K+→μ+νμννˉK^{+}\rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu and K+→e+νeννˉK^{+}\rightarrow e^{+}\nu_{e} \nu \bar \nu decays within the Chiral Perturbation Theory

Decays $K^{+} \rightarrow \mu^{+}\nu_{\mu} \nu \bar \nu$ and $K^{+}\rightarrow e^{+}\nu_{e} \nu \bar \nu$ are examined to the leading order in momenta in the framework of Chiral Perturbation Theory. Predictions of the Standard Model for the muon and electron differential energy spectra and branching ratios of $K_{\mu 3 \nu}$ and $K_{e 3 \nu}$ are presented.Comment: 10 pages, 4 figures; v2: Introduction and Conclusion extended, journal versio

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 $k$.

Notes about Noise in Gravitational Wave Antennas Created by Cosmic Rays

Thermodynamical fluctuations of temperature in mirrors may produce surface fluctuations not only through thermal expansion in mirror body but also through thermal expansion in mirror coating. We analyze the last "surface" effect which can be larger than the first "volume" one due to larger thermal expansion coefficient of coating material and smaller effective volume. In particular, these fluctuations may be important in laser interferometric gravitational antennae.Comment: 9 pages, LaTe

Implementation of a Systematic Approach to the Design a Communal Car CM

The article presents an analysis of the implementation of a systematic approach to the design of CM at the enterprise of the military-industrial complex without experience in the development of civilian products using requirements engineering. The advantages of architectural and modular principles in the design are described and how these principles are integrated into a single system of design documentation is shown. Annotation: utility vehicle, modular principle, unified system of design documentation

Waveguide mode imaging and dispersion analysis with terahertz near-field microscopy

Propagation of terahertz waves in hollow metallic waveguides depends on the waveguide mode. Near-field scanning probe terahertz microscopy is applied to identify the mode structure and composition in dielectric-lined hollow metallic waveguides. Spatial profiles, relative amplitudes, and group velocities of three main waveguide modes are experimentally measured and matched to the HE11, HE12, and TE11 modes. The combination of near-field microscopy with terahertz time-resolved spectroscopy opens the possibility of waveguide mode characterization in the terahertz band

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