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

Asymptotic normalization coefficients (nuclear vertex constants) for p+7Be→8Bp+^7Be\to ^8B and the direct 7Be(p,γ)8B^7Be(p,\gamma)^8B astrophysical S-factors at solar energies

A new analysis of the precise experimental astrophysical S-factors for the direct capture $^7Be(p,\gamma)$ $^8B$ reaction [A.J.Junghans et al.Phys.Rev. C 68 (2003) 065803 and L.T. Baby et al. Phys.Rev. C 67 (2003) 065805] is carried out based on the modified two - body potential approach in which the direct astrophysical S-factor, ${\rm S_{17}(E)}$, is expressed in terms of the asymptotic normalization constants for $p+^7Be\to ^8B$ and two additional conditions are involved to verify the peripheral character of the reaction under consideration. The Woods-Saxon potential form is used for the bound ($p+^7Be$)- state wave function and for the $p^7Be$- scattering wave function. New estimates are obtained for the ^{\glqq}indirectly measured\grqq values of the asymptotic normalization constants (the nuclear vertex constants) for the $p+^7Be\to ^8B$ and $S_{17}(E)$ at E$\le$ 115 keV, including $E$=0. These values of $S_{17}(E)$ and asymptotic normalization constants have been used for getting information about the ^{\glqq}indirectly measured\grqq values of the $s$ wave average scattering length and the $p$ wave effective range parameters for $p^7Be$- scattering.Comment: 27 pages, 6 figure

Extraction of gold from heap cyanic solutions of polymetallic ores by polycondensational anionites

The object of the research are polycondensational anionites on the basis of Diglicydil Resorcin Ether (DGRE), Allyl-Bromide (АB) and Poly-2-Methyl-5-Vinylpyridine (PMVP) – Ional A-7; Allyl-Glycide Ether (AGE) with PMVP – Ional A-13, model and technological solutions having different microbiological concentration of cyanide complexes of gold and extrinsic metals. The goal of the work lies in setting the main physico-chemical rules of gold and competitive extrinsic metals behavior in ion exchange system, and in developing an effective method to extract gold from multicomponent cyanic solutions by means of using less expensive ionites. Standardized analysis, potentiometer titration, element, chemical, infrared spectroscopic, spectral, and roentgen-phase analysis methods were used in the present research. Scientific and applied researches defined and scientifically justified sorption characteristics of kazakhstani resins Ional A-7 and Ional A-13, possessing the same relative turgescence in water as anionite AM-2B. Ional A-7 and Ional A-13 as anionite AM-2B are related to anionites of mixed basicity, containing relatively same quantity of Quaternary Aluminium Base (QAB). Resin AM-2B is exceeded by Anionite Ional A-7 regarding its capacity and kinetic characteristics, and by Anionite Ional А-13 on selectivity according to iones of gold cyanic complexes. It is justified by higher concentration of QAB in the first ionite and, admittedly, higher density of structural links lacing of the second ionite