Allowable irreducible representations of the point groups with five-fold rotational axes

Allowable irreducible representations of the point groups with five-fold rotations – that represent the symmetry of the quasicrystals in two and three dimensions – are derived by employing the little group technique in conjunction with the solvability property. The point groups D $_{5h} ({\overline {10} {\text{{\emph m}}}2})$ and ${\text{{\emph I}}}_h (\frac{2}{\text{{\emph m}}}\overline 3 \,\overline 5)$ are taken to illustrate the method.     

Spherical means in annular regions in the <Emphasis Type="Italic">n</Emphasis>-dimensional real hyperbolic spaces

Let Z _r,R be the class of all continuous functions f on the annulus Ann(r, R) in the real hyperbolic space \(\mathbb B^n\) with spherical means M _s f(x)?=?0, whenever s?>?0 and \(x\in\mathbb B^n\) are such that the sphere S _s (x)???Ann(r, R) and \(B_r(o)\subseteq B_s(x).\) In this article, we give a characterization for functions in Z _r,R . In the case R?=?∞, this result gives a new proof of Helgason’s support theorem for spherical means in the real hyperbolic spaces.     

Erratum to: Allowable irreducible representations of the point groups with five-fold rotational axes†

Allowable irreducible representations of the point groups with five-fold rotations – that represent the symmetry of the quasicrystals in two and three dimensions – are derived by employing the little group technique in conjunction with the solvability property. The point groups D $_{5h} ({\overline {10}}{m}2)$ and ${I}_h \left(\frac{2}{m}\overline {3} \,\overline {5}\right)$ are taken to illustrate the method.     

中空纤维三相液相微萃取荧光光度法测定绿豆芽中的吲哚类植物生长素

基于中空纤维液相微萃取技术,建立了绿豆芽中吲哚类植物生长素的荧光检测方法。通过L9(34)正交实验,对中空纤维液相微萃取条件进行优化,得到的优化条件为:样品溶液的p H值调为4.0,萃取溶剂为正辛醇,接受相为p H 12.0的Na OH,搅拌速度为1 000 r/min,萃取时间为60 min。在最优萃取条件下,吲哚类植物生长素的富集倍数可达92倍。供体相中吲哚类植物生长素的质量浓度在1.71~50.0 mg/L范围内呈良好的线性关系,相关系数为0.997 9,检出限(S/N=3)为0.57 mg/L,样品的加标回收率为88.6%~100.7%,相对标准偏差(RSD)不大于4.8%。该方法操作简单,环境友好,可用于绿豆芽中吲哚类植物生长素含量的准确快速测定。     

Size-independent peak shift between normal and upconversion photoluminescence in MPA-capped CdTe nanoparticles

In this article, we report size-dependent measurement of the shift in peak of upconversion photoluminescence spectra compared to that of normal photoluminescence using a 800 nm femtosecond laser and its second harmonic. It has been shown that the upconversion photoluminescence is always red-shifted compared to that of normal PL in all the samples. By measuring the power-dependent upconversion photoluminescence (UCPL), it has been shown that the origin of UCPL from MPA-capped CdTe nanoparticles is mainly of two-photon absorption     

Tunable third-harmonic probe for non-degenerate ultrafast pump–probe measurements

In this article, we report a method to achieve a precisely tunable highly stable probe beam generation for performing pump–probe experiment around a given wavelength by tilting a sum frequency generation (SFG) crystal angle. The width of the generated third-harmonic beam is of the order of 2 nm throughout the tunable range. This method of probe beam generation has its application in isolating contributions from closely separated excitation states.     

Coherent oscillations of holes in GaAs0.86P0.14/Al0.7Ga0.3As surface quantum well

We show that in a GaAs_0.86P_0.14/Al_0.7Ga_0.3As near-surface quantum well, there is coherent oscillation of holes observed in time-resolved reflectivity signal when the top barrier of the quantum well is sufficiently thin. The quantum well states interact with the surface states under the influence of the surface electric field. The time period of the observed oscillation is 120±10 fs.     

A comparative study of the static third-order polarizabilities of bowl/non-cage to cage structures: a structure-property correlation study

The average static third-order polarizabilities (γ) have been computed for the bowls and cages having the same number of carbon atoms. The bowls have higher (γ) than their corresponding cages. The dependence of (γ) on the average pyrimidalized angle (Θ_p) and maximal length L can be deduced. Near cages, having one open window (C₇₂ isomers), are capped with C₆ to generate five isolated pentagon rule (IPR) isomers of C₇₈ fullerenes following a circumscribing algorithm. The (γ) values for the C₇₈'s and C₇₂′s are correlated with (Θ_p) and L. The change in (γ) from C₇₂′s to C₇₈′s are correlated with a local parameter like the capped angle (α).     

A Convenient Synthesis of 6,8-Dimethoxy-3-[（2-（4-methoxyphenyl）ethyl）isocoumarin

6,8-Dimethoxy-3-[2-（4-methoxyphenyl）ethyl]isocoumarin was synthesized by condensation of 5,7-dimethoxyhompophthalic acid with 3-（4-methoxyphenyl）propanoyl chloride. The structure of the synthesized compound was confirmed by its mass spectrometric studies. The synthesized compound serves as a model for synthesis of DL-agrimonolide.