Equations over free inverse monoids with idempotent variables

We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEXPTIME) whether a system of equations in idempotent variables over a free inverse monoid has a solution. The result is proved by a direct reduction to solve language equations with one-sided concatenation and a known complexity result by Baader and Narendran: Unification of concept terms in description logics, 2001. We also show that the problem becomes DEXPTIME hard , as soon as the quotient group of the free inverse monoid has rank at least two. Decidability for systems of typed equations over a free inverse monoid with one irreducible variable and at least one unbalanced equation is proved with the same complexity for the upper bound. Our results improve known complexity bounds by Deis, Meakin, and Senizergues: Equations in free inverse monoids, 2007. Our results also apply to larger families of equations where no decidability has been previously known.Comment: 28 pages. The conference version of this paper appeared in the proceedings of 10th International Computer Science Symposium in Russia, CSR 2015, Listvyanka, Russia, July 13-17, 2015. Springer LNCS 9139, pp. 173-188 (2015

Modeling the deformation of an elastic element of a small spacecraft in its plane during temperature shock

A basic mathematical model of the deformation of a large elastic element of a small spacecraft in its plane is constructed. Deformations are caused by a temperature shock after a small spacecraft leaves the Earth’s shadow on the solar portion of the orbit. The model is used to conduct a computational experiment with the aim of assessing perturbations acting on a small spacecraft due to temperature shock. The temperature distribution during thermal shock is described by a one-dimensional model of thermal conductivity. The classical theory of thin plates is used to determine the deformations. The results of the estimation of disturbing factors are obtained as a result of a computational experiment for a model small spacecraft. These results indicate the need to compensate for the impact of temperature shock for small technological spacecraft. The data obtained can be used in the design of small space-craft for technological purposes

Modeling the deformation of an elastic element of a small spacecraft in its plane during temperature shock

A basic mathematical model of the deformation of a large elastic element of a small spacecraft in its plane is constructed. Deformations are caused by a temperature shock after a small spacecraft leaves the Earth’s shadow on the solar portion of the orbit. The model is used to conduct a computational experiment with the aim of assessing perturbations acting on a small spacecraft due to temperature shock. The temperature distribution during thermal shock is described by a one-dimensional model of thermal conductivity. The classical theory of thin plates is used to determine the deformations. The results of the estimation of disturbing factors are obtained as a result of a computational experiment for a model small spacecraft. These results indicate the need to compensate for the impact of temperature shock for small technological spacecraft. The data obtained can be used in the design of small space-craft for technological purposes

Present tectonics of the southeast of Russia as seen from GPS observations

The present tectonics of Northeast Asia has been extensively investigated during the last 12 yr by using GPS techniques. Nevertheless, crustal velocity field of the southeast of Russia near the northeastern boundaries of the hypothesized Amurian microplate has not been defined yet. The GPS data collected between 1997 February and 2009 April at sites of the regional geodynamic network were used to estimate the recent geodynamic activity of this area. The calculated GPS velocities indicate almost internal (between network sites) and external (with respect to the Eurasian tectonic plate) stability of the investigated region. We have not found clear evidences of any notable present-day tectonic activity of the Central Sikhote-Alin Fault as a whole. This fault is the main tectonic unit that determines the geological structure of the investigated region. The obtained results speak in favour of the existence of a few separate blocks and a more sophisticated structure of the proposed Amurian microplate in comparison with an indivisible plate approach

Synthesis and Antiviral Properties of Camphor-Derived Iminothiazolidine-4-Ones and 2,3-Dihydrothiazoles

A set of heterocyclic products was synthesized from natural (+)-camphor and semi-synthetic (−)-camphor. Then, 2-Imino-4-thiazolidinones and 2,3-dihydrothiazoles were obtained using a three-step procedure. For the synthesized compounds, their antiviral activity against the vaccinia virus and Marburg virus was studied. New promising agents active against both viruses were found among the tested compounds

Synthesis and Antiviral Activity of Camphene Derivatives against Different Types of Viruses

To date, the ‘one bug-one drug’ approach to antiviral drug development cannot effectively respond to the constant threat posed by an increasing diversity of viruses causing outbreaks of viral infections that turn out to be pathogenic for humans. Evidently, there is an urgent need for new strategies to develop efficient antiviral agents with broad-spectrum activities. In this paper, we identified camphene derivatives that showed broad antiviral activities in vitro against a panel of enveloped pathogenic viruses, including influenza virus A/PR/8/34 (H1N1), Ebola virus (EBOV), and the Hantaan virus. The lead-compound 2a, with pyrrolidine cycle in its structure, displayed antiviral activity against influenza virus (IC50 = 45.3 µM), Ebola pseudotype viruses (IC50 = 0.12 µM), and authentic EBOV (IC50 = 18.3 µM), as well as against pseudoviruses with Hantaan virus Gn-Gc glycoprotein (IC50 = 9.1 µM). The results of antiviral activity studies using pseudotype viruses and molecular modeling suggest that surface proteins of the viruses required for the fusion process between viral and cellular membranes are the likely target of compound 2a. The key structural fragments responsible for efficient binding are the bicyclic natural framework and the nitrogen atom. These data encourage us to conduct further investigations using bicyclic monoterpenoids as a scaffold for the rational design of membrane-fusion targeting inhibitors