Stability of constant retrial rate systems with NBU input*

We study the stability of a single-server retrial queueing system with constant retrial rate, general input and service processes. First, we present a review of some relevant recent results related to the stability criteria of similar systems. Sufficient stability conditions were obtained by Avrachenkov and Morozov (2014), which hold for a rather general retrial system. However, only in the case of Poisson input is an explicit expression provided; otherwise one has to rely on simulation. On the other hand, the stability criteria derived by Lillo (1996) can be easily computed but only hold for the case of exponential service times. We present new sufficient stability conditions, which are less tight than the ones obtained by Avrachenkov and Morozov (2010), but have an analytical expression under rather general assumptions. A key assumption is that interarrival times belongs to the class of new better than used (NBU) distributions. We illustrate the accuracy of the condition based on this assumption (in comparison with known conditions when possible) for a number of non-exponential distributions

Hydro-seismic-acoustical monitoring of submarine earthquakes preparation: observations and analysis

The results of laboratory experiments on rock sample destruction and the observation data obtained from several series of the hydro-acoustic observations in which the researchers succeeded to register the signals in the critical stage of the earthquake (EQ) preparation were compared. According to theoretical research (Alekseev et al., 2001) two distinct dilatant zones occur in the EQ preparation stage. The first one is located around the source and the second one represents the near-surface dilatant zone. Only high-frequency seismic-acoustic signals (SAS) radiated from the near-surface dilatant zone do not attenuate completely on the passage through a solid medium. Parameters of the SAS such as the source depth under the ocean floor, frequency maximum and the signal power level were estimated. It was shown that the critical stage of the EQ preparation continues several tens hours and this process has a hierarchical nature. At first the micro-ruptures are formed over a large area. Then the high frequency radiation begins to decrease, the SAS emission area begins to shrink and the micro-earthquakes occur in the area surrounding the epicenter. The obtained results are in close agreement with the theoretical conception about the evolution of the SAS in the surface dilatant zone and with the results of laboratory experiments

The relationship between parameters of the peyer's patches of the small intestine in intact rats

This paper deals with the study of the relationship between parameters of the Peyer’s patches of the small intestine in intact rats of different age groups. The correlation analysis revealed the direct relationship between the parameter

A Gaussian approximation of the distributed computing process

The authors propose a refinement of the stochastic model describing the dynamics of the Desktop Grid (DG) project with many hosts and many workunits to be performed, originally proposed by Morozov et al. in 2017. The target performance measure is the mean duration of the runtime of the project. To this end, the authors derive an asymptotic expression for the amount of the accumulated work to be done by means of limit theorems for superposed on-off sources that lead to a Gaussian approximation. In more detail, depending on the distribution of active and idle periods, Brownian or fractional Brownian processes are obtained. The authors present the analytic results related to the hitting time of the considered processes (including the case in which the overall amount of work is only known in a probabilistic way), and highlight how the runtime tail distribution could be estimated by simulation. Taking advantage of the properties of Gaussian processes and the Conditional Monte-Carlo (CMC) approach, the authors present a theoretical framework for evaluating the runtime tail distribution

On the interrelation between monopoles, vortices, topological charge and chiral symmetry breaking: an analysis using overlap fermions for SU(2)

We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of non-zero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with Q_{index}=0. The remaining (ultraviolet) monopoles without vortices and -- to a less extent -- the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble effects the monopoles and vortices only by smoothing, reducing the density only slightly.Comment: 13 pages, 5 figures, strongly revised, results added, one figure added, accepted for publication, title changed

The topological structure of SU(2) gluodynamics at T > 0 : an analysis using the Symanzik action and Neuberger overlap fermions

We study SU(2) gluodynamics at finite temperature on both sides of the deconfining phase transition. We create the lattice ensembles using the tree-level tadpole-improved Symanzik action. The Neuberger overlap Dirac operator is used to determine the following three aspects of vacuum structure: (i) The topological susceptibility is evaluated at various temperatures across the phase transition, (ii) the overlap fermion spectral density is determined and found to depend on the Polyakov loop above the phase transition and (iii) the corresponding localization properties of low-lying eigenmodes are investigated. Finally, we compare with zero temperature results.Comment: 20 pages, 21 figures, one new figure, two overloaded figures split in two, minor clarifying changes throughout the text, final version accepted by Physical Review

The incarnation of the Nersesyan-Tsvelik model in (NO)[Cu(NO3)3]

The topology of the magnetic interactions of the copper spins in the nitrosonium nitratocuprate (NO)[Cu(NO3)3] suggests that it could be a realization of the Nersesyan-Tsvelik model, whose ground state was argued to be either a resonating valence bond (RVB) state or a valence bond crystal (VBC). The measurement of thermodynamic and resonant properties reveals a behavior inherent to low dimensional spin S = 1/2 systems and provides indeed no evidence for the formation of long-range magnetic order down to 1.8 K.Comment: 12 pages, 6 figure

A-infinity structure on simplicial complexes

A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds. Various operations are explicitly defined on these forms, including exterior derivative and exterior product. The latter one is non-associative. Instead, as anticipated, it is a part of non-trivial A-infinity structure, involving a chain of poly-linear operations, constrained by nilpotency relation: (d + \wedge + m + ...)^n = 0 with n=2.Comment: final version. 29 page