Some constrained shortest-route problems

Summary This paper treats five constrained shortest-route problems: 1) determining the shortest route when it is constrained to pass through a given set of specified nodes; 2) determining the shortest route when it is constrained to pass through a given set of specified nodes and the specified nodes are to be visited in a fixed order; 3) finding an optimal route for the travelling-salesman problem; 4) determining the shortest route throughK sets of specified nodes when at least one node of every set of specified nodes is to occur on the shortest route; and 5) finding the shortest route through the sets of specified nodes when at least one node of every set of specified nodes is to occur on the shortest route and the sets of specified nodes are to be visited in a fixed order. The functional equation technique of dynamic programming is employed to solve problems 1), 3), and 4), while problems 2) and 5) are solved through simpler algorithms. The methods are illustrated by examples.

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Zusammenfassung Es werden fünf Kürzeste-Wege-Probleme mit besonderen Bedingungen behandelt: 1) Bestimmung des kürzesten Weges unter der Bedingung, daß die in einer gegebenen Menge spezifizierten Knoten passiert werden müssen, 2) Bestimmung des kürzesten Weges, wobei die in einer gegebenen Menge spezifizierten Knoten in einer bestimmten Reihenfolge passiert werden müssen, 3) Ermittlung der optimalen Rundreise im Travelling-Salesman Problem, 4) Bestimmung des kürzesten Weges durchK Mengen von spezifizierten Knoten, wobei aus jeder Menge wenigstens ein Knoten passiert werden muß, und 5) Bestimmung des kürzesten Weges durch Mengen von spezifizierten Knoten, wobei aus jeder Menge wenigstens ein Knoten passiert und die Mengen in einer vorgegebenen Reihenfolge aufgesucht werden müssen. Zur Lösung der Probleme 1), 3) und 4) wird die Technik der dynamischen Optimierung angewandt, während die Probleme 2) und 5) mit einfacheren Algorithmen behandelt werden. Die Methoden werden an Beispielen erläutert.

     

Effect of electron-phonon interaction on the binding energy of a wannier exciton in a polarizable medium

A new phenomenological effective interaction potential between an electron and a hole of a Wannier exciton in a polarizable medium is proposed. Binding energies of Wannier excitons are calculated variationally using this potential in several polar crystals. A close agreement between the theoretical values thus calculated and the experimental values is found in all polar crystals including thallium halides.     

Dynamic nuclear polarization at 9T using a novel 250 GHz gyrotron microwave source. 2003

In this communication, we report enhancements of nuclear spin polarization by dynamic nuclear polarization (DNP) in static and spinning solids at a magnetic field strength of 9 T (250 GHz for g = 2 electrons, 380 MHz for ¹H). In these experiments, ¹H enhancements of up to 170 ± 50 have been observed in 1-¹³C-glycine dispersed in a 60:40 glycerol/water matrix at temperatures of 20 K; in addition, we have observed significant enhancements in ¹⁵N spectra of unoriented pf1-bacteriophage. Finally, enhancements of ∼17 have been obtained in two-dimensional ¹³C–¹³C chemical shift correlation spectra of the amino acid U–¹³C, ¹⁵N-proline during magic angle spinning (MAS), demonstrating the stability of the DNP experiment for sustained acquisition and for quantitative experiments incorporating dipolar recoupling. In all cases, we have exploited the thermal mixing DNP mechanism with the nitroxide radical 4-amino-TEMPO as the paramagnetic dopant. These are the highest frequency DNP experiments performed to date and indicate that significant signal enhancements can be realized using the thermal mixing mechanism even at elevated magnetic fields. In large measure, this is due to the high microwave power output of the 250 GHz gyrotron oscillator used in these experiments.     

Direct evidence of Cd vacancies in CdSe nanoparticles: positron annihilation studies

Poly vinyl alcohol (PVA) capped CdSe nanoparticles having size in the range of 7–17 nm have been synthesized through chemical route and characterized using X-ray diffraction (XRD) and transmission electron microscopy (TEM). Positron coincidence Doppler broadening (CDB) measurements have been carried out in these nanoparticles. It is observed that the electron momentum distributions show a variation in the core electron momentum region with the particle size. In order to examine the influence of defects, first principle calculations of electron momentum distributions in bulk CdSe and in the presence of Cd as well as Se vacancy defects have been performed. Comparison of experimental data with the calculated momentum distribution reveals the presence of Cd vacancy defects, the concentration of which decreases with the increase in the particle size. The present study also indicates possible Se enrichment on the surface of the nanoparticles with the decrease in the particle size.     

Rate coefficients and products for gas‐phase reactions of chlorine atoms with cyclic unsaturated hydrocarbons at 298 K

Rate coefficients for the reaction of Cl atoms with cycloalkenes have been determined using the relative rate method, at 298 K and atmospheric pressure of N₂. Reference molecule was n‐hexane, and the concentrations of the organics were followed by gas chromatographic analysis. Cl atoms were prepared by photolysis of trichloroacetyl chloride at 254 nm. The relative rates of reactions of Cl atoms with cycloalkenes, with respect to n‐hexane, are measured as 1.12 ± 0.38, 1.31 ± 0.14, and 1.69 ± 0.18 for cyclopentene, cyclohexene, and cycloheptene, respectively. Considering the absolute value of the rate coefficient of the reaction of Cl atom with n‐hexane as 3.03 ± 0.06 × 10^?10 cm³ molecule^?1 s^?1, the rate coefficient values for cyclopentene, cyclohexene, and cycloheptene are calculated to be (3.39 ± 1.08) × 10^?10, (3.97 ± 0.43) × 10^?10, and (5.12 ± 0.55) × 10^?10 cm³ molecule^?1 s^?1, respectively. The experiments for each molecule were repeated six to eight times, and the slopes and the rate coefficients given above are the average values of these measurements, and the quoted error includes 2σ as well as all other uncertainties in the measurement and calculations. The rate coefficient increases linearly with the number of carbon atoms, with an increment per additional CH₂ group being (8.7 ± 1.6) × 10^?12 cm³ molecule^?1 s^?1. Chloroketones and chloroalcohols, along with unsaturated ketones and alcohols, were found to be the major products of Cl‐atom‐initiated oxidation of cycloalkenes in the presence of air. The atmospheric implications of these results are discussed, along with a comparison with the reported structure activity relationships. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 42: 98–105, 2010     

NURBS approximation of surface/surface intersection curves

We use a combination of both symbolic and numerical techniques to construct degree boundedC ^k -continuous, rational B-spline ε-approximations of real algebraic surface-surface intersection curves. The algebraic surfaces could be either in implicit or rational parametric form. At singular points, we use the classical Newton power series factorizations to determine the distinct branches of the space intersection curve. In addition to singular points, we obtain an adaptive selection of regular points about which the curve approximation yields a small number of curve segments yet achievesC ^k continuity between segments. Details of the implementation of these algorithms and approximation error bounds are also provided. Supported in part by NSF Grants CCR 92.22467, DMS 91-01424, AFOSR Grant F49620-10138 and NASA Grant NAG-1-1473. Supported in part by K.C. Wong Education Foundation, Hong Kong.     

Synthesis of enantiopure β-amino alcohols via AKR/ARO of epoxides using recyclable macrocyclic Cr(III) salen complexes

A series of chiral macrocyclic Cr(III) salen complexes 1-8 were synthesized and characterized. These complexes were found to be highly active, regio-, diastereo-, and enantioselective catalysts in aminolytic kinetic resolution (AKR) of racemic trans-epoxides as well as asymmetric ring opening (ARO) of prochiral meso-epoxides with various anilines as nucleophiles at room temperature in 18-24 h. Excellent yields (>99% with respect to the nucleophile) with high enantioselectivity (ee, >99%) of chiral anti-β-amino alcohols was achieved with concomitant recovery of corresponding epoxides in high ee (up to >99%). The complex 1 also catalyzed the ARO of meso-epoxides to provide corresponding syn-β-amino alcohols in high yield (99%) and ee (up to 91%). Due to built-in basic sites in the catalyst, no external base (as an additive) was required to promote AKR and ARO reactions. The catalyst 1 was conveniently recycled several times with retention of its performance. The AKR of trans-stilbene oxide with aniline was successfully demonstrated at relatively higher scale (10 mmol) using the catalyst 1.     

On the correlation between the magnetic structure and the electrical properties of EuB6

Single crystals of EuB₆ were prepared by the floating-zone method. Magnetic and electric measurements on these crystals in the temperature range 1.6–300 K revealed that the pure EuB₆ is an antiferromagnet with a Néel temperature of 5–6 K and has a carrier concentration of 4.2 × 10²⁰ cm^-3. It was found that in polycrystalline sample, defects of Eu ions reduce the carrier concentration and make the sample ferromagnetic. It is suggested that the conduction electrons in pure EuB₆ originate from the overlap of the 4f band tail and the conduction band.     

Effect of free carrier screening on the binding energy of D− centers in polar semiconductors

A calculation of the binding energy of a D^? center, defined as the energy required to remove one of the two electrons from the D^? center to infinity, in the presence of other free carriers is reported in polar crystals. It is assumed that the effective interaction between each of the two electrons and the positive ion is described by Thomas-Fermi potential. The effective interaction between the two electrons in polar crystals is, however, described by two recently proposed potentials. The binding energy of a D^? ion is calculated variationally in several polar crystals as a function of the screening parameter δ and the value of δ at which the binding energy goes to zero (D^? Mott transition) is determined. A possible experimental situations where this system may be studied is discussed.