Let g be a complex simple Lie algebra. Vogel derived a universal decomposition of S2g into (possibly virtual) Casimir eigenspaces, S2g = C⊕Y2 ⊕Y ′ 2 ⊕Y ′′ 2 which turns out to be a decomposition into irreducible modules. If we let 2t denote the Casimir eigenvalue of the adjoint representation (with respect to some invariant quadratic form), these modules respectively have Casimir eigenvalues 4t...

We present a simple formula for all the conserved charges of soliton theories, evaluated on the solutions belonging to the orbit of the vacuum under the group of dressing transformations. For pedagogical reasons we perform the explicit calculations for the case of the sine-Gordon model, taken as a prototype of soliton theories. We show that the energy and momentum are boundary terms for all the...

A new formula for the nuclear charge radius is proposed, dependent on the mass number A and neutron excess N−Z in the nucleus. It is simple and it reproduces all the experimentally available mean square radii and their isotopic shifts of even–even nuclei much better than other frequently used relations. PACS: 21.10.Dr, 21.60.Ev ∗This work is partly supported by the Polish Committee of Scientifi...

In previous work by M. E. Jones and colleagues, it was shown that mutation rate estimates can be improved and corresponding confidence intervals tightened by following a very easy modification of the standard fluctuation assay: cultures are grown to a larger-than-usual final density, and mutants are screened for in only a fraction of the culture. Surprisingly, this very promising development ha...

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].. Mathematical Association of America is collaborating with...

Given a prenex formula F of elementary real algebra having k free variables, the CAD method of quantiier elimination produces a truth invariant CAD, D, for F, that is, a CAD of k-dimensional real space in each cell of which F is truth-invariant, together with an assignment to each cell of its truth value. The method also produces a set P of irreducible projection polynomials, the real zeros of ...

P. G. Savvidis, J. J. Baumberg,* D. Porras, D. M. Whittaker, M. S. Skolnick, and J. S. Roberts Department of Physics & Astronomy, University of Southampton, SO17 1BJ, United Kingdom Departmento Fisica de Materiales, Universidad Autonoma de Madrid, E-28049, Spain Department of Physics, University of Sheffield, Sheffield S3 7RH, United Kingdom Department of Electronic and Electrical Engineering, ...

A simple formula for computing the generalized Hubbell radiation rectangular source integral [formula in text] is introduced. Tables are given to compare the numerical values derived from our approximation formula with those given earlier in the literature.

There are logics where necessity is defined by means of a given identity connective: φ := φ ≡ ⊤ (⊤ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity (PI) φ ≡ ψ can be defined by strict equivalence (SE) (φ ↔ ψ). All these approaches to modality involve a principle that we call the Collapse Axiom (CA): “There is only one necessary proposition....