Generating M-Indeterminate Probability Densities by Way of Quantum Mechanics

Probability densities that are not uniquely determined by their moments are said to be “moment-indeterminate,” or “M-indeterminate.” Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is a challenging problem with a long history. Quantum mechanics is inherently probabilistic, yet the way in which probability densities are obtained is dramatically different in comparison with standard probability theory, involving complex wave functions and operators, among other aspects. Nevertheless, the end results are standard probabilistic quantities, such as expectation values, moments and probability density functions. We show that the quantum mechanics procedure to obtain densities leads to a simple method to generate an infinite number of M-indeterminate densities. Different self-adjoint operators can lead to new classes of M-indeterminate densities. Depending on the operator, the method can produce densities that are of the Stieltjes class or new formulations that are not of the Stieltjes class. As such, the method complements and extends existing approaches and opens up new avenues for further development. The method applies to continuous and discrete probability densities. A number of examples are given.

     

Sharp Upper Bound to the First Nonzero Neumann Eigenvalue for Bounded Domains in Spaces of Constant Curvature

The main result of this paper is that for a domain containedin a hemisphere of the n-dimensional sphere Sⁿ the first nonzeroNeumann eigenvalue µ₁() is less than or equal to the firstnonzero Neumann eigenvalue µ₁(D) where D is a geodesicball in Sⁿ of the same measure as . Equality occurs if and onlyif is isometric to D. This result generalizes old results ofSzegö and Weinberger which gave the corresponding upperbound for µ₁() in the Euclidean case, and a result ofChavel for domains in Sⁿ which restricted to lie in a geodesicball of radius when n = 2and to even smaller geodesic balls for larger n. The techniquesused are analogous to those for our recent proof of the Payne-Pólya-Weinbergerconjecture: rearrangement inequalities and properties of specialfunctions are the key elements. The general approach is a directextension of Weinberger's for domains in Rⁿ.     

The μSR facilities at PSI

TheSR Facility Instruments presently available at PSI and the envisaged medium- and long-term developments are presented. The plans focus on further upgrades of the existing instruments and the development of new techniques using the very high fluxes becoming available at PSI, in particular the setup of a beamline with a fast kicker for muons on request (MORE) and the development of very low energy muon beams.     

A highly diastereoselective synthesis of 4-octulose and 2-deoxy-4-octulose from a -fructose derivative

Bishydroxylation of methyl

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1 with osmium tetraoxide proceeded with extremed high diastereoselectivity to give only methyl

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2. Configurations of the new stereogenic centers (C-2,3) in 2 were determined by degradation of the C-5,6,7,8 fragment to the well-known methyl

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7. Transformation of 2 into the required

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10, was achieved by a methodology that implied, protection to 8, reduction of the ester group in 8 to a hydroxymethyl group in 9, and finally deprotection to the free

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10. On the other hand, epoxidation reaction on

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11 afforded only the corresponding 2,3-anhydro derivative 12 with configuration, as could be demonstrated by degradation to (S)-1,2,4-trimetoxybutane 16, which synthesis is reported herein.     

Synthesis of Enantiopure Primary Amines by Stereoselective Ring Opening of Chiral Octahydro-1,3-benzoxazines by Grignard and Organoaluminum Reagents

Chiral 1,3-perhydrobenzoxazines 1, 2, and 9-14, prepared by condensation of 8-(benzylamino)menthol with different aldehydes, react with alkylmagnesium bromides and trimethylaluminum leading to the open amino alcohols 3a-d, 4a-d, and 15-20 in excellent chemical yields and good to excellent diastereomeric excess. The sequential elimination of the menthol appendage by heating with P(2)O(5) and the benzyl group by hydrogenolysis lead to primary amines 7a-d, 8a-d, and 27-30 in excellent chemical yields and ee. The addition of the alkyl group from the Grignard derivatives and the methyl group from the trimethylaluminum occurs from opposite sides of the heterocycle, yielding the final primary amines with the same stereochemistry.     

Thermal decomposition of lignocellulosic materials: comparison of the results obtained in different experimental systems

An experimental system that allows the use of large particle sizes and the simulation of different operating conditions was built to study the thermal decomposition of lignocellulosic materials. The values of solid conversion and of temperature obtained at different points using spherical particles of pine wood 2 cm in diameter are shown. The conversion values are compared with those calculated from the equations obtained in a thermobalance for small particle sizes.     

Polymer-supported Cinchona alkaloid-derived ammonium salts as recoverable phase-transfer catalysts for the asymmetric synthesis of alpha-amino acids

Alkaloids such as cinchonidine, quinine and N-methylephedrine have been N-alkylated using polymeric benzyl halides or co-polymerized and then N-alkylated, thus affording a series of polymer-supported chiral ammonium salts which have been employed as phase-transfer catalysts in the asymmetric benzylation of an N-(diphenylmethylene)glycine ester. These new polymeric catalysts can be easily recovered by simple filtration after the reaction and reused. The best ee's were achieved when Merrifield resin-anchored cinchonidinium ammonium salts were employed.     

Analysis of sterol oxidation products in foods

The main aspects related to the analysis of sterol oxidation products (SOP) in foods are comprehensively reviewed. Special emphasis is placed on the critical and controversial points of this analysis because these points affect crucial analytical parameters such as precision, accuracy, selectivity, and sensitivity. The effect of sample preparation and the conditions of quantification by gas chromatography and liquid chromatography on these parameters are also reviewed. The results show that, in order to choose an adequate method to analyze SOP in a certain food, the analyst must consider its SOP concentration and matrix complexity. The term SOP includes both cholesterol oxidation products (COP) and phytosterol oxidation products (POP). The state of the art of COP and POP analysis is quite different; many more studies have dealt with the analysis of COP than of POP. However, most of the results presented here about COP analysis may be extrapolated to POP analysis because both groups of compounds show similar structures and characteristics.     

Geometric structure and electronic properties of neutral and anionic Fe2C3 and Fe2C4 clusters, as obtained by density-functional calculations

We calculated the geometrical structures and electronic properties of neutral and anionic Fe2Cn clusters (n = 3,4) using a density-functional method that employs linear combinations of atomic orbitals as basis sets, standard nonlocal norm-conserving pseudopotentials, and the generalized gradient approximation to exchange and correlation. We show that the ground-state structures of Fe2C3 and Fe2C4 are essentially the same in the neutral and anionic states, namely, planar rings that feature nonadjacent Fe atoms. For the anionic clusters, these findings contrast with previously published results.     

Effects of trivalent phosphorus compounds on vinyl polymerizations—VII. A nonstationary state radical polymerization of methylmethacrylate in the presence of phenyldichlorophosphine

In the radical polymerization of methylmethacrylate in the presence of p-phenyldichlorophosphine, the initial rate and degree of polymerization increased with polymerization time. They first decreased with increase in the phosphine concentration but increased with further increase in the phosphine concentration. Termination was first order with respect to the initiator. The degree of polymerization was independent of the initiator concentration, but dependent on the conversion. The polymer contained no phosphorus units regardless of the phosphine concentration. The ESR spectra of system showed existence of a phosphorus radical. In order to explain these characteristics of the polymerization, it is proposed that there may be a nonstationary state in which the polymer radicals are regenerated during the polymerization from the phosphoranyl radicals.