Probe measurements in a discharge with liquid nonmetallic electrodes in air at atmospheric pressure

Discharges with liquid nonmetallic electrodes of much interest for applications are investigated. It is found that a dc discharge between two streams of tap water in air at atmospheric pressure is stable at a currentof 40≤I≤100 mA. The discharge exists in the diffuse (volume) form with a relatively low current density (∼0.2 A/cm²) and a high (above one kilovolt) voltage drop across the air gap (∼1 cm) between the water electrodes. The current density and voltage depend only slightly on the discharge current. Probe measurements show that three regions can be distinguished in the discharge: two electrode regions (1–2 mm in length) and a discharge column with a constant electric field of ≈0.8 kV/cm (i.e., E/N≈20 Td, because the gas in the discharge is heated up to 1500–2000 K). The average electric field strength near the electrodes is E≈2–3×10³ V/cm (E/N≈60–80 Td). The charged particle density in the column is n ∼ 10¹² cm⁻³. The probe measurements of n agree with the previous microwave absorption measurements. The water vapor concentration in the column is also estimated from probe measurements.     

Calculations of the Pressure of Polymorphic Transformation in Small Alkali-Halide Crystals

The present paper analyzes the properties of structural phase transitions under the extremal conditions of high pressures. In the context of the theory of density functional (TDF), the pressures of the B1–B2 transitions are calculated for small alkali-halide crystals as functions of the crystal size. The size effect of the B1–B2 transition – an increase in the transition pressure with the decreasing crystal grain radius – has been established for all investigated halides except lithium fluoride for which the dependence is reverse.     

On the Determination of the Absolute Intensities of Vibrational-Rotational Lines of XY3 Molecules with C 3v Symmetry

Analytical formulas are derived that describe the dependences of the transition probabilities in vibrational-rotational spectra of XY₃-type molecules with C _3v symmetry on the rotational quantum numbers.     

The electrical resistivity of some uranium tellurides

Electrical resistivity of U₃Tein4, U₂Te₃ (cubic) and UTe₃ has been measured over temperature range 4.2–300 K. The two former compounds appear to be semimetallic conductors while the last one has semiconducting character. The results are discussed in the terms of available magnetic data.     

Franck-Condon factors and relative strengths of the c1Σu → α1Δg,c1Σu → X3Σg electronic transitions in the O2 molecule

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 1, pp. 46–50, January, 1991.     

Whitham's dynamical principle for parabolic equations and its proof

A generalization of Whitham's asymptotic principle for parabolic equations is stated. An application of this principle to Fisher's one-dimensional nonlinear equation is considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 46–51, 1989.     

The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

State space and wave equation for Boson string with nontrivial topology of world sheet

We show that the wave functions of a string with nontrivial topology of the world sheet should be considered as sections of line bundles over the space of conformal classes of Riemann surfaces. We construct a BRST operator for the case of arbitrary topology and give it a geometric interpretation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 107–121, 1988.     

Christoffel-Darboux-type formulae and a recurrence for biorthogonal polynomials

It is proved that biorthogonal polynomials obey two different kinds of Christoffel-Darboux-type formulae, one linking polynomials with a different parameter and one combining polynomials with different degrees. This is used to produce a mixed recurrence relation, which is valid for all biorthogonal polynomials. This recurrence relation establishes several results on interlacing property of zeros of successive biorthogonal polynomials and leads to a new result on the interlace of zeros of orthogonal polynomials (of equal degrees) with respect to two distributionsdψ(x) andx ^p dψ(x), 0<p≤1, with support in either [0, 1] or [1, ∞).