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

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

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

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

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

Применение криптографических методов шифрования информации

Необходимость технических средств защиты диктуется тем, что Интернет – это источник информации, за который никто не несет ответственности, и вероятность получения из него недостоверной, оскорбительной, пиратской или запрещенной по другим причинам информации весьма велика.The need for technological protection measures dictated by the fact that the Internet - a source of information for which no one is responsible, and the probability of getting out of it inaccurate, abusive, pirated or illegal for other reasons information is very high

Chemical fidelity of an RNA polymerase ribozyme

The emergence of catalytically active RNA enzymes (ribozymes) is widely believed to have been an important transition in the origin of life. In the context of a likely heterogeneous chemical environment, substrate specificity and selectivity of these primordial enzymes would have been critical for function. Here we have explored the chemical fidelity, i.e. substrate selectivity and specificity for both single and multiple catalytic steps of the Z RNA polymerase ribozyme - a modern day analogue of the primordial RNA replicase. Using a wide range of nucleotide analogues and ionic conditions, we observe strong energetic but weak geometric discrimination at the incorporation step, indicative of an open active site. In contrast, stringent selectivity is exerted at the extension steps through specific down and upstream interactions with the 3’-terminal nucleoside as well as nascent product and template strands. Our results indicate specificity mechanisms that are found in functionally analogous forms in natural polymerases. They also reveal a level of chemical fidelity over multiple catalytic steps that is remarkable for a comparatively unoptimized enzyme developed de novo from a random sequence pool. The convergent evolution of specificity mechanisms in phylogenetically unrelated proteinaceous polymerases and polymerase ribozymes suggests that chemical as well as informational fidelity are emergent properties of polymerase enzymes. © 2013 Royal Society of Chemistry.status: publishe