Hausdorff Dimension of Operator Stable Sample Paths

The Hausdorff dimension of the sample paths of a stochastic process with stationary independent operator stable increments is computed. With probability one, every sample path has the same dimension, depending on the real parts of the eigenvalues of the operator stable exponent.     

Exact results for the persistent current in an aharonov-bohm ring with a quantum impurity

We consider the problem of a persistent current in a one-dimensional mesoscopic ring with the electrons coupled by a spin exchange to a magnetic impurity. We show that this problem can be mapped onto an integrable model with a quadratic dispersion (with the latter property allowing for an unambiguous definition of the persistent current). We have solved the model exactly by a Bethe ansatz and found that the current is insensitive to the presence of the impurity. We conjecture that this result holds for any integrable quantum impurity model with an electronic dispersionε(k) that is an even function ofk.     

Generatrices of rational curves

We investigate the one-parametric set of projective subspaces that is generated by a set of rational curves in projective relation. The main theorem connects the algebraic degree of , the number of degenerate subspaces in and the dimension of the variety of all rational curves that can be used to generate . It generalizes classical results and is related to recent investigations on projective motions with trajectories in proper subspaces of the fixed space. Received 9 May 2001.     

Stereoselective Ring Opening of Electronically Excited Cyclohexa-2, 4-dienones: Cause and effect

The two conformers of a cyclohexa-2, 4-dienone with different substituents at C(6) on irradiation are believed to undergo ring opening stereospecifically affording a mixture of two configurationally isomeric diene-ketenes (and descendents thereof)- Exceptions are generally found for those dienones with one C and one O substituent or even with two C substituents, if one of them carries a polar group at a site able to interact through space with the ring C?O group. In these cases, only one of the two anticipated diene-ketenes (and descendents thereof) is produced. A thorough investigation of the photochemistry of a series of structurally different cyclohexa-2, 4-dienones on analytical as well as on preparative scale extends our mechanistic knowledge of the various routes from diene-ketenes into a variety of compound classes. Novel compound classes accessible to diene-ketenes are seven-membered carbocycles (by intramolecular aldolization of the zwitterion of appropriately substituted, transiently formed diene-(N, O)-ketene acetals) and β-lactams (by Staudinger reaction).     

Transitivity is neither hereditary nor finitely productive

We construct a transitive space that is the union of two subspaces homeomorphic to the (non-transitive) Kofner plane. Moreover, we show that the product of two transitive spaces need not be transitive. Finally, we observe that results of E.K. van Douwen establish that, under b = c, there exists a locally countable locally compact non-transitive zero-dimensional space. It follows that under b = c neither a locally transitive nor a compact space need be transitive.     

Rationale Tschebyscheff-Approximation über unbeschränkten Intervallen

Summary We consider rational best approximations to functions real-valued and continuous on closed unbounded intervals of the extended real numbers. The error of the best approximation is characterized by an alternant, whose length may be different from the well-known number for a bounded interval. Besides some exceptional cases the best approximation is unique.     

Über enolisierte Derivate der Chlorophyllreihe. 132-Desmethoxycarbonyl-173-desoxy-132,173-cyclochlorophyllid a-enol und eine Methode zur Einführung von Magnesium in porphinoide Ligandsysteme unter milden Bedingungen. (Vorläufige Mitteilung)

Enol derivatives in the chlorophyll series. 13²-Desmethoxycarbonyl-17³-desoxy-13²,17³-cyclochlorophyllide a-enol and a method for the introduction of magnesium into porphinoid ligands under mild conditions Magnesium transfer from the iodo-magnesium salt of 3,5-di-t-butyl-4-hydroxy-toluene (BHT) into methyl pheophorbide a is a fast process in methylenechloride/ether solution at ambient temperature. This procedure for the introduction of magnesium into labile chlorin ligands has made possible the preparation of a crystalline 13², 17³-cyclochlorophyllide a-enol. Concomitant use of the lithium salt of BHT facilitates the more critical insertion of magnesium into methyl bacteriopheophorbide a. The preparative success of these magnesium transfers depends crucially upon the solvent system used. Under conditions where the complexation of methyl pheophorbide a with iodo-magnesium-BHT is essentially complete within 2 minutes at 12° in methylenechloride/ether solution, strong inhibition of the magnesium transfer is observed by cosolvents such as pyridine, dimethylacetamide, dioxan or tetrahydrofuran.