Self-interactions can stabilize excited boson stars

We study the time evolution of spherical, excited (i.e. nodeful) boson star models. We consider a model including quartic self-interactions, controlled by a coupling Λ. Performing non-linear simulations of the Einstein-(complex)-Klein-Gordon system, using as initial data equilibrium boson stars solutions of that system, we assess the impact of Λ in the stability properties of the boson stars. In the absence of self-interactions (Λ = 0), we observe the known behaviour that the excited stars in the (candidate) stable branch decay to a non-excited star without a node; however, we show that for large enough values of the self-interactions coupling, these excited stars do not decay (up to timescales of about t ∼104). The stabilization of the excited states for large enough self-interactions is further supported by evidence that the nodeful states dynamically form through the gravitational cooling mechanism, starting from dilute initial data. Our results support the healing power (against dynamical instabilities) of self-interactions, recently unveiled in the context of the non-axisymmetric instabilities of spinning boson stars.

Antigen evolution from D614, to G614, and to Delta subtype of SARS-CoV-2

Since 2019, the antigens from Severe Acute Respiratory Syndrome Corona Virus 2 (SARS-CoV-2) are keeping in evolution from initial D614, to G614, to Delta, and to Omicron. Seven of the peptides from SARS-CoV-2 are analyzed. The finding is that, the rule or route for the evolution of their antigens are exactly from “rough” status to “precise”. In this paper, we would like to show the initial data how the antigens from initial D614, conducted evolution to G614, to Delta of SARS-CoV-2. This finding can help the development of reagents for detecting the both “rough” and “precise” antigens, or even help for the development of the vaccines against SARS-CoV-2. And finally, to help the control of epidemic covid-19. According to such rule or route, the “common precise” antigens of the SARS-CoV-2 can be designed in silicon, developed in laboratory, and confirmed in animals. The way should be very tough and long.

On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky Equation

<p style='text-indent:20px;'>We address the global existence and uniqueness of solutions for the anisotropically reduced 2D Kuramoto-Sivashinsky equations in a periodic domain with initial data <inline-formula><tex-math id="M1">\begin{document}$ u_{01} \in L^2 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ u_{02} \in H^{-1 + \eta} $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M3">\begin{document}$ \eta &gt; 0 $\end{document}</tex-math></inline-formula>.</p>

On the one dimensional cubic NLS in a critical space

<p style='text-indent:20px;'>In this note we study the initial value problem in a critical space for the one dimensional Schrödinger equation with a cubic non-linearity and under some smallness conditions. In particular the initial data is given by a sequence of Dirac deltas with different amplitudes but equispaced. This choice is motivated by a related geometrical problem; the one describing the flow of curves in three dimensions moving in the direction of the binormal with a velocity that is given by the curvature.</p>

On nonlinear Schrödinger equations with random initial data

<abstract><p>This note is concerned with the global well-posedness of nonlinear Schrödinger equations in the continuum with spatially homogeneous random initial data.</p></abstract>

METHODICAL APPROACHES TO IMPROVING THE INFORMATION PROVISION OF OCCUPATIONAL RISK MANAGEMENT

The article presents the results of the analysis of the current state of information support of the labor protection management system in the aspect of transition to the introduction of risk-oriented approach. It is noted that the system of labor protection management, which was formed in accordance with the command-administrative principles of the planned economy, in today's conditions was not effective enough, so it needs to improve its information support. One of the shortcomings of the existing information support of labor protection management can be considered unresolved issues of integration of various information systems (IS) in the field of labor protection, designed to solve management problems, which does not allow to form generalized information bases, to conduct analytical data processing. Assessment of occupational risks requires systematic monitoring of enterprise performance indicators, provides for forecasting the dynamics of changes in these indicators, as well as taking into account other factors that potentially affect occupational risks. To automate the process of collecting and analyzing initial data, modeling and calculating the forecast of occupational risk, it is proposed to create a specialized monitoring information system. Given the need for significant financial costs for the implementation of this project, other approaches to improving information support are the gradual creation of separate subsystems of the monitoring system. The main directions of improvement of information support of occupational risk management are formed, in particular modernization of information systems at the state level and enterprise level is offered. The statistics accumulated during the operation of these systems can be used as initial data for occupational risk assessment and further development of sound preventive measures.

Well-posedness, wave breaking, Holder continuity and periodic peakons for a nonlocal sine-µ-Camassa-Holm equation

In this paper, we investigate the initial value problem of a nonlocal sine-type µ-Camassa-Holm (µCH) equation, which is the µ-version of the sine-type CH equation. We first discuss its local well-posedness in the framework of Besov spaces. Then a sufficient condition on the initial data is provided to ensure the occurance of the wave-breaking phenomenon. We finally prove the H¨older continuity of the data-to-solution map, and find the explicit formula of the global weak periodic peakon solution.

INFORMATION MAPPING SYSTEM AS AN INSTRUMENTAL BASIS OF THE PROTECTED CYBERSPACE MAPPING

В работе предлагается новый класс программного обеспечения -информационно-картографические системы, предназначенные для построения и анализа информационных карт. Рассмотрены возможные архитектуры таких систем, отличающиеся организацией подсистем сбора, хранения, анализа и представления исходных данных. The paper proposes a new class of software - information mapping systems designed for the construction and analysis of information maps. The possible architectures of such systems, differing by the organization of subsystems of collection, storage, analysis and presentation of the initial data are considered.