Synthetic Approach to Kdo Glycosides Via Exo-Glycal Epoxides and Rationalization of the Stereo Chemical Outcome

Abstract

The use of epoxides obtained by dimethyldioxirane epoxidation of 2,3-anhydro-1,3-dideoxy-4,5:7,8-di-O-isopropylidene-D-manno-oct-1-enitol as glycosyl donors is described. This method offers a simple and stereoselective access to precursors of Kdo glycosides. The stereochemical outcome of the reaction is rationalized by means of semiempirical calculations of the transition states leading to glycosides formation.     

Switching Time and Parameter Optimization in Nonlinear Switched Systems with Multiple Time-Delays

In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the state system forward in time followed by a costate system backward in time. This gradient computation procedure can be combined with any gradient-based optimization method to determine the optimal switching times and parameters. We propose an effective optimization algorithm based on this idea. Finally, we consider three numerical examples, one involving the 1,3-propanediol fed-batch production process, to illustrate the effectiveness and applicability of the proposed algorithm.     

Rapid characterization of edible oils by direct matrix-assisted laser desorption/ionization time-of-flight mass spectrometry analysis using triacylglycerols

Direct matrix-assisted laser desorption/ionization time-of-flight mass spectrometric (MALDI-TOFMS) analysis of solutions of edible fats/oils yielded spectra useful for their rapid differentiation and classification. Results also reflected the individual fatty acid components and their degree of unsaturation. After dissolution in hexane, MALDI-MS analysis revealed spectra showing characteristic triacylglycerols (TAGs), the main fat/oil components, as sodium adduct ions. The Euclidean distances calculated using the mass and intensity values for 20 TAGs were used to evaluate and compare spectra. With cluster analysis, animal fats grouped together differently than vegetable oils and the individual oils grouped together by type. The ion abundances for the individual TAGs and their presumed compositions were used to approximate the overall fatty acid composition of canola, soybean, corn, olive and peanut oil, as well as lard. Using this approach the calculated fatty acid compositions and degree of unsaturation generally fell within about 4% of literature values. When the degree of saturation was compared with values calculated from the package labeling the differences were about 7%.     

Anchoring and electro-optical dynamics of thin liquid crystalline films in a polyimide cell: experiment and theory

The surface-dependent anchoring and electro-optical (EO) dynamics of thin liquid crystalline films have been examined using Fourier transform infrared spectroscopy. A simple nematic liquid crystal, 4-n-pentyl-4'-cyanobiphenyl (5CB), is confined as 40, 50, and 390 nm thick films in nanocavities defined by gold interdigitated electrode arrays (IDEAs) patterned on polyimide-coated zinc selenide (ZnSe) substrates [Noble et al., J. Am. Chem. Soc. 124, 15020 (2002)]. New strategies for controlling the anchoring interactions and EO dynamics are explored based on coating a ZnSe surface with an organic polyimide layer in order to both planarize the substrate and induce a planar alignment of the liquid crystalline film. The polyimide layer can be further treated so as to induce a strong alignment of the nematic director along a direction parallel to the electrode digits of the IDEA. Step-scan time-resolved spectroscopy measurements were made to determine the rate constants for the electric-field-induced orientation and thermal relaxation of the 5CB films. In an alternate set of experiments, uncoated ZnSe substrates were polished unidirectionally to produce a grooved surface presenting nanometer-scale corrugations. The dynamical rate constants measured for several nanoscale film thicknesses and equilibrium organizations of the director in these planar alignments show marked sensitivities. The orientation rates are found to vary strongly with both the magnitude of the applied potential and the initial anisotropy of the alignment of the director within the IDEA. The relaxation rates do not vary in this same way. The marked variations seen in EO dynamics can be accounted for by a simple coarse-grained dynamical model.     

Razumikhin-type theorems on exponential stability of impulsive delay systems

^** Corresponding author. Email: xzliu{at}math.uwaterloo.ca This paper studies the exponential stability of impulsive delaysystems. By employing the Razumikhin technique and Lyapunovfunctions, several exponential stability criteria are establishedfor both linear and non-linear impulsive delay systems. Someexamples are also worked through to illustrate our results.     

Necessary and Sufficient Optimality Conditions for Regular–Singular Stochastic Differential Games with Asymmetric Information

We consider a class of regular–singular stochastic differential games arising in the optimal investment and dividend problem of an insurer under model uncertainty. The information available to the two players is asymmetric partial information and the control variable of each player consists of two components: regular control and singular control. We establish the necessary and sufficient optimality conditions for the saddle point of the zero-sum game. Then, as an application, these conditions are applied to an optimal investment and dividend problem of an insurer under model uncertainty. Furthermore, we generalize our results to the nonzero-sum regular–singular game with asymmetric information, and then the Nash equilibrium point is characterized.