Solution of the Stieltjes truncated matrix moment problem

The truncated Stieltjes matrix moment problem consisting in the description of all matrix distributions $\boldsymbol{\sigma}(t)$ on $[0,\infty)$ with given first $2n+1$ power moments $(\mathbf{C}_j)_{n=0}^j$ is solved using known results on the corresponding Hamburger problem for which $\boldsymbol{\sigma}(t)$ are defined on $(-\infty,\infty)$. The criterion of solvability of the Stieltjes problem is given and all its solutions in the non-degenerate case are described by selection of the appropriate solutions among those of the Hamburger problem for the same set of moments. The results on extensions of non-negative operators are used and a purely algebraic algorithm for the solution of both Hamburger and Stieltjes problems is proposed

One-electron states and interband optical absorption in single-wall carbon nanotubes

Explicit expressions for the wave functions and dispersion equation for the band p - electrons in single-wall carbon nanotubes are obtained within the method of zero-range potentials. They are then used to investigate the absorption spectrum of polarized light caused by direct interband transitions in isolated nanotubes. It is shown that, at least, under the above approximations, the circular dichroism is absent in chiral nanotubes for the light wave propagating along the tube axis. The results obtained are compared with those calculated in a similar way for a graphite plane.Comment: 16 pages, 8 figures, 1 tabl

Scientific and methodological principles of forming an assessment of the level of environmental safety of construction projects in urban areas

At present, improving the environmental safety of capital construction objects for various purposes in urban areas is still an urgent goal and a rather complicated process to implement. To achieve it, you need, first of all, a scientifically based methodology for assessing the actual level of environmental safety of a particular construction object or urban economy and a list of necessary measures to increase it. Our earlier analysis of known methodological approaches to assessing the state of the urban environment allowed us to conclude that when assessing the level of environmental safety of capital construction objects for various purposes, it is necessary to take into account social, environmental, economic factors and take into account a number of limitations. In this regard, we conducted scientific research, on the basis of which the scientific and methodological principles of forming an assessment of the level of environmental safety of capital construction facilities for various purposes in urban areas were determined. At the same time, the basis for a consistent assessment of the level of environmental safety of construction objects for various purposes in urban areas, in our opinion, is a comprehensive consideration of environmental, economic and social criteria, each of which includes corresponding groups of parameters (environmental, social and economic) that determine the degree of environmental safety and sustainable development. Our approach allows, using the various characteristics of an urbanized area with different dimensions, to obtain the resulting criteria in a dimensionless form and thereby improve the methodology for calculating a comprehensive assessment of the environmental safety level of construction objects and urban facilities in urban areas

A Quantum Scattering Approach to Undecidable Problems: Preliminary Version

In [12] a probabilistic solution to the Infinite Merchant's Problem, an undecidable problem equivalent to the Halting Problem, was proposed. The solution uses a real Hilbert space and is based on the estimation of the exponential growth of an unbounded semigroup. The aim of this paper is to o#er an alternative solution in terms of scattering processes on quantum dots. We will reduce the problem to a special scattering problem, observe the results of multiple acts of scattering and, finally, estimate the deviation of the scattered data from the input data