Catalytic Asymmetric Torgov Cyclization: A Concise Total Synthesis of (+)‐Estrone

An asymmetric Torgov cyclization, catalyzed by a novel, highly Brønsted acidic dinitro‐substituted disulfonimide, is described. The reaction delivers the Torgov diene and various analogues with excellent yields and enantioselectivity. This method was applied in a very short synthesis of (+)‐estrone.     

Further remarks on simple flows of fluids with pressure-dependent viscosities

Recently Suslov and Tran (2008) [1] claimed to have found an error in one of the solutions given in the paper by Hron (2001) et al. [2] concerning the flows of fluids with pressure-dependent viscosities. We show that their arguments are related to the question of the continuity of the pressure, and we show that the original solution, although it is not a classical one, can be interpreted as a solution in a generalized sense. Mathematical and physical implications of such generalizations are briefly discussed. The discussion in the paper highlights the importance of recognizing what is meant by a “solution” to a partial differential equation, whether by a solution we mean a classical solution, a weak solution, or a solution in some other sense.     

A stereoselective synthesis of (+)-L-733,060 from ethyl (R)-(+)-2,3-epoxypropanoate

An asymmetric synthesis of neurokinin substance P receptor antagonist (+)-L-733,060 starting from enantiomerically pure ethyl (R)-(+)-2,3-epoxypropanoate (ethyl glycidate) is described. The synthesis relies on a diastereoselective reductive amination, regioselective intramolecular epoxide opening, and in situ cyclization as the key steps.     

Scale Invariance of the PNG Droplet and the Airy Process

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous sample paths, its single time (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has a slow decay of correlations as y ^–2. Roughly the Airy process describes the last line of Dyson's Brownian motion model for random matrices. Our construction uses a multi-layer version of the PNG model, which can be analyzed through fermionic techniques. Specializing our result to a fixed value of y, one reobtains the celebrated result of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation.     

Current partition in multiprobe conductors in the presence of slowly oscillating external potentials

In the presence of a static potential drop a carrier stream incident at a contact of the sample is partitioned into the other contacts according to the transmission probabilities of the sample. The bare response to oscillating potentials, on the other hand, violates current conservation due to the piling up of unscreened charges in the sample, and has to be modified by taking the induced screening potential into account. We present a novel derivation of the conductance response to oscillating external chemical potentials, find the response to an arbitrary internal potential in terms of functional derivatives with respect to the local potential of the scattering matrix of the conductor, and determine the screening potential for slowly oscillating potentials from the condition of local charge neutrality. We find that the current partitioning depends on ratios of local densities of states which reflect the injection and emission properties of the contacts of the sample.     

A canonical partition theorem for equivalence relations on Zt

A canonical version of the multidimensional version of van der Waerden's theorem on arithmetic progressions is proved.     

Ein Distributivitätskriterium für Verbände

Those one-place functions on a latticeL with values inL which can be obtained from the identityx and the constant functions by means of the fundamental operations ofL in a finite number of steps are called one-place polynomial functions. —It is shown that a latticeL is distributive iff all its one-place polynomial functions can be represented by words such that in every word the indeterminatex occurs at most once.     

Canonical partition theorems for parameter sets

A canonical (i.e., unrestricted) version of the partition theorem for k-parameter sets of Graham and Rothschild (Trans. Amer. Math. Soc.159 (1971), 257–291) is proven. Some applications, e.g., canonical versions, of the Rado-Folkman-Sanders theorem and of the partition theorem for finite Boolean algebras are given. Also the Erdös-Rado canonization theorem (J. London Math. Soc.25 (1950), 249–255) turns out to be an immediate corollary.     

Exploration of the ultimate patterning potential achievable with high resolution focused ion beams

Controlled and reproducible fabrication of nano-structured materials will be one of the main industrial challenges in the next few years. We have recently proposed exploitation of the nano-structuring potential of a high resolution Focused Ion Beam Tool, to overcome basic limitations of current nano-fabrication techniques. The aim of this article is to present some new routes for material patterning, which benefit from ion-induced local property modifications or damage. In the experiments we describe hereafter an ultra-sharp pencil of 30 keV gallium ions is used to tailor the characteristics of several materials at a scale of a few nanometres. The experimental results are then compared to simulations. First, we simulate the control of collisional defects generated in a thin magnetic layer under FIB irradiation. The results explain the stable magnetic structures we have obtained experimentally. This was achieved with a low surface ion dose (10¹² to 10¹⁴ ions/cm²). In addition we have explored the promising direction of Bottom-up or self-organization processes using a FIB instrument. We have defined artificial surface defects. These defects created by the impact of an 8-nm FWHM probe were used to pin the diffusion and to organize nanometre-sized gold clusters on a graphite surface. PACS 79.20.Rf; 81.07.-b     

Maximal regularity for evolution equations in weighted <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>-spaces

Let X be a Banach space and let A be a closed linear operator on X. It is shown that the abstract Cauchy problem enjoys maximal regularity in weighted L _p -spaces with weights , where , if and only if it has the property of maximal L _p -regularity. Moreover, it is also shown that the derivation operator admits an -calculus in weighted L _p -spaces. Received: 26 February 2003