ASYMPTOTIC BEHAVIOUR OF EIGENVALUES FOR THE DISCONTINUOUS BOUNDARY-VALUE PROBLEM WITH FUNCTIONAL-TRANSMISSION CONDITIONS

In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of innnit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.     

Complex formation, chemical exchange, species structure, and stereoselective effects in the copper(II)-L/DL-histidine systems

The formation of copper(II) complexes with L- and DL-histidine (HisH) has been studied by means of pH-potentiometry and spectrophotometry over a wide range of pH (2-14), ligand-to-metal ratio (1?:?1-15?:?1), and temperature (15-55 °C) in aqueous solutions with 1.0 mol dm(-3) KNO(3) as background. Formation constants and spectral characteristics of 13 complex types were found. Fine stereoselective effects have been detected with preferential coordination of two ligands with identical configuration in Cu(His)(HisH)(+) and opposite configuration in Cu(His)(2). The stereoselective effect for Cu(His)(HisH)(+) is explained by hydrogen bond formation between the carboxyl and imidazolyl groups of neighboring ligands at cis-arrangement of amino groups (3N(eq)-form). The opposite sign of stereoselective effect for Cu(His)(2) is derived from favourable axial coordination of the imidazole group in meso-form with cis-structure (3N(eq)N(ax)-form). A significant tetrahedral distortion was revealed for the first time in the prevalent cis-isomer of the Cu(L-His)(2) 4N(eq)-form. These findings were confirmed by EPR data and DFT computations at the B3LYP/TZVP level. The prevalence of cis-isomers for these complexes has been assigned to the rather strong trans effect of the amino groups. The structures of other detected complexes are briefly discussed on the basis of spectroscopic data. Chemical exchange reactions in the copper(II)-L/DL-hishidine systems have been investigated by the NMR relaxation of water protons. A unique proton exchange reaction with short-term proton dissociation from the coordinated imidazolyl group catalyzed by hydroxide ion was characterised for the first time. The discovered enantioselective effects in the ligand exchange reactions between Cu(His)(2) and HisH or His(-) species were attributed to the associative substitution mechanism.     

Investigation of the process e− + e+ → μ− + μ+ + γ in nonlocal theory taking particle polarization into account

The process e^– + e^{+ –} + ⁺ + is investigated in the nonlocal theory of interaction, taking particle polarization into account. A general expression for the effective differential cross section, the energy and angular dependences, and the degree of circular and linear polarization of the -quanta are obtained. The total cross sections calculated using the nonlocal and local theories are compared.     

Weak neutral currents in deep inelastic bremsstrahlung

We consider the role of weak neutral currents in the processesl ^± + Nl ^± + + X. In the quark-parton model, with regard to hadronic radiation as well as leptonic, we obtain the differential cross-section of the processes, and investigate various P-odd effects that allow us to distinguish the weak current contribution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 25–29, December, 1987.     

Simulation and interpretation of the vibrational spectra of heterofullerenes

This paper reports on a computer simulation of the vibrational spectra of C₅₉B, C₅₉N, C₅₉BN, and C₅₉HN. The modes whose frequencies are most sensitive to carbon substitution by heteroatoms are revealed. It is shown that the new bands at 818, 839, and 845 cm⁻¹ in the experimental IR spectrum of C₅₉HN arise from changes in selection rules and by removal of degeneracies due to a reduction in the symmetry of the molecule and force field perturbation. In the Raman spectrum of C₅₉HN, the shifts of the 1460 and 491 cm⁻¹ bands to the low-frequency region by 7 and 3 cm⁻¹, respectively, relative to two A_g modes of C₆₀ are explained by the perturbation induced by the N and C(H) atoms in the force field of adjacent CC bonds not containing these atoms. Institute of Spectroscopy, Russian Academy of Sciences (Troitsk, Moscow Region). Scientific and Production Association “Complex.” Scientific and Production Association “Tekhon.” Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 401–411, May–June, 1998.     

Pair production of particles with spin 5/2 in colliding electron-positron beams

The process is considered. Expressions are obtained for the effective differential cross section in the case of arbitrarily polarized leptons and for the total cross section for annihilation of an unpolarized lepton pair into a pair of particles with spin 5/2. Relations are also obtained between the invariant and physical form factors of the particles with spin 5/2.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 42–48, November, 1980.