Cluster sets of subharmonic functions and associated measures in a cone

A study is conducted of the relationship between the asymptotic behavior of a subharmonic function of finite order in a cone and the distribution of the measure associated with it.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 247–261, Febraury, 1991.     

Comments concerning the HPLC separation of acrolein from other C3 carbonyl compounds as 2,4-dinitrophenylhydrazones: A proposal for improvement

The separation of the toxicologically important aldehyde acrolein from other carbonyl compounds by high performance liquid chromatography after derivatization to 2,4-dinitrophenylhydrazones is critically discussed on the basis of a selection of published methods. A method is proposed whereby the compounds acrolein, acetone, and propanal may be reproducibly separated to baseline by a reversed phase HPLC procedure employing a ternary mixture of methanol, water, and acetonitrile as mobile phase.     

Trace norm estimates for products of integral operators and diffusion semigroups

We give trace norm estimates for products of integral operators and for diffusion semigroups. These are applied to differences of heat semigroups. A natural example of an integral operator with finite trace which is not trace class is given.     

On the instability of parallel weakly interacting dislocations in soft-mode crystals

The instability of the rectilinear form of parallel weakly interacting dislocations, manifesting itself in their spontaneous wave-like bending, has been investigated. It is shown that softening of a crystal leads to the enhancement of this instability.     

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.     

Strong asymptotics in Lagrange interpolation with equidistant nodes

In this paper we prove three conjectures of Revers on Lagrange interpolation for f_λ(t)=|t|^λ,λ>0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants L_N( f_λ,t) for 0<|t|<1, and discuss their convergence at t=0. We also establish an asymptotic relation for max_|t|1| |t|^λ−L_N( f_λ,t)|. The proofs are based on strong asymptotics for |t|^λ−L_N( f_λ,t), 0|t|<1.     

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.