibrium equations. The body forcecan be further described in a form relating with the electromagneticstress tensor. The complex variable method in conjunction withthe rational mapping function technique is used in the analysisfor both magnetic field and mechanical field. Governing equationsand boundary conditions are expressed in terms of complex functions.Complex magnetic potential and stress functions are obtainedusing Cauchy integrals for the paramagnetic and soft ferromagneticmaterials, respectively. The distributions of magnetic fieldand the stress components are shown for certain directions ofprimary magnetic fields in an infinite plane with a square hole,as an example. It is found that the stress distributions forthe two types of materials are identical despite the differenceof magnetic fields. The extreme cases of a free and a fixedhole reduced to a crack and a rigid fibre, respectively, arealso investigated. The stress intensity factors at the tipsof crack and rigid fibre are computed, and their variation forcertain directions of primary magnetic field is shown.     

Supramolecular dimeric structures of pyrazole-containing meso-oxo carbaphlorin analogues

Synthesis and properties of a novel meso-oxo carbaphlorin analogue embedded with an N-free pyrazole moiety are described. The N-benzyl precursor was prepared by a [3 + 1]-MacDonald condensation of N-benzyl pyrazole dialdehyde and β-alkyl-substituted tripyrrane dicarboxylic acid and subsequent oxidation by ferric chloride. Upon deprotection of the benzyl group, the resulting N-free oxophlorin analogue formed a unique supramolecular dimer through mutual hydrogen bonding interactions between the pyrazole NH and meso-carbonyl group. The assembled behaviour was characterised by various spectroscopies, X-ray crystallographic analysis and vapour pressure osmometry. Under the similar reaction conditions, the condensation of meso-phenyl-substituted tripyrrane derivative afforded an unprecedented tetrapyrrolic macrocycle fused with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone unit at their α-pyrrolic positions. The X-ray crystallographic analysis of the macrocycle revealed a twisted core structure, and nonaromatic nature was elucidated.     

Chemically amplified kojic acid responses of tyrosinase-based biosensor, based on inhibitory effect to substrate recycling driven by tyrosinase and -ascorbic acid

A tyrosinase-based chemically amplified biosensor, based on the substrate recycling of polyphenols driven by tyrosinase-catalyzed oxidation and chemical reduction by -ascorbic acid (AsA), has been utilized for the highly sensitive detection of inhibitors of tyrosinase such as kojic acid, benzoic and SCN⁻ ion. The amplified current response of immobilized tyrosinase-coupling oxygen electrode due to the recycling was suppressed by the addition of inhibitors, and a highly amplified response to kojic acid over other inhibitors was observed in the presence of 5 mM AsA. The amplification factor (AF) of kojic acid is substantially proportional to the AF of substrates, and the AF for 1 × 10⁻⁷ M kojic acid was increased by up to a factor of 143 when 1 × 10⁻⁵ M dopamine was used as a competitive substrate in the presence of 5 mM AsA. The amplified calibration curve of kojic acid obtained with 5 mM AsA was shifted towards more than a two decades lower concentration range compared with that of the non-amplified response, and the detection limit of kojic acid was lowered to 7 × 10⁻⁸ M.     

The Solid-State and Solution Conformations of (+)-Chelidonine

The solid-state and solution conformations of (+)-chelidonine ( 1 ), a biologically active alkaloid, were determined by X-ray diffraction and ¹H-NMR spectroscopy, X-Ray diffraction analysis revealed a conformer with B/C ‘anti-type’ cis conjunction, a half-chair of ring B , and a twist half-chair of ring C. One H₂O molecule per one alkaloid molecule was cocrystallized and stabilized by H-bonding with OH? C(11). Analysis of the thermal behavior of the crystal showed more thermal stability in the monohydrate than the anhydrate. The NMR measurement of concentration and temperature dependences in CDCl₃ and in (CD₃)₂SO suggested that the OH group of 1 was intramolecularly H -bonded to N(5) in (CD₃)₂SO and intermolecularly H-bonded to the solvent in CDCl₃. Conformational-energy calculations by the MNDO method showed that the intramolecular H -bond was little affected by the conformational stabilization of 1 .     

Chemically amplified kojic acid responses of tyrosinase-based biosensor, based on inhibitory effect to substrate recycling driven by tyrosinase and l-ascorbic acid

A tyrosinase-based chemically amplified biosensor, based on the substrate recycling of polyphenols driven by tyrosinase-catalyzed oxidation and chemical reduction by l-ascorbic acid (AsA), has been utilized for the highly sensitive detection of inhibitors of tyrosinase such as kojic acid, benzoic and SCN(-) ion. The amplified current response of immobilized tyrosinase-coupling oxygen electrode due to the recycling was suppressed by the addition of inhibitors, and a highly amplified response to kojic acid over other inhibitors was observed in the presence of 5 mM AsA. The amplification factor (AF) of kojic acid is substantially proportional to the AF of substrates, and the AF for 1 x 10(-7)M kojic acid was increased by up to a factor of 143 when 1 x 10(-5)M dopamine was used as a competitive substrate in the presence of 5 mM AsA. The amplified calibration curve of kojic acid obtained with 5 mM AsA was shifted towards more than a two decades lower concentration range compared with that of the non-amplified response, and the detection limit of kojic acid was lowered to 7 x 10(-8)M.     

Electrochemical Sensing Platform Based on Lotus Stem-derived Porous Carbon for the Simultaneous Determination of Hydroquinone,Catechol and Nitrite

A simple and highly selective electrochemical sensor based on carbonized lotus stem (CLS) was developed for the simultaneous determination of hydroquinone (HQ), catechol (CC), and nitrite (NT) by using cyclic voltammetry (CV) and amperometry (AMP) methods. The CLS was characterized by the methods including field emission scanning electron microscopy (FE-SEM), Raman spectrum, FT-IR spectrum and X-ray diffraction (XRD). Brunauer-Emmett-Teller (BET) method was used to evaluate the pore structure and surface area of CLS. The oxidation peaks for HQ (116.2 mV), CC (220.1 mV), and NT (818.9 mV) were well separated under optimized conditions, which improved their simultaneous determination. The CLS modified electrode showed a good linear range between 1.0×10 ⁻⁶ to 7.0×10 ⁻⁴ M for HQ, and the detection limit was calculated as 0.15 μM. For CC the linear relationship was 1.0×10 ⁻⁶ to 3.0×10 ⁻³ M with the detection limit of 0.11 μM. For NT the linear relationship was 5.0×10 ⁻⁷ to 4.0×10 ⁻³ M with the detection limit of 0.09 μM. The results indicated that the intrinsic structure of natural biomass can be expected to design porous carbon for electrochemical sensors.     

Raising Operators of Row Type for Macdonald Polynomials

We construct certain raising operators of row type for Macdonald's symmetric polynomials by an interpolation method.     

Mean theoretic approach to the grand Furuta inequality

Very recently, Furuta obtained the grand Furuta inequality which is a parameteric formula interpolating the Furuta inequality and the Ando-Hiai inequality as follows : If and is invertible, then for each ,

is a decreasing function of both and for all and . In this note, we employ a mean theoretic approach to the grand Furuta inequality. Consequently we propose a basic inequality, by which we present a simple proof of the grand Furuta inequality.