This is a very nice follow-up paper to a previously reported kinetic resolution ofα-hydroxy esters by Toste and co-workers (J. Am. Chem. Soc. 2005, 127, 1090-1091). A variety of enantioenriched tetrahydrofurans and tetrahydropyrans can be accessed by this method. High diastereoselectivities and enantioselectivies were obtained through careful optimization of the conditions. Acetone was found to be the solvent of choice, giving the best yields of the desired products.
Using the notion of fading memory we prove very strong versions of two folk theorems. The first is that any time-invariant (TI) continuous nonlinear operator can be approximated by a Volterra series operator, and the second is that the approximating operator can be realized as a finite-dimensional linear dynamical system with a nonlinear readout map. While previous approximation results are valid over finite time intervals and for signals in compact sets, the approximations presented here hold for all time and for signals in useful (noncompact) sets. The discretetime analog of the second theorem asserts that any TI operator with fading memory can be approximated (in our strong sense) by a nonlinear moving- average operator. Some further discussion of the notion of fading memory is given.
An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
This stage of our journey through the universe of one-dimensional binary Cellular Automata is devoted to period-1 rules, constituting the first of the six groups in which we systematized the 88 globally-independent CA rules. The first part of this article is mainly dedicated to reviewing the terminology and the empirical results found in the previous papers of our quest. We also introduce the concept of the ω-limit orbit with the purpose of linking our work to the classical theory of nonlinear dynamical systems. Moreover, we present the basin tree diagrams of all period-1 rules — except for rule [Formula: see text], which is trivial — along with their Boolean cubes and time-1 characteristic functions. In the second part, we prove a theorem demonstrating that all rules belonging to group 1 have robust period-1 rules for any finite, and infinite, bit-string length L. This is the first time we give analytical results on the behavior of CA local rules for large values of L and, consequently, for bi-infinite bit strings. The theoretical treatment is complemented by two remarkable practical results: an explicit formula for generating isomorphic basin trees, and an algorithm for creating new periodic orbits by concatenation. We also provide several examples of both of them, showing how they help to avoid tedious simulations.
Sum frequency generation (SFG) surface vibrational spectroscopy has been used to identify reactive surface intermediates in situ during catalytic dehydrogenation reactions of high-pressure cyclohexane (C(6)H(12)) on the Pt(111) crystal surface in the presence and absence of high-pressure hydrogen. These experiments provide the first spectroscopic evidence of cyclohexyl (C(6)H(11)) as a reactive surface intermediate during the cyclohexane catalytic conversion to benzene at high pressure in the presence of excess hydrogen. In addition, it was proposed from temperature-dependent SFG experiments that dehydrogenation of cyclohexyl is a rate-limiting step in the cyclohexane catalytic conversion to benzene.
