Nuclear Spin–Lattice Relaxation of Single Crystal Sr14Cu24O41

Nuclear spin–lattice relaxation rate T ₁ ⁻¹ has been measured for the ladder sites of two single crystals Sr₁₄Cu₂₄O₄₁ (Sr14-A,B) by ⁶³Cu NMR/NQR. The hole localization around 100 K appears as a peak in the T variation of T ₁ ⁻¹(NQR). On the other hand, it is suppressed in the T ₁ ⁻¹ (NMR) data under the magnetic field H ∼ 11 T, and a new peak appears around 20 K. T ₁ ⁻¹(NMR) around the peak is more enlarged for Sr14-B than for Sr14-A. Hence, holes on the ladders of Sr14-B tend to be more localized. This is considered to be an origin for the occurrence of the magnetic order in Sr14-B under H ∼ 11 T.     

Three New Diterpenoids from Euphorbia wallichii

Three new abietane diterpene lactones, 3α-hydroxyjolkinolide A (1), ent-8α, 14β-dihydroxy-13(15)-ene-16(12α)-abietanolide (2) and ent-8α,14α-dihydroxy-13(15)-ene-16(12α)-abietanolide (3) as well as a known abietane diterpene jolkinolide A (4) were isolated from the roots of Euphorbia wallichii. Their structures were elucidated on the basis of spectroscopic analysis.     

A priori error estimates for approximate solutions to convex conservation laws

Summary. We introduce a new technique for proving a priori error estimates between the entropy weak solution of a scalar conservation law and a finite–difference approximation calculated with the scheme of Engquist-Osher, Lax-Friedrichs, or Godunov. This technique is a discrete counterpart of the duality technique introduced by Tadmor [SIAM J. Numer. Anal. 1991]. The error is related to the consistency error of cell averages of the entropy weak solution. This consistency error can be estimated by exploiting a regularity structure of the entropy weak solution. One ends up with optimal error estimates. Received December 21, 2001 / Revised version received February 18, 2002 / Published online June 17, 2002     

Positive definiteness in the numerical solution of Riccati differential equations

Summary. In this work we address the issue of integrating symmetric Riccati and Lyapunov matrix differential equations. In many cases -- typical in applications -- the solutions are positive definite matrices. Our goal is to study when and how this property is maintained for a numerically computed solution. There are two classes of solution methods: direct and indirect algorithms. The first class consists of the schemes resulting from direct discretization of the equations. The second class consists of algorithms which recover the solution by exploiting some special formulae that these solutions are known to satisfy. We show first that using a direct algorithm -- a one-step scheme or a strictly stable multistep scheme (explicit or implicit) -- limits the order of the numerical method to one if we want to guarantee that the computed solution stays positive definite. Then we show two ways to obtain positive definite higher order approximations by using indirect algorithms. The first is to apply a symplectic integrator to an associated Hamiltonian system. The other uses stepwise linearization. Received April 21, 1993     

Spaces from pieces IV

We are going to investigate simultaneous extensions of various topological structures (i.e. traces on several subsets at the same time are prescribed), also with separation axioms T₀, T₁, symmetry (in the sense of Part I, § 3), Riesz property, Lodato property. The following questions will be considered: (i) Under what conditions is there an extension? (ii) How can the finest extension be described? (iii) Is there a coarsest extension? (iv) Can we say more about extensions of two structures than in the general case? (v) Assume that certain subfamilies (e.g. the finite ones) can be extended; does the whole family have an extension, too? The general categorial results from Part I will be applied whenever possible (even they are not really needed).     

Holomorphic vector bundles on compact complex non-algebraic surfaces

LetX be a smooth complex compact surface without non-constant meromorphic functions. Here we prove the existence of rank holomorphic vector bundles onX containing exactly one rank one saturated subsheaf.

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Sunto SiaX una superficie complessa compatta non singolare senza funzioni meromorfe non costanti. In questo lavoro si domstra cheX possiede molti fibrati olomorfi di rango 2 contenenti un unico fibrato in rette.