On the minimal solution for some variational inequalities

Applying an asymptotic method, the existence of the minimal solution to some variational elliptic inequalities defined on bounded or unbounded domains is established. The minimal solution is obtained as limit of solutions to some classical variational inequalities defined on domains becoming unbounded when some parameter tends to infinity. The considered quasilinear operators are only monotone (not strictly) and noncoercive. Some related comparison principles are also investigated.     

Triple-quantum MAS-NMR of quadrupolar nuclei

From two-dimensional multiquantum NMR spectra of quadrupolar nuclei, it is now possible to obtain much greater resolution than in a classical single-quantum magic-angle spinning or variable-angle spinning spectrum. We describe here a very simple pulse scheme which efficiently excites the desired multiquantum NMR coherence and a new acquisition procedure which yields to pure-absorption mode 2D spectra. Experimental spectra for ⁸⁷Rb in polycrystalline rubidium nitrate illustrate the method.     

UV picosecond laser-induced formation of amino acids from aqueous solutions of ammonic salts of dicarboxylic acids

It is shown for the first time that the irradiation of the ammonic-salt aqueous solutions of the dicarboxylic acids by powerful ultrashort uv pulses provokes the formation of the related amino acids. The amino-acid quantum yield depends on the intensity and for the aspartic acid, in particular, it reaches 40% at the intensity of about 1 GW/cm².     

Generalized intersection bodies are not equivalent

In [A. Koldobsky, A functional analytic approach to intersection bodies, Geom. Funct. Anal. 10 (2000) 1507-1526], A. Koldobsky asked whether two types of generalizations of the notion of an intersection body are in fact equivalent. The structures of these two types of generalized intersection bodies have been studied by the author in [E. Milman, Generalized intersection bodies, J. Funct. Anal. 240 (2) (2006) 530-567], providing substantial evidence for a positive answer to this question. The purpose of this note is to construct a counter-example, which provides a surprising negative answer to this question in a strong sense. This implies the existence of non-trivial non-negative functions in the range of the spherical Radon transform, and the existence of non-trivial spaces which embed in Lp for certain negative values of p.     

On the connectivity of diamond-free graphs

Let G be a graph of order n(G), minimum degree δ(G) and connectivity κ(G). Chartrand and Harary [Graphs with prescribed connectivities, in: P. Erdös, G. Katona (Eds.), Theory of Graphs, Academic Press, New York, 1968, pp. 61-63] gave the following lower bound on the connectivity

κ(G)?2δ(G)+2-n(G).     

Modular Conjugation and the Implementation of Supersymmetry

Any 87825311t31406/11005_2006_132_Article_IEq1.gif" alt="$$\mathbb{Z}_{2}$$" align="middle" border="0">-graded C ^*-dynamical system with a self-adjoint graded-Kubo-Martin-Schwinger (KMS) functional on it can be represented (canonically) as a 87825311t31406/11005_2006_132_Article_IEq2.gif" alt="$$\mathbb{Z}_{2}$$" align="middle" border="0">-graded algebra of bounded operators on a 87825311t31406/11005_2006_132_Article_IEq3.gif" alt="$$\mathbb{Z}_{2}$$" align="middle" border="0">-graded Hilbert space, so that the grading of the latter is compatible with the functional. The modular conjugation operator plays a crucial role in this reconstruction. The results are generalized to the case of an unbounded graded-KMS functional having as dense domain the union of a net of C ^*-subalgebras. It is shown that the modulus of such an unbounded graded-KMS functional is KMS.      

Torus Equivariant Spectral Triples for Odd-Dimensional Quantum Spheres Coming from <Emphasis Type="Italic">C</Emphasis><Superscript>*</Superscript>-Extensions

The torus group (S ¹)^ℓ+1 has a canonical action on the odd-dimensional sphere S _q ^2ℓ+1. We take the natural Hilbert space representation where this action is implemented and characterize all odd spectral triples acting on that space and equivariant with respect to that action. This characterization gives a construction of an optimum family of equivariant spectral triples having nontrivial K-homology class thus generalizing our earlier results for SU _q (2). We also relate the triple we construct with the C ^*-extension      

Compatible maps and invariant approximations

The existence of invariant best approximations for compatible maps is proved. Our results unify, and generalize various known results to a more general class of noncommuting mappings.