Magnetic calorimeter for registration of small energy release

A scheme of magnetic calorimeter for registration of rare events characterized by small energy release (cosmic rays, WIMPs, solitary X-ray quanta) is proposed. The calorimeter is brought to operation by adiabatic demagnetization, and its magnetic response is measured by a quantum interferometer (SQUID, A. Barone and G. Paterno, Physics and applications of Josephson Effect). Special consideration is given to the specific features of calorimeter operation in the ferromagnetic transition region. The trigger registration of ultrasmall energy release by a ferromagnetic system in the metastable state is described.     

The (1+1) Dimensional Dirac Equation With Pseudoscalar Potentials: Path Integral Treatment

The supersymetric path integrals in solving the problem of relativistic spinning particle interacting with pseudoscalar potentials is examined. The relative propagator is presented by means of path integral, where the spin degrees of freedom are described by odd Grassmannian variables and the gauge invariant part of the effective action has a form similar to the standard pseudoclassical action given by Berezin and Marinov. After integrating over fermionic variables (Grassmannian variables), the problem is reduced to a nonrelativistic one with an effective supersymetric potential. Some explicit examples are considered, where we have extracted the energy spectrum of the electron and the wave functions. PACS numbers: 03.65. Ca-Formalism, 03.65. Db-Functional analytical methods, 03.65. Pm-Relativistic wave equations.     

Structural conversions of rhodamines in solution

A study has been made of the acidic ionization, structural conversions, and prototropic tautomerism of rhodamine chromogens in methanol and dimethyl sulfoxide, using IR, ¹³ C NMR, and electronic spectroscopy. The lactone structure has been established for the colorless form of rhodamines in DMSO. For rhodamine B in mixtures of water with DMSO, the lactone/zwitterion ratio has been estimated.V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Moscow 117975. Khar'kov State University, Khar'kov 310077. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 512–521, March, 1992.     

The exponential characteristic of the Volterra integral operator with kernel depending on 2<Emphasis Type="Italic">N</Emphasis> variables

Exponential growth is estimated for integral operators with continuous periodic kernels of exponential type. The result is applied to the boundary-value problem for a general hyperbolic differential equation having periodic coefficients with Goursat boundary conditions. It is proved that the exponential characteristic for such a boundary-value problem has canonical form. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal Conference-2004, Part 3, 2006.     

Derivation techniques on the Hermitian surface

We discuss derivation‐like techniques for transforming one locally Hermitian partial ovoid of the Hermitian surface H(3,q²) into another one. These techniques correspond to replacing a regulus by its opposite in some naturally associated projective 3‐space PG(3,q) over a square root subfield. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 478–486, 2007     

An invariance of geometric mean with respect to Lagrangian means

The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g.     

Monotonic solutions of a quadratic integral equation of fractional order

In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with the Hausdorff measure of noncompactness.     

On a certain nonlocal problem for a hyperbolic equation

The author proves the existence and uniqueness of a generalized solution of a nonlocal problem with an integral condition for a hyperbolic equation with n spatial variables. This work is a continuation of the studies started in [3–5], where the solvability problem of nonlocal problems with an integral condition was studied for hyperbolic equations on the plane. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.