On the monotonicity of sequences of quadrature formulae

Summary LetI(f)L(f)= _k=0 ^r ₌₀ ^vk–1 a _k f ⁽⁾(X _k ) be a quadrature formula, and let {S _n (f)} _n=1 be successive approximations of the definite integralI(f)= ₀ ¹ f(x)dx obtained by the composition ofL, i.e.,S _n(f)=L( _n ), where .We prove sufficient conditions for monotonicity of the sequence {S _n (f)} _n=1 . As particular cases the monotonicity of well-known Newton-Cotes and Gauss quadratures is shown. Finally, a recovery theorem based on the monotonicity results is presented     

On the topology of compact smooth three-dimensional Levi-flat hypersurfaces

We study topological conditions that must be satisfied by a compactC ^∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ^∞ boundary such that Ω ? ?².     

Chern forms,chern numbers and curvature conditions on a Kähler-Einstein surface

In this paper we considered curvature conditions on a Kähler-Einstein surface of general type. In particular we showed that it has negative holomorphic sectional curvature if theL ²-norm of (3C ₂ ?C ₁ ² )/C ₁ ² is sufficiently small, whereC ₁ andC ₂ are the first and second Chern classes of the surfaces. This generalizes a result of Yau on the uniformization of Kähler-Einstein surfaces of general type and with 3C ₂ ?C ₁ ² = 0. Also in the process, we obtain a necessary condition in terms of an inequality between Chern numbers for a Kähler-Einstein metric to have negative holomorphic sectional curvature.     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, ) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, ), or (ii)f is strictly concave on [0, ). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.     

Fortschritte in der Auswertung von Markierungsversuchen an dynamischen Systemen

In einem dynamischen System vollziehen sich kontinuierlich ablaufende Stoffwandlungen, deren Ausgangsstoffe dem System ständig zufließen und deren Folgeprodukte das System kontinuierlich verlassen. Es wird das Verhalten eines solchen Systems mit drei Pools bei Markierungsexperimenten untersucht. Die Ergebnisse dieser mathematischen Untersuchungen werden auf die Erforschung des Stickstoffstoffwechsels laktierender Rinder mit Hilfe des stabilen Isotops ¹⁵N angewandt. In diesem Fall enthält das dynamische System zwei kleine stoffwechselaktive Pools und einen großen, niclit intensiv am Stoffwechsel beteiligten Körpereiweiβ-Pool.     

Probenchemische Methode zur Bestimmung von 15N an in Gesteinen fixiertem Stickstoff

Zur Klärung geologischer Prozesse werden in zunchmendem Maße die Isotopenvariationen des Stickstoffs herangezogen. Da der größte Teil des Stickstoffs der Gesteine in gebundener Form als Ammoniumstickstoff [1–6] vorliegt, kommt der Untersuchung der Isotopenvariationen desselben eine große Bedeutung zu.     

Untersuchungen zur Empfindlichkeit der β-Rückstreumethode bei der Messung dünner Auftragsschichten mit einem 11C-Spezialpräparat

Die Bestimmung dünner Auftragsschichten auf bewegten Trāgermaterialien mit der β-Rūckstreumethode hängt wesentlich von der Empfindlichkeit der Messung und der Dynamik des Prozesses ab.

In diesem Beitrag wird für spezielle Stoffe der Einfluβ der Trāgermaterialien bei Mehrschichtproblemen auf die Empfindlichkeit untersucht.     

Estimation of isotropic nuclear magnetic shieldings in the CCSD(T) and MP2 complete basis set limit using affordable correlation calculations

A linear correlation between isotropic nuclear magnetic shielding constants for seven model molecules (CH₂O, H₂O, HF, F₂, HCN, SiH₄ and H₂S) calculated with 37 methods (34 density functionals, RHF, MP2 and CCSD(T)), with affordable pcS‐2 basis set and corresponding complete basis set results, estimated from calculations with the family of polarization‐consistent pcS‐n basis sets is reported. This dependence was also supported by inspection of profiles of deviation between CBS estimated nuclear shieldings and shieldings obtained with the significantly smaller basis sets pcS‐2 and aug‐cc‐pVTZ‐J for the selected set of 37 calculation methods. It was possible to formulate a practical approach of estimating the values of isotropic nuclear magnetic shielding constants at the CCSD(T)/CBS and MP2/CBS levels from affordable CCSD(T)/pcS‐2, MP2/pcS‐2 and DFT/CBS calculations with pcS‐n basis sets. The proposed method leads to a fairly accurate estimation of nuclear magnetic shieldings and considerable saving of computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.