A closed-form representation of mixed-integer program value functions

We identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed-integer programs with rational constraint coefficients.     

Separation and Enrichment of the Active Component of Carbon Based Paramagnetic Materials for Use in EPR Oximetry

Carbon based paramagnetic materials are frequently used for EPR oximetry, especiallyin vivo,but the EPR spectra of these materials often have more than one paramagnetic center and/or relatively low signal intensity. To determine whether the multi-components of carbon based materials could be separated and enriched in the active component, we used density gradient centrifugation to separate the materials into several fractions. We studied two types of coals, gloxy and Pocahontas, and found these materials to have large density distribution. The separated density fractions had very different EPR spectra and intensities. The active component from the coal material had a more homogeneous EPR signal and significantly increased EPR signal intensity, whereas for India ink, only slight changes were observed. This result can be very useful in the development of better probes for EPR oximetry.