Areal objects and the problem of the λ term in the theory of gravitation

The following areal objects are considered: an ether thread contracting two material points and a multidimensional ether fibre in the pseudo-Euclidean world of events. An ether space-time model with an arbitrarily determined Riemannian metric is constructed and the problem of the λ term in Einstein equations is discussed in this regard.     

A distance-regular graph with the intersection array {8, 7, 5; 1, 1, 4} and its automorphisms

Possible orders and subgraphs of the fixed points of a distance-regular graph with the intersection array {8, 7, 5; 1, 1, 4} are found. It is shown that such a graph is not vertex-transitive.     

A computational study into the reactivity of epichlorohydrin and epibromohydrin under basic conditions in the gas phase and solution

Ab initio molecular orbital calculations were carried out on epibromohydrin (EBH) and epichlorohydrin (ECH) in an attempt to elucidate their reactivity with respect to a hard nucleophile, hydroxide. These systems were modeled in both the gas phase and a polar solvent under basic conditions. In the gas phase, it was determined that a direct displacement mechanism (nucleophilic attack at the C1 position) was operative for EBH, while an indirect pathway (nucleophilic attack at the C3 position and subsequent intramolecular displacement) was followed for ECH. In an acetone solution, only the indirect displacement mechanism was found to occur. An electrostatic argument is advanced to account for this behavior in polar solution. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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 solution existence of general variational inclusion problems

We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclusion problems, quasioptimization problems, equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers.     

On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls

We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints.