Lattic path proofs of extended Bressoud-Wei and Koike skew Schur function identities

Our recent paper provides extensions to two classical determinantal results of Bressoud and Wei, and of Koike. The proofs in that paper were algebraic. The present paper contains combinatorial lattice path proofs

Particle production in strong interactions

Imperial Users onl

Comments on “Electric current and electric field induced in a human body when exposed to an incident electric field near the resonant frequency”

[For original paper see R. W. P. King, IEEE Trans. Microwave Theory Tech., vol. 48, no. 9, pp. 147-53 (2000).] The author makes two observations on the original article. The commentator questions whether a seated person is well modeled as a right circular cylinder. The second observation is that King cites only microwave studies on mice to show that electromagnetic radiation causes malignancies. These studies themselves are widely disputed. He then uses simple dimensional scaling to show that 2.45 GHz for a mouse scales to 100 MHz for a man. Such a scaling law may be useful in calculating the resonant frequency for a human subject versus a mouse when treated as antennas, but such scaling is meaningless when the physics of a hypothetical carcinogenic process are unknown

The Hopf Algebra Structure of the Character Rings of Classical Groups

The character ring \CGL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra \Sym$ of symmetric functions. Here we study the character rings \CO and \CSp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that \CO and \CSp also admit natural Hopf algebra structures that are isomorphic to that of \CGL, and hence to \Sym. The isomorphisms are determined explicitly, along with the specification of standard bases for \CO and \CSp analogous to those used for \Sym. A major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic Schur-Hall scalar products. Significantly, the adjoint with respect to multiplication no longer coincides, as it does in the \CGL case, with a Foulkes derivative or skew operation. The adjoint and Foulkes derivative now require separate definitions, and their properties are explored here in the orthogonal and symplectic cases. Moreover, the Hopf algebras \CO and \CSp are not self-dual. The dual Hopf algebras \CO^* and \CSp^* are identified. Finally, the Hopf algebra of the universal rational character ring \CGLrat of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified.Comment: 38 pages, uses pstricks; new version is a major update, new title, new material on rational character

Motivations of UK students to study abroad: a survey of school-leavers

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