Probe method and a Carleman function

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions which is called a {\it needle sequence}. The needle sequence blows up on a special curve which connects a given point inside the domain with a point on the boundary of the domain and is convergent locally outside the curve. The sequence yields a reconstruction formula of unknown discontinuity, such as cavity, inclusion in a given medium from the Dirichlet-to-Neumann map. In this paper, an explicit needle sequence in {\it three dimensions} is given in a closed form. It is an application of a Carleman function introduced by Yarmukhamedov. Furthermore, an explicit needle sequence in the probe method applied to the reduction of inverse obstacle scattering problems with an {\it arbitrary} fixed wave number to inverse boundary value problems for the Helmholtz equation is also given.Comment: 2 figures, final versio

Investigation and Simulation of a Noise-Resistant 16-Qam Demodulator in A Dvb-T2 Standard Digital Tv System Using the Matlab/Simulink Program Environment

In this work, a noise-immune 16-QAM demodulator in a digital television system of the DVB-T2 standard is investigated and modeled using the Matlab/Simulink software environment. The requirements for normalized technical parameters that determine the quality and noise immunity of a 16-QAM demodulator in the DVB-T2 standard have been analyzed and investigated. Various communication channels are modeled and investigated, such as: the Gaussian, Rice and Rayleigh channel to determine and measure the signal-to-noise ratio, the theoretical and practical influence of communication channels on noise immunity without a filter and with a filter. The results of researches on the dependence of the bit error probability and the number of bits received with an error on Eb/N0, the spectrum of 16-QAM signals and constellation diagrams are presented

Theoretical research and computer simulation of composite transistors made of a semiconductor material with the same of the forbidden band.

Presents the results of theoretical research and computer simulation of composite transistors made of a semiconductor material with the same of the forbidden band. To study the volt-ampere characteristics of such composite transistors, an interactive computer simulation program was developed in the programming environment of Delphi-6. It is shown that the proposed transistors make it possible to improve manufacturability when it is manufactured industrially. The proposed composite transistors are designed for the final cascades of power amplifiers, radio transmitting devices

Connection between effective-range expansion and nuclear vertex constant or asymptotic normalization coefficient

Explicit relations between the effective-range expansion and the nuclear vertex constant or asymptotic normalization coefficient (ANC) for the virtual decay $B\to A+a$ are derived for an arbitrary orbital momentum together with the corresponding location condition for the ($A+a$) bound-state energy. They are valid both for the charged case and for the neutral case. Combining these relations with the standard effective-range function up to order six makes it possible to reduce to two the number of free effective-range parameters if an ANC value is known from experiment. Values for the scattering length, effective range, and form parameter are determined in this way for the $^{16}$O+$p$, $\alpha+t$ and $\alpha+^3$He collisions in partial waves where a bound state exists by using available ANCs deduced from experiments. The resulting effective-range expansions for these collisions are valid up to energies larger 5 MeV.Comment: 17 pages, 6 figure