Sign patterns of rational matrices with large rank II

It is known that, for any real m-by-n matrix A of rank n-2, there is a rational m-by-n matrix which has rank n-2 and sign pattern equal to that of A. We prove a more general result conjectured in the recent literature.

Determination of the Uncertainties in S-Curve Logistic Fits

Look-up tables and graphs are provided for determining the uncertainties during logistic fits, on the three parameters M, α and to describing an S-curve of the form: S(t) = M/(1+exp(-α(t-t0))).The uncertainties and the associated confidence levels are given as a function of the uncertainty on the data points and the length of the historical period. Correlations between these variables are also examined; they make “what-if” games possible even before doing the fit.The study is based on some 35,000 S-curve fits on simulated data covering a variety of conditions and carried out via a χ2 minimization technique. A rule-of-thumb general result is that, given at least half of the S-curve range and a precision of better than 10% on each historical point, the uncertainty on M will be less than 20% with 90% confidence level.

Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems

<p style='text-indent:20px;'>In this paper we study generalized Poincaré-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-dimensional manifolds satisfying some suitable conditions. This result allows us to obtain sharper Hopf bifurcation theorems for fixed points in the general case and other attractors in low dimensional manifolds. Topological techniques based on the notion of concentricity of manifolds play a substantial role in the paper.</p>

Ringing of the Regular Black Hole with Asymptotically Minkowski Core

A Regge–Wheeler analysis is performed for a novel black hole mimicker ‘the regular black hole with asymptotically Minkowski core’, followed by an approximation of the permitted quasi-normal modes for propagating waveforms. A first-order WKB approximation is computed for spin zero and spin one perturbations of the candidate spacetime. Subsequently, numerical results analysing the respective fundamental modes are compiled for various values of the a parameter (which quantifies the distortion from Schwarzschild spacetime), and for various multipole numbers ℓ. Both electromagnetic spin one fluctuations and scalar spin zero fluctuations on the background spacetime are found to possess shorter-lived, higher-energy signals than their Schwarzschild counterparts for a specific range of interesting values of the a parameter. Comparison between these results and some analogous results for both the Bardeen and Hayward regular black holes is considered. Analysis as to what happens when one permits perturbations of the Regge–Wheeler potential itself is then conducted, first in full generality, before specialising to Schwarzschild spacetime. A general result is presented explicating the shift in quasi-normal modes under perturbation of the Regge–Wheeler potential.

A functorial approach to monomorphism categories for species I

We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalized species over locally bounded quivers. We prove that analogues of the kernel and cokernel functor send almost split sequences over the path algebra and the preprojective algebra to split or almost split sequences in the monomorphism category. We derive this from a general result on preservation of almost split morphisms under adjoint functors whose counit is a monomorphism. Despite of its generality, our monomorphism categories still allow for explicit computations as in the case of Ringel and Schmidmeier.

On the completeness of total spaces of horizontally conformal submersions

In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of g-natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem.

TRANSLATION OF THE KHAKASS HEROIC EPIC: NEW FACTS AND TEXTS

Statement of the problem. The article is devoted to the translation tradition of the Khakass heroic epic, existing since the second half of the 19 th century and traced to the end of the first decade of the 21 st century. Over the past 10 years, new information about the facts and texts of translations has appeared. This information has been published in various publications, and its connection with the mentioned above translation tradition is not clearly expressed. The establishment of the genesis and general result of the translation tradition of the Khakass heroic epic is relevant in relation to the history and development of intercultural relations in Siberia and Russia as a whole. The purpose of the article is to present new information about the translation tradition of the Khakass heroic epic in its connection with the overall result of translations and to determine its significance against the background of the already known amount of information. Conclusion. The translation tradition of the Khakass heroic epic continues to be relevant as a multifaceted means of intercultural communication.

Completing Partial Transversals of Cayley Tables of Abelian Groups

In 2003 Grüttmüller proved that if $n\geqslant 3$ is odd, then a partial transversal of the Cayley table of $\mathbb{Z}_n$ with length $2$ is completable to a transversal. Additionally, he conjectured that a partial transversal of the Cayley table of $\mathbb{Z}_n$ with length $k$ is completable to a transversal if and only if $n$ is odd and either $n \in \{k, k + 1\}$ or $n \geqslant 3k - 1$. Cavenagh, Hämäläinen, and Nelson (in 2009) showed the conjecture is true when $k = 3$ and $n$ is prime. In this paper, we prove Grüttmüller’s conjecture for $k = 2$ and $k = 3$ by establishing a more general result for Cayley tables of Abelian groups of odd order.

On characterization of a finite group by the set of conjugacy class sizes

Let [Formula: see text] be a finite group and [Formula: see text] be the set of its conjugacy class sizes. In the 1980s, Thompson conjectured that the equality [Formula: see text], where [Formula: see text] and [Formula: see text] is simple, implies the isomorphism [Formula: see text]. In a series of papers of different authors, Thompson’s conjecture was proved. In this paper, we show that in some cases it is possible to omit the conditions [Formula: see text] and [Formula: see text] is simple and prove a more general result.

Fermat’s principle in constant gravitational field

Recently (Int. J. Mod. Phys. D 27 (2018) 1847025) an interesting property of closed light rings in Kerr black holes has been noticed. We explain its origin and derive a slightly more general result.