Congruence of Siegel modular forms and special values of their standard zeta functions

In this paper, we consider the relationship between the congruence of cuspidal Hecke eigenforms with respect to Sp _n (Z) and the special values of their standard zeta functions. In particular, we propose a conjecture concerning the congruence between Saito-Kurokawa lifts and non-Saito-Kurokawa lifts, and prove it under certain condition. Partially supported by Grant-in-Aid for Scientific Research C-17540003, JSPS.     

A certain Dirichlet series of Rankin-Selberg type associated with the Ikeda lifting

We consider a certain Dirichlet series of Rankin-Selberg type associated with two Siegel cusp forms of the same integral weight with respect to Spn(Z). In particular, we give an explicit formula for the Dirichlet series associated with the Ikeda lifting of cuspidal Hecke eigenforms with respect to SL₂(Z). We also comment on a contribution to the Ikeda's conjecture on the period of the lifting.     

Elementary aspects of vortex motion

Several aspects of vortex motion are considered, with a special stress on the present status of idealization, such as point vortices or vortex filament. As an introduction, elements of vortices induced by the transient flow past an obstacle are considered and their role and development are stated.

Following this introduction, a general survey of the issues in this symposium is made sketchily. As an example, the motion of point vortices in the presence of an external flow or a boundary is discussed on the basis of the Hamiltonian formalism. The cases of linear flow and semicircular boundary are taken as examples of regular and chaotic motions. Secular behaviour of a pair of vortices in the flow is remarked.     

Origins of hole doping and relevant optoelectronic properties of wide gap p-type semiconductor, LaCuOSe

LaCuOSe is a wide band gap (～2.8 eV) semiconductor with unique optoelectronic properties, including room-temperature stable excitons, high hole mobility ～8 cm(2)/(Vs), and the capability of high-density hole doping (up to 1.7 × 10(21) cm(-3) using Mg). Moreover, its carrier transport and doping behaviors exhibit nonconventional results, e.g., the hole concentration increases with decreasing temperature and the high hole doping does not correlate with other properties such as optical absorption. Herein, secondary ion mass spectroscopy and photoemission spectroscopy reveal that aliovalent ion substitution of Mg at the La site is not the main source of hole doping and the Fermi level does not shift even in heavily doped LaCuOSe:Mg. As the hole concentration increases, the subgap optical absorption becomes more intense, but the increase in intensity does not correlate quantitatively. Transmission electron microscopy indicates that planar defects composed of Cu and Se deficiencies are easily created in LaCuOSe. These observations can be explained via the existence of a degenerate low-mobility layer and formation of complex Cu and Se vacancy defects with the assistance of generalized gradient approximation band calculations.     

Explicit formulas for the twisted Koecher–Maaß series of the Duke–Imamoglu–Ikeda lift and their applications

We give an explicit formula for the twisted Koecher–Maaß series of the Duke–Imamoglu–Ikeda lift. As an application we prove a certain algebraicity result for the values of twisted Rankin–Selberg series at integers of half-integral weight modular forms, which was not treated by Shimura (J Math Soc Japan 33:649–672, 1981).     

Estimation of single-nucleotide polymorphism allele frequency by alternately binding probe competitive polymerase chain reaction

A modified solvent microextraction with back extraction method (SME/BE) combined with high performance liquid chromatography and fluorescence detection (HPLC-FD) was developed for the determination of citalopram in human plasma. Extraction process was performed in a home-made total glass vial without using a teflon ring, usually employed in SME/BE. Citalopram was first extracted from 0.5 mL of plasma, modified with sodium hydroxide, into hexane. Back extraction step was then performed into 5.2 μL of 45 mM ammonium formate solution (pH 4) using a GC microsyringe. The extract was subsequently transferred into a liner-like vial and then injected into the HPLC system. An enrichment factor of 150 along with a good sample clean-up was obtained. The calibration curve showed linearity in the range of 1.0–130.0 ng mL⁻¹ with regression coefficient corresponding to 0.992. This range covers therapeutic window and even lower amounts which is important in pharmacokinetic studies. Limits of detection and quantification, based on a signal to noise ratio (S/N) of 3 and 10, were 0.3 and 0.8 ng mL⁻¹, respectively. The method was also applied for the determination of citalopram in plasma samples after oral administration of 40 mg single dose of citalopram.     

Uniaxially aligned carbon nanofibers derived from electrospun precursor yarns

Unlike conventional electrospun polymer fibers deposited on a target electrode as a randomly oriented mesh, poly(p‐xylenetetrahydrothiophenium chloride) was electrospun into centimeters‐long yarns vertically on the surface of the electrode but parallel to the electric field. The diameter of the yarn was strongly affected by the concentration, spinning rate, and viscosity of the polymer solution, but less dependent on the applied voltage. The subsequent carbonization of thus‐electrospun yarns at 600–1000 °C resulted in uniaxially aligned carbon nanofibers with average diameters of 127–184 nm. On the basis of Raman spectra, the graphitic crystallite size and the molar fraction of graphite were estimated to be 1.2–1.4 and 0.21–0.24 nm, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 305–310, 2008     

Novel synthesis of alkoxy substituted oxa[9]helicenes by the reaction of helical quinone with alcohols

The reaction of helical quinone with alcohols in the presence of Brønsted acid such as para-toluenesulfonic acid (pTSA) or HCl proceeded smoothly to produce the corresponding alkoxy substituted oxa[9]helicenes in good yields.