On sparse spanners of weighted graphs

Given a graphG, a subgraphG' is at-spanner ofG if, for everyu,v V, the distance fromu tov inG' is at mostt times longer than the distance inG. In this paper we give a simple algorithm for constructing sparse spanners for arbitrary weighted graphs. We then apply this algorithm to obtain specific results for planar graphs and Euclidean graphs. We discuss the optimality of our results and present several nearly matching lower bounds.The work of G. Das and D. Joseph was supported by NSF PYI Grant DCR-8402375. The work of D. Dobkin was supported by NSF Grant CCR-8700917. The work of J. Soares was supported by CNPq proc 203039/87.4 (Brazil) and NSF Grant CCR-9014562. This research was accomplished while G. Das was a student at the University of Wisconsin-Madison. A preliminary version was presented at the Second Scandinavian Workshop on Algorithm Theory, Bergen, Norway, 1990, under the title Generating Sparse Spanners for Weighted Graphs, and proceedings appear in the series Lecture Notes in Computer Science, Springer-Verlag. The preliminary version also appears as Princeton University Technical Report CS-TR-261-90, and as University of Wisconsin-Madison Computer Sciences Technical Report 882.     

Synthesis of a symmetrical dithiirane

The reaction of p-xylene with epichlorohydrin in the presence of aluminum chloride gave 1,4-dimethyl-2,5-bis(1-chloro-2-hydroxypropyl)benzene, which serves as the starting compound for the synthesis of the corresponding symmetrical dithiirane.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1319–1321, October, 1985.     

Contribution a l'etude de la determination du fluor a la surface des metaux par detection des photons gamma prompts de la reaction19F(p, αγ)16O

The 837 keV resonance is used for the rapid and non-destructive determination of the gradient of fluorine on the surface of metallic samples. The precise yield curve of this resonance for thick target and the experimental sensitivity of the method have been determined. With this method less than 5·10^?4 μg·cm^?2 fluorine content can be measured. The resolution is of the order of 1000 Å in aluminium and the concentration profiles can be measured to the depth of 1 μm. The time requirement of a surface analysis is 15–30 min, and 2–3 hrs of a gradient measurement. In addition, this method is simpler and more sensitive than the detection of the 1350 keV alpha-particles from the¹⁹F(p, α_o)¹⁶O reaction.     

Zur Diels-Alder-Reaktion der Dihydro-6-styryl-2(1H)-pyrimidinone

Dihydro-6-styryl-2(1H)-pyrimidinones react with dienophiles such as maleic anhydride in form of aDiels—Alder reaction.     

Ring expansion approach for the synthesis of the (3S,4S)-hexahydroazepine core of balanol and ophiocordin

A new and efficient formal total synthesis of (3S,4S)-balanol, a potent protein kinase C inhibitor, was accomplished from tri-O-acetyl-d-glucal. Balanol and ophiocordin consists of a chiral hexahydro azepine-containing fragment and a benzophenone fragment. The azepine core was prepared in chiral form through intramolecular aza Wittig reaction. A triphenylphosphine mediated ring expansion process was employed to form the seven-membered nitrogen heterocycle. The aldehyde equivalent key intermediate was treated with triphenylphosphine to give the azepine core. To demonstrate the applicability of the new route, a synthesis of the balanol is described.     

Effect of asymmetry on the electronic delocalization in diiron and iron-cobalt mixed valence metallocenic compounds

In this work, we report the synthesis and a study on the degree of electronic delocalization in the asymmetric mixed valence complexes [CpFe(C(8)H(6))Fe(C(8)H(7))](+), 3a(+), and [CpCo(C(8)H(6))Fe(C(8)H(7))](+), 3b(+), (Cp = C(5)Me(5), C(8)H(6) = pentalenyde, C(8)H(7) = hydropentalenyde, and = ((3,5(CF(3))(2)C(6)H(3))(4)B(-))). Electrochemical methods, (57)Fe M?ssbauer spectroscopy, electronic spectroscopy, and electron paramagnetic resonance were used for this purpose. Although the anti conformation of the complexes precludes any metal-metal interaction, all the techniques employed show that 3a(+) is a electronic delocalized system, while 3b(+) behaves as two individual metallic centers with localized electron density.     

Determination des fonctions d'excitation des reactions19F(p, α0)16O et7Li(p, α0)4He entre 150 et 1800 keV

The experimental device used is described. Excitation functions are given for an angle of observation 150° with respect to the incident beam. The possibilities of applying these reactions to the measurement of surface lithium and fluorine concentrations are considered. The detection limits for these two elements are shown to be 5·10⁻³ μg·cm⁻² with protons of energy between 1,350 and 1,500 keV. The method is compared with that based on the detection of prompt γ-rays from the reactions⁷Li(p, γ)⁸Be and¹⁹F(p, α γ)¹⁶O.      

Effect of absolute laser phase on reaction paths in laser-induced chemical reactions

Potential surfaces, dipole moments, and polarizabilities are calculated by ab initio methods [unrestricted MP2(full)/6-311++G(2d,2p)] along the reaction paths of the F+CH4 and Cl+CH4 reaction systems. It is found that in general dipole moments and polarizabilities exhibit peaks near the transition state. In the case of X=F these peaks are on the products side and in the case of X=Cl they are on the reactants side indicating an early transition state in the case of fluorine and a late transition state in the case of chlorine. An analysis of the geometric changes along the reaction paths reveals a one-to-one correspondence between the peaks in the electric properties and peaks in the rate of change of certain internal geometric coordinates along the reaction path. Interaction with short infrared intense laser fields pulses leads to the possibility of interferences between the dipole and polarizability laser-molecule interactions as a function of laser phase. The larger dipole moment in the Cl+CH4 reaction can lead to the creation of deep wells (instead of energy barriers) and new strongly bound states in the transition state region. This suggests possible coherent control of the reaction path as a function of the absolute phase of the incident field, by significant modification of the potential surfaces along the reaction path and, in particular, in the transition state region.