Inverse problems of symbolic dynamics

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by substitutional system, and dynamical properties are considered as criteria of superword being generated by interval exchange transformation. As a consequence, one can get a morphic word appearing in interval exchange transformation such that frequencies of letters are algebraic numbers of an arbitrary degree. Concerning multydimensional systems, our main result is the following. Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word $w$ (w=(w_n), n\in \nit) consists of a sequence of first binary numbers of $\{P(n)\}$ i.e. $w_n=[2\{P(n)\}]$. Denote the number of different subwords of $w$ of length $k$ by $T(k)$ . \medskip {\bf Theorem.} {\it There exists a polynomial $Q(k)$, depending only on the power of the polynomial $P$, such that $T(k)=Q(k)$ for sufficiently great $k$.

Non-relativistic limit of multidimensional gravity: exact solutions and applications

It is found the exact solution of the Poisson equation for the multidimensional space with topology $M_{3+d}=\mathbb{R}^3\times T^d$. This solution describes smooth transition from the newtonian behavior $1/r_3$ for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior $1/r^{1+d}_{3+d}$ in opposite limit. In the case of one extra dimension $d=1$, the gravitational potential is expressed via compact and elegant formula. These exact solutions are applied to some practical problems to get the gravitational potentials for considered configurations. Found potentials are used to calculate the acceleration for point masses and gravitational self-energy.It is proposed models where the test masses are smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3 smeared extra dimensions, it is shown that the size of 3 rest extra dimensions can be enlarged up to submillimeter for the case of 1TeV fundamental Planck scale $M_{Pl(10)}$. In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the newtonian one regardless of size of the extra dimensions. Nevertheless, the hierarchy problem can be solved in these models.Comment: LaTex file, 18 pages, 4 figure

On cogrowth function of algebras and its logarithmical gap

Let $A \cong k\langle X \rangle / I$ be an associative algebra. A finite word over alphabet $X$ is $I${\it-reducible} if its image in $A$ is a $k$-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal $I$-reducible word. A {\em cogrowth} function is number of obstructions of length $\le n$. We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth.Comment: 5 page

Detection and masking of Trojan Circuits in sequential logic

A technique of finding a set of sequential circui

Off-limb EUV observations of the solar corona and transients with the CORONAS-F/SPIRIT telescope-coronagraph

The SPIRIT telescope aboard the CORONAS-F satellite (in orbit from 26 July 2001 to 5 December 2005), observed the off-limb solar corona in the 175 Å (Fe IX, X and XI lines) and 304 Å (He II and Si XI lines) bands. In the coronagraphic mode the mirror was tilted to image the corona at the distance of 1.1...5 <I>R</I><sub>sun</sub> from the solar center, the outer occulter blocked the disk radiation and the detector sensitivity was enhanced. This intermediate region between the fields of view of ordinary extreme-ultraviolet (EUV) telescopes and most of the white-light (WL) coronagraphs is responsible for forming the streamer belt, acceleration of ejected matter and emergence of slow and fast solar wind. We present here the results of continuous coronagraphic EUV observations of the solar corona carried out during two weeks in June and December 2002. The images showed a "diffuse" (unresolved) component of the corona seen in both bands, and non-radial, ray-like structures seen only in the 175 Å band, which can be associated with a streamer base. The correlations between latitudinal distributions of the EUV brightness in the corona and at the limb were found to be high in 304 Å at all distances and in 175 Å only below 1.5 <I>R</I><sub>sun</sub>. The temporal correlation of the coronal brightness along the west radial line, with the brightness at the underlying limb region was significant in both bands, independent of the distance. On 2 February 2003 SPIRIT observed an expansion of a transient associated with a prominence eruption seen only in the 304 Å band. The SPIRIT data have been compared with the corresponding data of the SOHO LASCO, EIT and UVCS instruments