Delta-semidefinite and delta-convex quadratic forms in Banach spaces

A continuous quadratic form ("quadratic form", in short) on a Banach space $X$ is: (a) delta-semidefinite (i.e., representable as a difference of two nonnegative quadratic forms) if and only if the corresponding symmetric linear operator $T\colon X\to X^*$ factors through a Hilbert space; (b) delta-convex (i.e., representable as a difference of two continuous convex functions) if and only if $T$ is a UMD-operator. It follows, for instance, that each quadratic form on an infinite-dimensional $L_p(\mu)$ space ($1\le p \le\infty$) is: (a) delta-semidefinite iff $p \ge 2$; (b) delta-convex iff $p>1$. Some other related results concerning delta-convexity are proved and some open problems are stated.Comment: 19 page

Effect of a realistic three-body force on the spectra of medium-mass hypernuclei

We adopt the Hartree-Fock (HF) method in the proton-neutron-$\Lambda$ (p-n-$\Lambda$) formalism and the nucleon-$\Lambda$ Tamm-Dancoff Approximation (N$\Lambda$ TDA) to study the energy spectra of medium-mass hypernuclei. The formalism is developed for a potential derived from effective field theories which includes explicitly the 3-body $NNN$ forces plus the $YN$ LO potential. The energy spectra of selected medium-mass hypernuclei are presented and their properties discussed. The present calculation is the first step of a project devoted to {\it ab initio} studies of hypernuclei in medium and heavy mass regions. This may provide a guide for a better understanding of the $YN$ interactions at momentum scales not accessible in few-body hypernuclei.Comment: 7 pages, 9 figures, accepted in Physica Script

Chaos in pp-wave spacetimes

We demonstrate chaotic behavior of timelike, null and spacelike geodesics in non-homogeneous vacuum pp-wave solutions. This seems to be the first known example of a chaotic motion in exact radiative spacetime.Comment: 4 pages, revtex, 3 figures (.pcx

Auslegung: A journal of philosophy, volume 27, number 2 (summer/fall, 2004) book review

Review of Jacqueline Broad's "Women Philosophers of the Seventeenth Century