Complete Carton-13 Assignments of the Sesquiterpene Lactone 11,13,-Dihydroparthenolide Using 2D-Inadequate

The complete ¹³C NMR resonances for the sesquiterpene lactone 11,13-dihydroparthenolide were established by the application of 2D-INADEQUATE.     

Local behavior of an iterative framework for generalized equations with nonisolated solutions

 An iterative framework for solving generalized equations with nonisolated solutions is presented. For generalized equations with the structure , where is a multifunction and F is single-valued, the framework covers methods that, at each step, solve subproblems of the type . The multifunction approximates F around s. Besides a condition on the quality of this approximation, two other basic assumptions are employed to show Q-superlinear or Q-quadratic convergence of the iterates to a solution. A key assumption is the upper Lipschitz-continuity of the solution set map of the perturbed generalized equation . Moreover, the solvability of the subproblems is required. Conditions that ensure these assumptions are discussed in general and by means of several applications. They include monotone mixed complementarity problems, Karush-Kuhn-Tucker systems arising from nonlinear programs, and nonlinear equations. Particular results deal with error bounds and upper Lipschitz-continuity properties for these problems. Received: November 2001 / Accepted: November 2002 Published online: December 9, 2002 Key Words. generalized equation – nonisolated solutions – Newton's method – superlinear convergence – upper Lipschitz-continuity – mixed complementarity problem – error bounds Mathematics Subject Classification (1991): 90C30, 65K05, 90C31, 90C33     

Polymer chain dynamics under nanoscopic confinements

It is shown that the confinement of polymer melts in nanopores leads to chain dynamics dramatically different from bulk behavior. This so-called corset effect occurs both above and below the critical molecular mass and induces the dynamic features predicted for reptation. A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined to nanoscopic strands that are in turn embedded in a quasi-solid and impenetrable methacrylate matrix. Both the molecular weight of the PEO and the mean diameter of the strands were varied to a certain degree. The chain dynamics of the PEO in the molten state was examined with the aid of field-gradient NMR diffusometry (time scale, 10(-2)-10(0) s) and field-cycling NMR relaxometry (time scale, 10(-9)-10(-4) s). The dominating mechanism for translational displacements probed in the nanoscopic strands by either technique is shown to be reptation. On the time scale of spin-lattice relaxation time measurements, the frequency dependence signature of reptation (i.e., T1 approximately nu(3/4)) showed up in all samples. A "tube" diameter of only 0.6 nm was concluded to be effective on this time scale even when the strand diameter was larger than the radius of gyration of the PEO random coils. This corset effect is traced back to the lack of the local fluctuation capacity of the free volume in nanoscopic confinements. The confinement dimension is estimated at which the crossover from confined to bulk chain dynamics is expected.     

Minimum residual methods for augmented systems

For large systems of linear equations, iterative methods provide attractive solution techniques. We describe the applicability and convergence of iterative methods of Krylov subspace type for an important class of symmetric and indefinite matrix problems, namely augmented (or KKT) systems. Specifically, we consider preconditioned minimum residual methods and discuss indefinite versus positive definite preconditioning. For a natural choice of starting vector we prove that when the definite and indenfinite preconditioners are related in the obvious way, MINRES (which is applicable in the case of positive definite preconditioning) and full GMRES (which is applicable in the case of indefinite preconditioning) give residual vectors with identical Euclidean norm at each iteration. Moreover, we show that the convergence of both methods is related to a system of normal equations for which the LSQR algorithm can be employed. As a side result, we give a rare example of a non-trivial normal(1) matrix where the corresponding inner product is explicitly known: a conjugate gradient method therefore exists and can be employed in this case. This work was supported by British Council/German Academic Exchange Service Research Collaboration Project 465 and NATO Collaborative Research Grant CRG 960782     

Soft X‐ray characterization technique for Li batteries under operating conditions

O K‐edge and Co L‐edge near‐edge X‐ray absorption fine structure has been used to examine the cathode of an intact solid‐state lithium ion battery. The novel technique allowed for the simultaneous acquisition of partial electron yield and fluorescence yield data during the first charge cycle of a LiCoO₂‐based battery below the intercalation voltage. The chemical environments of oxygen and cobalt at the surface are shown to differ chemically from those in the bulk. The present design enables a wide variety of in situ spectroscopies, microscopies and scattering techniques.     

Cichoń’s diagram,regularity properties and {\varvec{\Delta}^1_3} sets of reals

We study regularity properties related to Cohen, random, Laver, Miller and Sacks forcing, for sets of real numbers on the \({\varvec{\Delta}^1_3}\) level of the projective hieararchy. For \({\varvec{\Delta}^1_2}\) and \({\varvec{\Sigma}^1_2}\) sets, the relationships between these properties follows the pattern of the well-known Cichoń diagram for cardinal characteristics of the continuum. It is known that assuming suitable large cardinals, the same relationships lift to higher projective levels, but the questions become more challenging without such assumptions. Consequently, all our results are proved on the basis of ZFC alone or ZFC with an inaccessible cardinal. We also prove partial results concerning \({\varvec{\Sigma}^1_3}\) and \({\varvec{\Delta}^1_4}\) sets.     

Performance of a four‐element Si drift detector for X‐ray absorption fine‐structure spectroscopy: resolution, maximum count rate,and dead‐time correction with incorporation into the ATHENA data analysis software

The performance of a four‐element Si drift detector for energy‐dispersive fluorescence‐yield X‐ray absorption fine‐structure measurements is reported, operating at the National Institute of Standards and Technology beamline X23A2 at the National Synchrotron Light Source. The detector can acquire X‐ray absorption fine‐structure spectra with a throughput exceeding 4 × 10⁵ counts per second per detector element (>1.6 × 10⁶ total counts per second summed over all four channels). At this count rate the resolution at 6 keV is approximately 220 eV, which adequately resolves the Mn Kα and Kβ fluorescence lines. Accurate dead‐time correction is demonstrated, and it has been incorporated into the ATHENA data analysis program. To maintain counting efficiency and high signal to background, it is suggested that the incoming count rate should not exceed ～70% of the maximum throughput.     

o-minimal analytic separation of sets in dimension 2

We study the Hardy field associated with an o-minimal expansion of the real numbers. If the set of analytic germs is dense in the Hardy field, then we can definably analytically separate sets in ${\mathbb{R}}^2$, and we can definably analytically approximate definable continuous unary functions. A similar statement holds for definable smooth functions.     

Synthese,Struktur und einige Reaktionen [N-(N′,N′,N″,N″-tetramethyl)-guanidinyl]-substituierter Phosphorylverbindungen

Synthesis, Structure, and some Reactions of N-(N′,N′,N″,N″-tetramethyl)guanidinyl-substituted Phosphoryl Compounds The tetramethylguanidinyl-substituted phosphoryl compounds 1 – 10 were prepared in the reaction of the appropriate chlorophosphoryl compounds with either N′,N′,N″,N″-tetramethylguanidine (HTMG) or N-trimethylsilyl-(N′,N′,N″,N″-tetramethyl)guanidine (TMSTMG). With methyl iodide 1 reacted with N-alkylation to give the ammonium salt 11. 1 reacted with BF₃ · Et₂O at both imino nitrogen atoms with formation of the bis-BF₃-adduct 12 . The X-ray structure determination of phenylphosphonic acid-bis(N′,N′,N″,N″-tetramethylguanidinide) 3 shows shortened PN-bonds and widened PNC-angles, consistent with the partial double bond character of the PN-bond.     

Femtosecond dynamics of electron transfer in a neutral organic mixed-valence compound

In this article we report a femtosecond time-resolved transient absorption study of a neutral organic mixed-valence (MV) compound with the aim to gain insight into its charge-transfer dynamics upon optical excitation. The back-electron transfer was investigated in five different solvents, toluene, dibutyl ether, methyl-tert-butyl ether (MTBE), benzonitrile and n-hexane. In the pump step, the molecule was excited at 760 nm and 850 nm into the intervalence charge-transfer band. The resulting transients can be described by two time constant. We assign one time constant to the rearrangement of solvent molecules in the charge-transfer state and the second time constant to back-electron transfer to the electronic ground state. Back-electron transfer rates range from 1.5 × 10¹² s⁻¹ in benzonitrile through 8.3 × 10¹¹ s⁻¹ in MTBE, around 1.6 × 10¹¹ s⁻¹ in dibutylether and toluene and to 3.8 × 10⁹ s⁻¹ in n-hexane.