Multiple finite Riemann zeta functions

Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then, describe the location of zeros. We study further multi-variable and multi-parameter versions of the multiple finite Riemann zeta functions and their infinite counterparts in connection with symmetric polynomials and some arithmetic quantities called powerful numbers.Comment: 19 page

Site-specific biotinylation of RNA molecules by transcription using unnatural base pairs

Direct site-specific biotinylation of RNA molecules was achieved by specific transcription mediated by unnatural base pairs. Unnatural base pairs between 2-amino-6-(2-thienyl)purine (denoted by s) and 2-oxo(1H)pyridine (denoted by y), or 2-amino-6-(2-thiazolyl)purine (denoted as v) and y specifically function in T7 transcription. Using these unnatural base pairs, the substrate of biotinylated-y (Bio-yTP) was selectively incorporated into RNA, opposite s or v in the DNA templates, by T7 RNA polymerase. This method was applied to the immobilization of an RNA aptamer on sensor chips, and the aptamer accurately recognized its target protein. This direct site-specific biotinylation will provide a tool for RNA-based biotechnologies

SMW Wall for Seepage Control in Levee Reconstruction

An SMW wall was installed as a cutoff wall for seepage control during high floods in a narrow levee constructed in the early 1900\u27s using sandy soils. After part of the wall was installed, difficulties were encountered in evaluating the permeability of the as-built cutoff wall according to the project specifications. Methods used to evaluate the permeability of the cutoff wall included laboratory tests on bulk samples and core samples and in-situ permeability tests. Significant differences in test results were caused by various sample preparation and handling procedures, sampling disturbance, and different testing methods. The difficulties were resolved by performing a trial mix study and installing a full scale test section that resulted in changed installation, sampling, and testing procedures

Geometrical and band-structure effects on phonon-limited hole mobility in rectangular cross-sectional germanium nanowires

We calculated the phonon-limited hole mobility in rectangular cross-sectional [001], [110], [111], and [112]-oriented germanium nanowires, and the hole transport characteristics were investigated. A tight-binding approximation was used for holes, and phonons were described by a valence force field model. Then, scattering probability of holes by phonons was calculated taking account of hole-phonon interaction atomistically, and the linearized Boltzmann's transport equation was solved to calculate the hole mobility at low longitudinal field. The dependence of the hole mobility on nanowire geometry was analyzed in terms of the valence band structure of germanium nanowires, and it was found that the dependence was qualitatively reproduced by considering an average effective mass and the density of states of holes. The calculation revealed that [110] germanium nanowires with large height along the [001] direction show high hole mobility. Germanium nanowires with this geometry are also expected to exhibit high electron mobility in our previous work, and thus they are promising for complementary metal-oxide-semiconductor (CMOS) applications

Hierarchy of the Selberg zeta functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Comment: 14 page

Synapse efficiency diverges due to synaptic pruning following over-growth

In the development of the brain, it is known that synapses are pruned following over-growth. This pruning following over-growth seems to be a universal phenomenon that occurs in almost all areas -- visual cortex, motor area, association area, and so on. It has been shown numerically that the synapse efficiency is increased by systematic deletion. We discuss the synapse efficiency to evaluate the effect of pruning following over-growth, and analytically show that the synapse efficiency diverges as O(log c) at the limit where connecting rate c is extremely small. Under a fixed synapse number criterion, the optimal connecting rate, which maximize memory performance, exists.Comment: 15 pages, 16 figure

Solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction

We describe a solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction. We derive self-consistent equations of the order parameters and obtain three non-trivial solutions characterized by the rotation number. We also derive relevant characteristics such as the location-dependent distributions of the resultant frequencies of desynchronized oscillators. Simulation results closely agree with the theoretical ones