Optimal random coding

We consider a stochastic method for representing a real number x by a finite sequence of bits. The method is symmetrical with respect to interchange of the bits: it is characterized by a single function p (x) which gives the probability that any particular bit is on as a function of the real number x that is being encoded. We then consider the problem of reconstructing x from its representation. In the limiting case in which the number of bits is large, we determine the function p (x) that minimizes the expected k-th power of the absolute error in this reconstruction. The optimal choice of p (x) is independent of k.     

Asymptotic neutrality of large ions

It is proved that a nucleus of chargeZ can bind at mostZ+O(Z ^a) electrons, witha=47/56.Partially supported by a NSF grant at Princeton UniversitySupported by a Sloan Foundation Dissertation Fellowship at Princeton University     

Site planning for clinical NMR systems

The installation of a nuclear magnetic resonance imaging system (NMR or MRI) in a clinical environment requires detailed planning to insure adequate safety and optimal system performance. The important considerations of site planning are discussed in this paper and solutions suggested by various system manufacturers are detailed. In addition, experimental results illustrating the effects of improper site planning are also presented.     

Ueber die maassanalytische Bestimmung der Phosphors?ure mittelst Urannitrats

Ohne Zusammenfassung     

Key side products due to reactivity of dimethylmaleoyl moiety as amine protective group

Dimethylmaleoyl (DMM) moiety has become an important amine protective group in sugar chemistry. We disclose herein that DMM-containing D-glucosamine analogues, because of their electrophilic nature, are prone to reactions with strong nucleophiles, such as hydrazine, resulting in a set of undesired side products that are difficult to detect, yet proved to be problematic for organic synthesis.     

Decompositions of metastable [C6H12O]+ ions with the oxygen on the third carbon: Ring-size preferences in [CnH2nO]+˙ ions

The isomerizations preceding the metastable decompositions in the mass spectrometer of a number of [C₆H₁₂O]⁺˙ ions with the oxygen on the third carbon are characterized utilizing deuterium labeling. Hydrogens are transferred in these ions by three-, five- and six-membered ring rearrangements, with propensities determined by features of the individual reactions. Three-membered ring hydrogen transfers between α and β-carbons are preferred to all five-membered ring hydrogen transfers. However, six-membered ring hydrogen transfers take place to the apparent exclusion of three-membered ring hydrogen transfers to enol carbons when the products are of comparable stability. The low-energy [C₆H₁₂O]⁺˙ isomerizations characterized are predictable from the behavior of their lower homologs. It is concluded that the determinants of these reactions are the same as those of other highly reactive organic intermediates.