Strong enantioselective self-recognition of a small chiral molecule

In the present report, we have crystallized a single enantiomer and the racemate of N-3,5-dinitrobenzoyl (DNB) leucine. In both cases, the X-ray structures show clear evidence of homochiral dimerization in the solid state. Moreover, only homochiral dimers were observed in the unit cell of the racemate, a result of solid-state enantioselective complexation. The crystal structures support a chiral recognition mechanism involving two hydrogen bonds and an offset pi-pi interaction between the DNB rings.     

Supramolecular triad and pentad composed of zinc-porphyrin(s), oxoporphyrinogen, and fullerene(s): design and electron-transfer studies

By adopting a "covalent-coordinate" bonding approach, novel supramolecular pentad and triad molecules composed of zinc-porphyrin(s), fullerene(s), and oxoporphyrinogen redox-/photoactive entities have been constructed, and also characterized by means of spectral and electrochemical techniques. The geometry and electronic structures of the pentad and the triad were deduced by means of DFT calculations. Free-energy calculations suggested that the photoinduced electron/energy transfer from the zinc-porphyrin (ZnP) singlet-excited state to the imidazole modified fullerene (ImC(60)) acceptor and oxoporphyrinogen (OxP) entities is feasible for both the triad and the pentad. The charge-separation rates (k(CS)) determined from picosecond time-resolved emission studies were higher for pentad (C(60)Im:ZnP)(2)-OxP than for the corresponding triad, C(60)Im:ZnP-OxP. A comparison of the k(CS) values previously reported for the covalently linked bis(zinc-porphyrin)-oxoporphyrinogen triad suggests that employing a fullerene acceptor improves the electron-transfer rates. Nanosecond transient absorption studies provide evidence for the occurrence of electron-transfer processes. Lifetimes of the radical ion pairs (tau(RIP)) are in the range of hundreds of nanoseconds, which indicates that there is charge stabilization in the supramolecular systems.     

Tautomerism in novel oxocorrologens

A novel corrole-type macrocycle, oxocorrologen (2), substituted with hemiquinone groups, has been synthesized. It was found to undergo multiple tautomerism of its exchangeable protons between electronegative atom sites at the macrocyclic core (nitrogen atoms) and periphery (phenol oxygen atoms). Alkylation at one macrocyclic nitrogen atom with a 4-nitrobenzyl group gave 3, which can exist in only two tautomeric forms depending on the solvent. Tautomerism has been studied by means of (1)H NMR spectroscopy in a variety of solvents and solvent mixtures. Tautomer structure assignments have been supported by DFT calculations of the relative energies of the tautomers. X-ray crystallography of the N-nitrobenzyl derivative has revealed that intramolecular hydrogen bonding may be responsible for stabilizing the observed tautomers. The solvent dependence of the tautomerism of 2 and 3 confers solvatochromism. Electrochemical measurements on 2 and 3 in their respective quinone forms have revealed irreversible processes, but indicate that they are both electron-deficient with a small HOMO-LUMO gap and first reduction potentials close to those of fullerene electron acceptors.     

Dolphin (Tursiops truncatus) echoic angular discrimination: effects of object separation and complexity

A bottlenose dolphin was tested on its ability to echoically discriminate horizontal angular differences between arrays of vertically oriented air-filled PVC rods. The blindfolded dolphin was required to station in a submerged hoop 2 radial m from the stimuli and indicate if an array with two rods (S+) was to the right or the left of a single rod (S-). The angular separation between the two rods (thetaw) was held constant within each experiment while the angle between the S+ and the S-stimuli (thetab) varied to produce angular differences (deltatheta= thetab-thetaw) ranging from 0.25 to 4 degrees. In experiment I, thetaw was maintained at 2 degrees and in experiment II, thetaw was maintained at 4 degrees. Resulting 75% correct thresholds (method of constant stimuli) were 1.5 and 0.7 degrees, respectively. The two main findings of this study are: (1) decreasing the number of targets does not aid in localization, and (2) increasing the space between the rods enhances localization. Taken as a whole, the experiments suggest dolphins have a well-developed ability to resolve spatial information through sonar.     

Loop Groups, Anyons and the Calogero–Sutherland Model

The positive energy representations of the loop group of U(1) are used to construct a boson-anyon correspondence. We compute all the correlation functions of our anyon fields and study an anyonic W-algebra of unbounded operators with a common dense domain. This algebra contains an operator with peculiar exchange relations with the anyon fields. This operator can be interpreted as a second quantized Calogero–Sutherland (CS) Hamiltonian and may be used to solve the CS model. In particular, we inductively construct all eigenfunctions of the CS model from anyon correlation functions, for all particle numbers and positive couplings. Received: 12 May 1998 / Accepted: 4 August 1998     

Scaling units via the canonical correlation analysis in the DEA context

This paper deals with the evaluation of decision making units which have multiple inputs and outputs. A new method (CCA/DEA) is developed where the Canonical Correlation Analysis (CCA) is utilized to provide a full rank scaling for all the units rather than a categorical classification (for efficient and inefficient units) as done by the Data Envelopment Analysis (DEA). The CCA/DEA approach is an attempt to bridge the gap between the frontier approach of DEA and the average tendencies of statistics (econometrics). Nonparametric statistical tests are employed to validate the consistency between the classification from the DEA and the postclassification that was generated by the CCA/DEA.     

AN ADAPTIVE FINITE ELEMENT SCHEME FOR HYDRAULIC FRACTURING WITH PROPPANT TRANSPORT

A mathematical model and adaptive finite element scheme are developed for describing the distribution of proppant in a propagating hydraulic fracture. The governing equation for proppant concentration is derived by applying the conservation law of mass to the proppant and to the proppant-laden fluid. Shah's empirical equation, which relates the proppant concentration and the indices of the non-Newtonian fluid, is used to describe the proppant-laden fluid. The proppant distribution inside a hydraulic fracture can then be obtained by solving the proppant concentration equation together with the governing equations of fluid and elasticity for a hydraulic fracturing. A novel moving grid scheme is developed that combines grid point insertion with redistribution. Four examples corresponding to different in situ stress distributions are computed to demonstrate the scheme. © 1997 by John Wiley & Sons, Ltd.     

Free-surface flow over curved surfaces: Part I: Perturbation analysis

The standard two-dimensional shallow water equation formulation assumes a mild bed slope and no curvature effect. These assumptions limit the applicability of these equations for some important classes of problems. In particular, flow over a spillway is affected by the bed curvature via a decidedly non-hydrostatic pressure distribution. A detailed derivation of a more general equation set is given here in Part I. The method relies upon a perturbation expansion to simplify a bed-fitted co-ordinate configuration of the three-dimensional Euler equations. The resulting equations are essentially the equivalent of the two-dimensional shallow water equations but with curvature included and without the mild slope assumption. A finite element analysis and flume result are given in Part II. © 1998 John Wiley & Sons, Ltd.     

Spectral flow invariants and twisted cyclic theory for the Haar state on

In [A.L. Carey, J. Phillips, A. Rennie, Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras. arXiv:0801.4605], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only non-faithful traces, namely SU_q(2) and also KMS states. Our main results are index theorems (which calculate spectral flow), one using ordinary cyclic cohomology and the other using twisted cyclic cohomology, where the twisting comes from the generator of the modular group of the Haar state. In contrast to the Cuntz algebras studied in [A.L. Carey, J. Phillips, A. Rennie, Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras. arXiv:0801.4605], the computations are considerably more complex and interesting, because there are non-trivial ‘eta’ contributions to this index.