On Ramsey numbers for linear forests

For a graph G, the Ramsey number r(G) is the smallest natural number p such that given a graph H with p points. H or H? contains a G. An (n,j)-linear forest L is the disjoint union of nontrivial paths, j of which have an odd number of points, and such that the union has n points. If L is an (n,j)-linear forest, then we show that

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Nitrogen-15 nuclear magnetic resonance spectroscopic study of compounds with nitrogen?nitrogen bonds

The ¹⁵N NMR spectra of several substances with nitrogen—nitrogen bonds have been obtained at the natural-abundance level by high-resolution NMR spectroscopy. Azo (? N?N? ) nitrogens are 300–500 ppm deshielded compared with hydrazo (? NH? NH? ) nitrogens. The sensitivity of the ¹⁵N shifts in these types of substances to substituent changes are reported, along with ¹⁵N–¹H spin–spin couplings for some hydrazo compounds. Hydrogen-bonding effects arising from solvent changes on the ¹⁵N shifts of azoxybenzene are different for its two kinds of nitrogen. The ¹⁵N NMR spectrum of N,N'-dinitrosopiperazine in dimethyl sulfoxide at room temperature is consistent with the presence of two different conformations about the N? NO bonds.     

Pressure broadening theory of assymmetric-top molecules using the methods of irreducible tensor operators

Contributions to the second-order collision efficiency function used in Anderson and Murphy-Boggs pressure-broadening theories due to dipole-dipole, dipole-quadrupole, quadrupole-dipole, and quadrupole-quadrupole interactions are derived by the method of irreducible spherical tensor operators for molecules of arbitrary symmetry. Results are given explicitly in terms of dipole and quadrupole line strengths. General expressions for dipole line strength in the asymmetric rotor basis, as well as quadrupole moment line strength for the special case of molecules with two independent quadrupole moment components, are derived.     

How to continue the predictions of perturbative QCD from the spacelike region where they are derived to the timelike regime where experiments are performed

The predictions of perturbative QCD are derived in the deep euclidean region, whereas the physical region for most observables is timelike. The confrontation of these predictions with experiment thus necessitates an analytic continuation. This we find introduces large higher order corrections in terms of α_s(|Q²|), the usual choice ofperturbative expansion parameter. These corrections are naturally absorbed by changing to the expansion parameter $\text{a}\text{(Q}{}^2\text{) = |α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|(}\text{Re}\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)/|α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|)}{}^{\mathrm{<mtext>(n?2)</mtext><mtext>3</mtext>}}$, where α_s(Q²)ⁿ is the leading term in the spacelike region. For the intermediate range of Q² experimentally accessible at present, where $\text{a}\text{(Q}{}^2\text{)}$ is significantly smaller than α_s(|Q²|), we find the resulting phenomenology is improved. In particular, we demonstrate how the values of $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}$ obtained from analyses of quarkonium decays become consistent.     

Das papierchromatographische Verhalten und den Nachweis zahlreicher Phenolk?rper

Ohne Zusammenfassung