Fundamental solution of a multidimensional axisymmetric equation

© 2017 Informa UK Limited, trading as Taylor & Francis Group For the axisymmetric Helmholtz equation (Formula presented.) it is shown that fundamental solutions constructed by the Gellerstedt method and by means of a transmutation operator are coinciding

Fundamental solution of multidimensional axisymmetric Helmholtz equation

© 2016 Informa UK Limited, trading as Taylor & Francis GroupFor axisymmetric Helmholtz equation(Formula presented.) fundamental solutions have been constructed. Those are written explicitly via confluent Horn functions. The obtained fundamental solutions have been proved to possess a power singularity (Formula presented.)

Boundary value problem for B-parabolic equation with integral condition of the first kind

The article deals with the boundary value problem with integral condition of the first kind for a parabolic equation with Bessel operator, and proves its equivalence to the boundary value problem for the same equation with usual local boundary condition. Uniqueness of solution of the problem is proven. The said solution is made as a sum of series by eigenfunctions of the corresponding eigenvalue and eigenfunction problem

Double-layer potential of axially symmetric Helmholtz lowest term equation

© 2016,International Journal of Pharmacy and Technology. All rights reserved.1. The classical method for solving boundary value problems is the potential method. Potential kernels are recorded as linear combinations of normal derivatives of the fundamental solutions relating to the corresponding equations. For equations with constant coefficients,the fundamental solutions have,as a rule,a simple form. And as a consequence,it is not difficult to calculate any normal derivatives of them. This topic is described in some university textbooks. Due to numerous applications,the study of equations with singular coefficients is significant in the modern theory of differential equations with partial derivatives. The fundamental solutions are usually recorded as a power series for singular equations; they are limited to the first term in the further studies,and evaluation formulas are used for everything else. Finding a fundamental solution in an explicit form is in itself a significant result. 2. For a singular equation,which is the generalized Helmholtz equation,both with the lowest term and without it,a double-layer potential is found in this work. Potential kernel is a normal derivative of the fundamental solution. In order to find this derivative a special function unit is used. 3. The fundamental solution to the considered equation is expressed in terms of the confluent Horn function. Formula for calculating the normal derivative of this fundamental solution is obtained in the article. The result is written in an explicit form using the same Horn function. Relevance of calculating the normal derivative of the fundamental solution to the axially symmetric Helmholtz equation is determined by its demand in applications and absence of a general theory for this type of equations. 4. When using the formulas associated with the special hypergeometric functions,there was a wide choice to the authors. Using the so-called transformation formula,the result could be recorded in various ways,and not always compactly. The result is recorded in such a way that in calculating the limit values of the potentials the relevant terms will be able to be combined. 5. The potential constructed in this work can be applied to solve any boundary value problems for axially symmetric Helmholtz equation. According to the same scheme,potentials for higher-order equations can be constructed

Spin Crossover [Fe(qsal)2]X (X = Cl, SCN, CF3SO3) Complexes: EPR and DFT Study

The compounds [Fe(qsal)2]X (X = Cl, SCN, CF3SO3) were synthesized and investigated by electron paramagnetic resonance (EPR). The dependence of the Fe(III) spin state on the type of counterion X and on the temperature was established. On the basis of the density functional calculations, the geometrical parameters of compounds in high- and low-spin states were optimized and the difference in their internal energies was calculated. A correlation between the experimental EPR data and the theoretically calculated energy difference between the high-spin and the low-spin states of the compounds with different anions was obtained. © 2010 Springer-Verlag

The current status of orbital experiments for UHECR studies

Two types of orbital detectors of extreme energy cosmic rays are being developed nowadays: (i) TUS and KLYPVE with reflecting optical systems (mirrors) and (ii) JEM-EUSO with high-transmittance Fresnel lenses. They will cover much larger areas than existing ground-based arrays and almost uniformly monitor the celestial sphere. The TUS detector is the pioneering mission developed in SINP MSU in cooperation with several Russian and foreign institutions. It has relatively small field of view (+/-4.5 deg), which corresponds to a ground area of 6.4x10^3 sq.km. The telescope consists of a Fresnel-type mirror-concentrator (~2 sq.m) and a photo receiver (a matrix of 16x16 photomultiplier tubes). It is to be deployed on the Lomonosov satellite, and is currently at the final stage of preflight tests. Recently, SINP MSU began the KLYPVE project to be installed on board of the Russian segment of the ISS. The optical system of this detector contains a larger primary mirror (10 sq.m), which allows decreasing the energy threshold. The total effective field of view will be at least +/-14 degrees to exceed the annual exposure of the existing ground-based experiments. Several configurations of the detector are being currently considered. Finally, JEM-EUSO is a wide field of view (+/-30 deg) detector. The optics is composed of two curved double-sided Fresnel lenses with 2.65 m external diameter, a precision diffractive middle lens and a pupil. The ultraviolet photons are focused onto the focal surface, which consists of nearly 5000 multi-anode photomultipliers. It is developed by a large international collaboration. All three orbital detectors have multi-purpose character due to continuous monitoring of various atmospheric phenomena. The present status of development of the TUS and KLYPVE missions is reported, and a brief comparison of the projects with JEM-EUSO is given.Comment: 18 pages; based on the rapporteur talk given by M.I. Panasyuk at ECRS-2014; v2: a few minor language issues fixed thanks to the editor; to be published in the proceeding

Dynamic NMR study of cyclic derivatives of pyridoxine

Copyright © 2014 John Wiley & Sons, Ltd. A series of pyridoxine derivatives was investigated by 1H and 2D nuclear overhauser enhancement spectroscopy (NOESY) NMR. The free energies of activation for the pyridyl-oxygen rotation of the 2,4-dinitrophenyl ether of the seven-membered acetals of pyridoxine were measured by dynamic NMR. A conformational exchange between the chair and twist forms of the seven-membered acetal ring was confirmed by dynamic NMR and STO3G computations