On the exceptional series,and its descendantsLa série exceptionnelle,et sa descendance

Many of the striking similarities which occur for the adjoint representation of groups in the exceptional series (cf. [1–3]) also occur for certain representations of specific reductive subgroups. The tensor algebras on these representations are easier to describe (cf. [4,5,7]), and may offer clues to the original situation.The subgroups which occur form a Magic Triangle, which extends Freudenthal's Magic Square of Lie algebras. We describe these groups from the perspective of dual pairs, and their representations from the action of the dual pair on an exceptional Lie algebra. To cite this article: P. Deligne, B.H. Gross, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 877–881.     

Electromagnetic field singularities

An integral transform based method is given for determining information about the locating and properties of singularities of electromagnetic fields associated with axially symmetric radiating sources.     

Spectra and Transport in Almost Periodic Dimers

We study spectral properties of discrete Schrödinger operators with potentials obtained via dimerization of a class of aperiodic sequences. It is shown that both the nature of the autocorrelation measure of a regular sequence and the presence of generic (full probability) singular continuous spectrum in the hull of primitive and palindromic (four block substitution) potentials are robust under dimerization. Generic results also hold for circle potentials. We illustrate these results with numerical studies of the quantum mean square displacement as a function of time. The numerical techniques provide a very fast algorithm for the time evolution of wave packets.     

An M/G/1 Retrial Queueing System with Two-Phase Service and Preemptive Resume

An M/G/1 retrial queueing system with additional phase of service and possible preemptive resume service discipline is considered. For an arbitrarily distributed retrial time distribution, the necessary and sufficient condition for the system stability is obtained, assuming that only the customer at the head of the orbit has priority access to the server. The steady-state distributions of the server state and the number of customers in the orbit are obtained along with other performance measures. The effects of various parameters on the system performance are analysed numerically. A general decomposition law for this retrial queueing system is established.     

Thoms Effect as Influenced by the Concentration and Molecular Parameters of the Cationic Copolymer of Acrylamide

The Thoms effect observed with water-soluble cationic copolymer of acrylamide was studied in relation to the concentration, molecular weight, and molecular weight polydispersity of the polymeric additive, with its composition and composition polydispersity being constant.     

A nondestructive numerical-experimental method of determining the residual stresses in welded shells of revolution

We propose a numerical-experimental method of determining the residual stresses in welded shells of revolution. We solve the inverse conditionally correct problem of recovering the complete picture of the residual stress state from part of the experimental values obtained by the method of photoelasticity. We apply the numerical spline-collocation method. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 149–151.     

Characters of irreducibleG-modules and cohomology ofG/P for the lie supergroupG=Q(N)

We prove a character formula for any finite-dimensional irreducible representationV of the “queer” Lie superalgebra g=q(n). It expresses chV in terms of the multiplicities of the irreducible g-subquotients of the cohomology groups of certain dominant g-bundles on the Π-symmetric projective spaces (i.e., on the homogeneous superspacesG/P whose reduced space is a projective space, whereG=Q(n)). We also establish recurrent relations for the above multiplicities, and this enables us to compute explicitly chV for any givenV. This provides a complete solution to the Kac character problem for the Lie superalgebraq(n). Finally, we consider the particular cases ofq(2), q(3), andq(4) in which we compare the new character formula with the generic character formula of [12]. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 41, Algebraic Geometry-7, 1997.     

Investigation of solvability of the multidimensional two-phase Stefan and the nonstationary filtration Florin problems for second order parabolic equations in weighted Hölder spaces of functions

Multidimensional two-phase Stefan (k=1) and nonstationary filtration Florin (k=0) problems for second order parabolic equations in the case when the free boundary is a graph of a functionx _n =Ψ _k (x′t),x′∈ ^n?1 ,n≥2,t∈(0,T) are studied. A unique solvability theorem in weighted Hölder spaces of functions with time power weight is proved, coercive estimates for solutions are obtained. Bibliography: 30 titles.     

Antiferromagnetic and superconducting states in the three-band two-dimensional repulsive Hubbard model

The three-band two-dimensional repulsive Hubbard model in the formalism of the temperature Green function is investigated. The applicability of the weak coupling approach at the values of the dimensionless coupling constant U/t≈10–11 is justified. The normal state, the antiferromagnetic state with Neel magnetic ordering on the “copper” sublattice, and the superconducting state with nontrivial Cooper pairing in channels with odd angular momenta are studied. The possibility of other magnetic states in the model is discussed. Bibliography: 20 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 194–228. Translated by K. Malyshev.