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

Parametric study of transport aircraft systems cost and weight

The results of a NASA study to develop production cost estimating relationships (CERs) and weight estimating relationships (WERs) for commercial and military transport aircraft at the system level are presented. The systems considered correspond to the standard weight groups defined in Military Standard 1374 and are listed. These systems make up a complete aircraft exclusive of engines. The CER for each system (or CERs in several cases) utilize weight as the key parameter. Weights may be determined from detailed weight statements, if available, or by using the WERs developed, which are based on technical and performance characteristics generally available during preliminary design. The CERs that were developed provide a very useful tool for making preliminary estimates of the production cost of an aircraft. Likewise, the WERs provide a very useful tool for making preliminary estimates of the weight of aircraft based on conceptual design information

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

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

Chemo- and Thermosensory Responsiveness of Grueneberg Ganglion Neurons Relies on Cyclic Guanosine Monophosphate Signaling Elements

Neurons of the Grueneberg ganglion (GG) in the anterior nasal region of mouse pups respond to cool temperatures and to a small set of odorants. While the thermosensory reactivity appears to be mediated by elements of a cyclic guanosine monophosphate (cGMP) cascade, the molecular mechanisms underlying the odor-induced responses are unclear. Since odor-responsive GG cells are endowed with elements of a cGMP pathway, specifically the transmembrane guanylyl cyclase subtype GC-G and the cyclic nucleotide-gated ion channel CNGA3, the possibility was explored whether these cGMP signaling elements may also be involved in chemosensory GG responses. Experiments with transgenic mice deficient for GC-G or CNGA3 revealed that GG responsiveness to given odorants was significantly diminished in these knockout animals. These findings suggest that a cGMP cascade may be important for both olfactory and thermosensory signaling in the GG. However, in contrast to the thermosensory reactivity, which did not decline over time, the chemosensory response underwent adaptation upon extended stimulation, suggesting that the two transduction processes only partially overlap. Copyright (C) 2011 S. Karger AG, Base