Generalized Lerch formulas: Examples of zeta-regularized products

AbstractWe prove∏ˆm=0∞(∏j=1n(m+zj))=∏j=1n2πΓ(zj)=∏j=1n(∏ˆm=0∞(m+zj)), where ∏ˆnan is the zeta-regularized product of the sequence {an}n and Γ(z) is Euler's gamma function. As a part of our result, we obtain the formula of Lerch, Kurokawa and Wakayama. Moreover this result gives an example of a pair of sequences {an},{bn} which satisfies ∏ˆn(an⋅bn)=∏ˆnan⋅∏ˆnbn, although this equality does not hold in general. We also give two-dimensional analogue and q-analogue of our result. Barnes' double gamma functions and Jackson's q-gamma functions appear instead of Euler's gamma function Γ(z)

Linear dependence of certain L-values of half-integral weight modular forms

For two holomorphic modular forms h1(z) = 1∑ m=

On p-adic Hermitian Eisenstein series and p-adic Siegel cusp forms

AbstractWe study two kinds of p-adic Hermitian Eisenstein series of degree 2 over Q(−1). It is shown that they are actual Hermitian modular forms of level p. In particular, the one is just a Hermitian Eisenstein series of level p. Moreover, the cuspidality of p-adic limits of Siegel cusp form is discussed based on some examples

Regional Inequality Simulations Based on Asset Exchange Models with Exchange Range and Local Support Bias

To gain insights into the problem of regional inequality, we proposed new regional asset exchange models based on existing kinetic income-exchange models in economic physics. We did this by setting the spatial exchange range and adding bias to asset fraction probability in equivalent exchanges. Simulations of asset distribution and Gini coefficients showed that suppressing regional inequality requires, firstly an increase in the intra-regional economic circulation rate, and secondly the narrowing down of the exchange range (inter-regional economic zone). However, avoiding over-concentration of assets due to repeat exchanges requires adding a third measure; the local support bias (distribution norm). A comprehensive solution incorporating these three measures enabled shifting the asset distribution from over-concentration to exponential distribution and eventually approaching the normal distribution, reducing the Gini coefficient further. Going forward, we will expand these models by setting production capacity based on assets, path dependency on two-dimensional space, bias according to disparity, and verify measures to reduce regional inequality in actual communities.Comment: 14 pages, 8 figures. Published online at http://redfame.com/journal/index.php/aef/article/view/494

The Second Survey of the Molecular Clouds in the Large Magellanic Cloud by NANTEN I: Catalog of Molecular Clouds

The second survey of the molecular clouds in 12CO (J = 1-0) was carried out in the Large Magellanic Cloud by NANTEN. The sensitivity of this survey is twice as high as that of the previous NANTEN survey, leading to a detection of molecular clouds with M_CO > 2 x 10^4 M_sun. We identified 272 molecular clouds, 230 of which are detected at three or more observed positions. We derived the physical properties, such as size, line width, virial mass, of the 164 GMCs which have an extent more than the beam size of NANTEN in both the major and minor axes. The CO luminosity and virial mass of the clouds show a good correlation of M_VIR propto L_CO^{1.1 +- 0.1} with a Spearman rank correlation of 0.8 suggesting that the clouds are in nearly virial equilibrium. Assuming the clouds are in virial equilibrium, we derived an X_CO-factor to be ~ 7 x 10^20 cm^-2 (K km s^-1)^-1. The mass spectrum of the clouds is fitted well by a power law of N_cloud(>M_CO) proportional to M_CO^{-0.75 +- 0.06} above the completeness limit of 5 x 10^4 M_sun. The slope of the mass spectrum becomes steeper if we fit only the massive clouds; e.g., N_cloud (>M_CO) is proportional to M_CO^{-1.2 +- 0.2} for M_CO > 3 x 10^5 M_sun.Comment: 54 pages in total, 18 figures (21 files) and 4 tables, to appear in Astrophysical Journal Supplement Series. A full color version with higher resolution figures is available at http://www.a.phys.nagoya-u.ac.jp/~kawamura/research/NANTEN_LMC_1_preprint_highres.pd

Turbulent boundary layers and channels at moderate Reynolds numbers

The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/¿=0.3¿0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Re¿ ¿ 2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/

Method for Identifying Type of Eddy-Current Displacement Sensor

Eddy-current (EC) displacement sensors are used in a device for measuring the shaft vibration of turbines. An EC displacement sensor is composed of a sensor probe and an impedance/output voltage (Z/V) converter. In a power plant in the U. S., the type of the sensor probe and the displacement from the turbine shaft to the tip of the sensor probe (displacement x) are not controlled. For this reason, when only the Z/V converter breaks down, the plant is stopped and dismantled, and both the Z/V converter and the sensor probe are replaced. This results in two problems, i.e., the unstable supply of electric power when the power plant is stopped and the high cost of dismantling the plant. If both the type of the sensor probe and x are identified during turbine operation, the aforementioned problems could be solved. In this paper, we describe that the three types of the sensor probe and x can be identified by comparing the measured the maximum quality factor Q(EC) (max) and frequency f(o) at Q(EC) (max) with the Q(EC) (max) versus f(o) characteristics of sensor probes.ArticleIEEE TRANSACTIONS ON MAGNETICS. 47(10):3554-3557 (2011)journal articl

Comparison of recovery of mobility and self-efficacy after total knee arthroplasty based on two different protocols: A prospective cohort study

Objectives: The purpose of this study was to compare the recovery of mobility and self-efficacy following total knee arthroplasty (TKA) between the 5-day and the 28-day protocol. This prospective cohort study was carried out at two hospitals. Methods: In total, 104 patients who underwent TKA were enrolled. The primary outcomes measured were Life Space Assessment (LSA) for mobility and modified-Gait Efficacy Scale (mGES) for self-efficacy. Knee Society Score (KSS) was used to estimate the functional outcomes. These assessments were performed in all patients preoperatively, and at 1, 3, and 6 months postoperatively. After calculating the propensity score using covariates, such as patient characteristics, LSA, mGES, and KSS at baseline, propensity score-adjusted multivariate analysis of covariance (MANCOVA) was performed. Results: MANCOVA revealed significant differences in LSA and mGES, but not in KSS, between the two protocols. The adjusted means of LSA and mGES in the 28-day protocol were significantly greater than those in the 5-day protocol in all the postoperative assessments. Conclusion: Mobility and self-efficacy were greater following the 28-day protocol than the 5-day protocol after TKA. Our findings suggest that the modified treatment procedure for improving mobility and self-efficacy is necessary to introduce the early discharge protocol in Japan