Joint value-distribution theorems on Lerch zeta-functions. II

We give corrected statements of some theorems from [5] and [6] on joint value-distribution of Lerch zeta-functions (limit theorems, universality, functional independence). We also present a new direct proof of a joint limit theorem in the space of analytic functions and an extension of a joint universality theorem. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 332–350, July–September, 2006.     

Dual simplex method for GUB problems

The dual simplex method for generalized upper bound (GUB) problems is presented. One of the major operations in the dual simplex method is to update the elements of therth row, wherer is the index for the leaving basic variable. Those updated elements are used for the ratio test to determine the entering basic variabble. A very simple formula for therth row update for the dual simplex method for a GUB problem is derived, which is similar to the formula for the standard linear program. This derivation is based on the change key operation, which is to exchange the key column and its counterpart in the nonkey section. The change key operation is possible because of a theorem that guarantees the existence of such a counterpart.     

Achievement of a 920-MHz high resolution NMR

We have developed a 920-MHz NMR system and performed the proton NMR measurement of H(2)O and ethylbenzene using the superconducting magnet operating at 21.6 T (920 MHz for proton), which is the highest field produced by a superconducting NMR magnet in the persistent mode. From the NMR measurements, it is verified that both homogeneity and stability of the magnet have a specification sufficient for a high resolution NMR.     

Application of pressure sensitive paint measurement to a low-solidity cascade diffuser of a transonic centrifugal compressor

A pressure sensitive paint (PSP) measurement has been known as a pressure field measurement technique based on the oxygen quenching phenomenon of luminescence of specific luminophores. A PSP measurement was applied for pressure field measurement in a low-solidity circular cascade diffuser of a single-stage transonic centrifugal compressor with 5 in pressure ratio for HFC134a gas. The oxygen concentration was about 500 ppm. Ru (bath-phen) was adsorbed on a silica-gel thinlayer chromatography sheet, and the sheet was pasted onto the side-wall between the cascade vanes. A drastic change in luminescent intensity was recognized during a surge condition. Also the pressure variations based on luminescent intensity agreed well with the pressure fluctuations measured using a semiconductor pressure sensor with high-frequency-response. It was shown that a PSP measurement worked well to investigate the unsteady pressure fields in a circular cascade diffuser of a transonic centrifugal compressor. Moreover, the time response of PSP becomes clear as a problem to be overcome for the present.     

Synchrotron radiation photoelectron spectroscopy and near-edge X-ray absorption fine structure study on oxidative etching of diamond-like carbon films by hyperthermal atomic oxygen

Surface structural changes of a hydrogenated diamond-like carbon (DLC) film exposed to a hyperthermal atomic oxygen beam were investigated by Rutherford backscattering spectroscopy (RBS), synchrotron radiation photoelectron spectroscopy (SR-PES), and near-edge X-ray absorption fine structure (NEXAFS). It was confirmed that the DLC surface was oxidized and etched by high-energy collisions of atomic oxygen. RBS and real-time mass-loss data showed a linear relationship between etching and atomic oxygen fluence. SR-PES data suggested that the oxide layer was restricted to the topmost surface of the DLC film. NEXAFS data were interpreted to mean that the sp² structure at the DLC surface was selectively etched by collisions with hyperthermal atomic oxygen, and an sp³-rich region remained at the topmost DLC surface. The formation of an sp³-rich layer at the DLC surface led to surface roughening and a reduced erosion yield relative to the pristine DLC surface.     

Interpolation inequality of logarithmic type in abstract Besov spaces and an application to semilinear evolution equations

An abstract version of Besov spaces is introduced by using the resolvent of nonnegative operators. Interpolation inequalities with respect to abstract Besov spaces and generalized Lorentz spaces are obtained. These inequalities provide a generalization of Sobolev inequalities of logarithmic type. Uniqueness problems to abstract semilinear evolution equations are also discussed (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of a high-dimensional chaotic attractor

The nature of a very high-dimensional chaotic attractor in an infinite-dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high-dimensional attractor in the phase space. We introduce two complementary bases from which the attractor is observed, one the Lyapunov basis composed of the Lyapunov vectors and the another the Fourier basis composed of the Fourier modes. We introduce the exterior subspaces on the basis of the Lyapunov vectors and observe the chaotic motion projected onto these exteriors. It is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace goes out of the attractor. The origin of such a phenomenon is attributed to more fundamental features of our attractor, which become manifest when the attractor is observed from the Lyapunov basis. A counterpart of the phenomenon can be observed also on the Fourier basis because there is a statistical one-to-one correspondence between the Lyapunov vectors and the Fourier modes. In particular, a statistical property of the high-pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor.     

Bose-Einstein correlations for pions produced inp p collisions at 360 GeV/c

Zeitschrift für Physik C Particles and Fields - Correlations among identically charged pions were measured for pions produced inp p collisions at 360 GeV/c using the EHS spectrometer. The...     

Singularities of Euler Flow? Not Out of the Blue!

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.