A Note on Long non-Hamiltonian Cycles in One Class of Digraphs

Let $D$ be a strong digraph on $n\geq 4$ vertices. In [3, Discrete Applied Math., 95 (1999) 77-87)], J. Bang-Jensen, Y. Guo and A. Yeo proved the following theorem: if (*) $d(x)+d(y)\geq 2n-1$ and $min \{d^+(x)+ d^-(y),d^-(x)+ d^+(y)\}\geq n-1$ for every pair of non-adjacent vertices $x, y$ with a common in-neighbour or a common out-neighbour, then $D$ is hamiltonian. In this note we show that: if $D$ is not directed cycle and satisfies the condition (*), then $D$ contains a cycle of length $n-1$ or $n-2$.Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1207.564

Measurements of energy spectra of relativistic electrons and gamma-rays from avalanches developed in the thunderous atmosphere with Aragats Solar Neutron Telescope

Aragats solar neutron telescope (ASNT) is a unique instrument allowing to measure the energy spectra of electrons accelerated and multiplied in the strong electric fields of the atmosphere. We describe the instrument setup, its operation condition, software, and hardware triggers. We present energy spectra of a very large thunderstorm ground enhancement (TGE) event observed on 6 October 2021. The detector response function, algorithm to recover energy spectra from the energy release histograms also are presented. The spectra recovery procedure is verified by simulation of the response function of the SEVAN detector, operating nearby ASNT. SEVAN is a stacked 3 layered detector, interlayered by lead filters registering both charged and neutral species of cosmic rays. The simulated and measured count rates of all 3 layers of the SEVAN detector show good agreement within 20%

A New Approach to Population Sizing for Memetic Algorithms: A Case Study for the Multidimensional Assignment Problem

Memetic algorithms are known to be a powerful technique in solving hard optimization problems. To design a memetic algorithm, one needs to make a host of decisions. Selecting the population size is one of the most important among them. Most of the algorithms in the literature fix the population size to a certain constant value. This reduces the algorithm's quality since the optimal population size varies for different instances, local search procedures, and runtimes. In this paper we propose an adjustable population size. It is calculated as a function of the runtime of the whole algorithm and the average runtime of the local search for the given instance. Note that in many applications the runtime of a heuristic should be limited and, therefore, we use this bound as a parameter of the algorithm. The average runtime of the local search procedure is measured during the algorithm's run. Some coefficients which are independent of the instance and the local search are to be tuned at the design time;we provide a procedure to find these coefficients. The proposed approach was used to develop a memetic algorithm for the multidimensional assignment problem (MAP). We show that our adjustable population size makes the algorithm flexible to perform efficiently for a wide range of running times and local searches and this does not require any additional tuning of the algorithm

Supernovae and their host galaxies - V. The vertical distribution of supernovae in disc galaxies

We present an analysis of the height distributions of the different types of supernovae (SNe) from the plane of their host galaxies. We use a well-defined sample of 102 nearby SNe appeared inside high-inclined (i > 85 deg), morphologically non-disturbed S0-Sd host galaxies from the Sloan Digital Sky Survey. For the first time, we show that in all the subsamples of spirals, the vertical distribution of core-collapse (CC) SNe is about twice closer to the plane of host disc than the distribution of SNe Ia. In Sb-Sc hosts, the exponential scale height of CC SNe is consistent with those of the younger stellar population in the Milky Way (MW) thin disc, while the scale height of SNe Ia is consistent with those of the old population in the MW thick disc. We show that the ratio of scale lengths to scale heights of the distribution of CC SNe is consistent with those of the resolved young stars with ages from ~ 10 Myr up to ~ 100 Myr in nearby edge-on galaxies and the unresolved stellar population of extragalactic thin discs. The corresponding ratio for SNe Ia is consistent with the same ratios of the two populations of resolved stars with ages from a few 100 Myr up to a few Gyr and from a few Gyr up to ~ 10 Gyr, as well as with the unresolved population of the thick disc. These results can be explained considering the age-scale height relation of the distribution of stellar population and the mean age difference between Type Ia and CC SNe progenitors.Comment: 11 pages, 6 figures, 6 tables, accepted for publication in MNRA