Ancient astronomical instrument from Srubna burial of kurgan field Tavriya-1 (Northern Black Sea Coast)

The article presents the results of analysis of the spatial arrangement of the wells on the unique slab from Srubna burial of kurgan field Tavriya-1 (Rostov region, Russia) by astronomical methods. At the slab revealed two interrelated groups of wells, one of which - in the form of a circle, is proposed to interpret how analemmatic sundial, and second group, consisting of disparate wells, as auxiliary astronomical markers of rising luminaries directions, to correct the position of the gnomon. Simultaneous location of both groups of wells on the same slab is a possible indication of one of the stages of development of the design features analemmatic sundial - setting movable gnomon and technology of measuring time with it. It may point to local origin, as the very idea of analemmatic sundial as well technology measurement of time with them. The article also describes the model analemmatic sundial, hour marks which in many cases coincide with the wells arranged in a circle, particularly in a working range from 6 to 18 hours. In the study proposed a method which can identify moments of solstices and equinoxes in ancient times with the help of the gnomon of analemmatic sundial and mobile gnomons, installed in wells belonging to the second group. The opportunity of use analemmatic sundial as moondial in a full moon night. Slab with two groups of wells is proposed to consider, as the oldest astronomical instrument discovered in the Northern Black Sea coast, which allowed to observe the apparent motion of the Sun and the Moon and allowed measure the time during the day, using analemmatic sundial and at night during the full Moon - with the help of moondial. Keywords: analemmatic sundial, moondial, srubna burial, slab, wells, cupped depressions, gnomon, model, technology, astronomical methods, archaeoastronomy.Comment: Published version of the articl

Fisher's zeros of quasi-Gaussian densities of states

We discuss apparent paradoxes regarding the location of the zeros of the partition function in the complex $\beta$ plane (Fisher's zeros) of a pure SU(2) lattice gauge theory in 4 dimensions. We propose a new criterion to draw the region of the complex $\beta$ plane where reweighting methods can be trusted when the density of states is almost but not exactly Gaussian. We propose new methods to infer the existence of zeros outside of this region. We demonstrate the reliability of these proposals with quasi Gaussian Monte Carlo distributions where the locations of the zeros can be calculated by independent numerical methods. The results are presented in such way that the methods can be applied for general lattice models. Applications to specific lattice models will be discussed in a separate publication.Comment: 11 pages, 21 figures, with minor correction

Observation of small scale structure using sextupole lensing

Weak gravitational lensing seeks to determine shear by measuring induced quadrupole (elliptical) shapes in background galaxy images. Small impact parameter (a few kpc) gravitational lensing by foreground core masses between 2 10^{9} and 2 10^{12} M_\odot will additionally induce a sextupole shape with the quadrupole and sextupole minima aligned. This correlation in relative orientation of the quadrupole and sextupole provides a sensitive method to identify images which have been slightly curved by lensing events. A general theoretical framework for sextupole lensing is developed which includes several low order coefficients in a general lensing map. Tools to impute map coefficients from the galaxy images are described and applied to the north Hubble deep field. Instrumental PSFs, camera charge diffusion, and image composition methods are modelled in the coefficient determination process. Estimates of Poisson counting noise for each galaxy are used to cut galaxies with signals too small to reliably establish curvature. Curved galaxies are found to be spatially clumped, as would be expected if the curving were due to small impact parameter lensing by localized ensembles of dark matter haloes. Simulations provide an estimate of the total required lensing mass and the acceptable mass range of the constituent haloes. The overdensities and underdensities of visible galaxies and their locations in the Hubble foreground is found to be consistent with our observations and their interpretation as lensing events.Comment: 40 pages, 44 figure

Mixed Polling with Rerouting and Applications

Queueing systems with a single server in which customers wait to be served at a finite number of distinct locations (buffers/queues) are called discrete polling systems. Polling systems in which arrivals of users occur anywhere in a continuum are called continuous polling systems. Often one encounters a combination of the two systems: the users can either arrive in a continuum or wait in a finite set (i.e. wait at a finite number of queues). We call these systems mixed polling systems. Also, in some applications, customers are rerouted to a new location (for another service) after their service is completed. In this work, we study mixed polling systems with rerouting. We obtain their steady state performance by discretization using the known pseudo conservation laws of discrete polling systems. Their stationary expected workload is obtained as a limit of the stationary expected workload of a discrete system. The main tools for our analysis are: a) the fixed point analysis of infinite dimensional operators and; b) the convergence of Riemann sums to an integral. We analyze two applications using our results on mixed polling systems and discuss the optimal system design. We consider a local area network, in which a moving ferry facilitates communication (data transfer) using a wireless link. We also consider a distributed waste collection system and derive the optimal collection point. In both examples, the service requests can arrive anywhere in a subset of the two dimensional plane. Namely, some users arrive in a continuous set while others wait for their service in a finite set. The only polling systems that can model these applications are mixed systems with rerouting as introduced in this manuscript.Comment: to appear in Performance Evaluatio