X-RAY INDUCED VISIBLE LUMINESCENCE OF PORPHYRINS

A concept has been presented whereby X-ray irradiation can be used to induce visible luminescence of chromophores such as porphyrins. The essential aspects of the idea have been demonstrated in a supramolecular assembly consisting of a water-dispersed polystyrene latex with an embedded scintillating compound, 2,5-diphenyloxa-zole, and an externally attached hematoporphyrin. X-ray excitation of the assembly yields an emission spectra typical for hematoporphyrin with fluorescent yields. of up to 3% with respect to 2,5-diphenyloxazole emission. Significant quenching in the presence of dioxygen indicates that singlet oxygen is formed at atmospheric conditions.     

Kilohertz laser frequency sensing with Brillouin mutually modulated cross-gain modulation

Using mutually modulated cross-gain modulation, Stokes optical frequency changes are converted into modulation phase changes with high sensitivity. In the slow-light transition regime, we demonstrate kilohertz sensitivity to the Stokes optical carrier frequency. The sensitivity is inversely proportional to the modulation frequency of the pump and Stokes beams.     

Generating uniform random vectors over a simplex with implications to the volume of a certain polytope and to multivariate extremes

A uniform random vector over a simplex is generated. An explicit expression for the first moment of its largest spacing is derived. The result is used in a proposed diagnostic tool which examines the validity of random number generators. It is then shown that the first moment of the largest uniform spacing is related to the dependence measure of random vectors following any extreme value distribution. The main result is proved by a geometric proof as well as by a probabilistic one.     

High-multiplicity N-fold IP via configuration LP

Mathematical Programming - N-fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and successfully...     

Optimization over Young diagrams

Journal of Algebraic Combinatorics - We consider the problem of finding a Young diagram minimizing the sum of evaluations of a given pair of functions on the parts of the associated pair of...     

Proximal-isometric (P J) flows

We develop some new tools for the study of minimal transformation groups (flows) and apply these tools to extend the classification theory of minimal flows to a larger class than has previously been classified. The tools we develop arise from a simplification and unification of the techniques used by Furstenberg, Ellis, and Veech in their proofs of structure theorems about distal and point distal flows. This simplification is made possible largely through the use of recent results of Glasner on the structure of 2^X (whose points consist of closed subsets of the phase space X of a given flow).     

Interpolation,the Rudimentary Geometry of Spaces of Lipschitz Functions,and Geometric Complexity

Foundations of Computational Mathematics - We consider seriously the analogy between interpolation of nonlinear functions and manifold learning from samples, and examine the results of transferring...