Ramanujan type congruences for the Klingen-Eisenstein series

In the case of Siegel modular forms of degree \(n\) , we prove that, for almost all prime ideals \(\mathfrak {p}\) in any ring of algebraic integers, mod \(\mathfrak {p}^m\) cusp forms are congruent to true cusp forms of the same weight. As an application we give congruences for the Klingen-Eisenstein series and cusp forms, which can be regarded as a generalization of Ramanujan’s congruence. We will conclude by giving numerical examples.     

An unusual fatigue crack-tip plastic zone: The epsilon plastic zone of polycarbonate

Polycarbonate exhibits an extraordinary crack-tip plastic zone under certain fatigue loading conditions. During discontinuous growth (multiple load cycles per crack jump), the plastic zone consists of a leading craze and a pair of sharply delineated shear bands, which together look like the Greek letter epsilon. The kinetics of the development of the epsilon plastic zone and the nature of the transition from discontinuous growth to a shear fatigue fracture mode are discussed.     

Theta operator on Hermitian modular forms over the Eisenstein field

The Ramanujan Journal - The mod p kernel of the theta operator on Hermitian modular forms is studied in the case that the base field is the Eisenstein field.     

Highly sensitive multistage mass spectrometry enables small-scale analysis of protein glycosylation from two-dimensional polyacrylamide gels

Structural characterization of glycoproteins remains among the most challenging areas of glycomics due to the requirement of large quantities of samples and laborious biochemical steps involved in the analytical procedure. Here we report the structural characterization of glycoproteins separated on a 2-D gel by using a MALDI-QIT-TOF MS where QIT is quadrupole IT. The combination of MALDI-ion source and QIT appears to generate a unique tendency to cause fragmentation of glycopeptides without collision-induced dissociation. The majority of such fragmentations observed in our study result from the cleavage of sugar linkages, but not of peptide-peptide or peptide-sugar linkages. This unique feature allows us to perform pseudo-MS3 analysis of a fragmented glycopeptide. A small gel spot of a glycoprotein in the abundance range of low picomoles was enough for the mass spectrometer to analyze fragmentation pathway of the sugar linkage and peptide backbone. In this study, we demonstrate direct determination of glycosylation sites and N-linked glycan-sequences of the tryptic glycopeptides of Drosophila glycoproteins. Glycopeptides with various MWs up to approximately 4000 Da were suitable for structural analysis, including its attachment site and the amino acid sequence, of the glycopeptide through multistage mass spectrometric analysis.     

Search for supernova relic neutrinos at Super-Kamiokande

A search for the relic neutrinos from all past core-collapse supernovae was conducted using 1496 days of data from the Super-Kamiokande detector. This analysis looked for electron-type antineutrinos that had produced a positron with an energy greater than 18 MeV. In the absence of a signal, 90% C.L. upper limits on the total flux were set for several theoretical models; these limits ranged from 20 to 130 macro nu(e) cm(-2) s(-1). Additionally, an upper bound of 1.2 macro nu(e) cm(-2) s(-1) was set for the supernova relic neutrino flux in the energy region E(nu)>19.3 MeV.     

Limits on the neutrino magnetic moment using 1496 days of Super-Kamiokande-I solar neutrino data

A search for a nonzero neutrino magnetic moment has been conducted using 1496 live days of solar neutrino data from Super-Kamiokande-I. Specifically, we searched for distortions to the energy spectrum of recoil electrons arising from magnetic scattering due to a nonzero neutrino magnetic moment. In the absence of a clear signal, we found micro(nu)相似文献