Oscillations of Higher Order Neutral Differential Equations with Variable Coefficients

We obtain sufficient conditions for the oscillation of all solutions of the higher order neutral differential equation dⁿ/d^m[y(t) + P(t) y(t - μ)] + Q(t) y(t ?σ) = 0, t ≧ t₀ where n ≧ 1, P ? C[t₀, ∞), R ], Q ? C[t₀, ∞), R ] and τ, μ ? R ⁺. Our results extend and improve several known results in the literature.     

Kneser''s theorem and the multivalued generalized order complementarity problem

The Generalized Order Complementarity Problem studied by Isac and Kostreva is extended to multivalued mappings satisfying a condition proposed by Kneser. Existence of solutions to a related fixed point problem leads to existence theory for the new type of complementarity problem. Some important applications include problems in lubrication and in economics in which functions are set valued.     

BRST invariance and the conical pendulum

The Hamiltonian formulation of the BRST method for quantizing constrained systems developed recently by Nemeschanskyet al is applied to the well-known problem of the conical pendulum in classical mechanics. The similarity of the system to a gauge theory wherein the two constraints serve as generators of local Abelian gauge transformations is also pointed out. The definition of the physical states of the system as a gauge theory and also as a BRST invariant theory is then discussed in some detail.     

Estimating means from a non-I.I.D. Mixture of Poisson samples

In this paper, a family of estimators for estimating means when mixing two independent Poisson samples is proposed. This family is based on the probability-generating function of the Poisson distribution and is offered as an alternative to the maximum likelihood estimators, which have some drawbacks. These estimators include the method of moments estimators as a special limiting case.     

New Ln[B6O9(OH)3] borates (Ln = Sm-Lu): Structure, properties, and structural relation to cationic Li4[B7O12]Cl conductors (Li-Boracites)

Crystals of new rare earth borates of the composition Ln[B₆O₉ (OH)₃] (Ln = Sm-Lu), sp. gr. R3c are synthesized under hydrothermal conditions. Their crystal structures are determined on single crystals with Ln = Ho, Gd without preliminary determination of their chemical formulas. The polar anionic framework of the crystals consists of BO₃ triangles and BO₄ tetrahedra and has wide channels along the threefold axis of the structure, which are similar to the channels along the a, b, and c axes in cubic Li₄[B₇O₁₂]Cl boracite with Li conductivity. Rare earth atoms are arranged in the structure over the cubic F pseudolattice, whereas the analogous positions in Li boracites are filled with Cl anions. The squared optical nonlinearity of the new crystals is comparable with the nonlinearity of quartz, whereas the electrical conductivity in borates at 300°C exceeds 10⁻⁶ S/cm. __________ Translated from Kristallografiya, Vol. 49, No. 4, 2004, pp. 681–691. Original Russian Text Copyright ? 2004 by Belokoneva, Ivanova, Stefanovich, Dimitrova, Kurazhkovskaya.