Practical method for crystalline-liquid resolution of chrysanthemic acids utilizing chiral 1,1′-binaphthol monoethyl ethers directed for process chemistry

We have developed an efficient practical resolution method for (1R,3R)-trans-chrysanthemic acid 1 and (1R,3S)-trans-2,2-dimethyl-3-(2,2-dichloroethenyl)cyclopropanecarboxylic acid 2, based on the preliminary results of the simpler analogues, (1R)-2,2-dichlorocyclopropanecarboxylic acid 3 and (1R)-2,2-dimethylcyclopropanecarboxylic acid 4, using a crystalline-liquid separation procedure (without column chromatography) with chiral 1,1′-binaphthol monoethyl ethers (R)-5b as the key auxiliary. Direct esterifications of 1, 2, 3, and 4 with (R)-5b gave four sets of (1R)- and (1S)-diastereomeric esters 8, 9, 6, and 7, respectively, with markedly different melting points. All of these diastereomers were easily obtained using a simple and one-step crystalline-liquid separation. The separated diastereomers 8 and 9 were easily hydrolyzed to the desired enantiopure acids 1 (>98%) and 2 (>99%), respectively, with recovery of (R)-5b (>90%).     

Primal-Dual Active-Set Algorithm for Chemical Equilibrium Problems Related to the Modeling of Atmospheric Inorganic Aerosols

A general equilibrium model for multiphase multicomponent inorganic atmospheric aerosols is proposed. The thermodynamic equilibrium is given by the minimum of the Gibbs free energy for a system involving an aqueous phase, a gas phase, and solid salts. A primal-dual algorithm solving the Karush-Kuhn-Tucker conditions is detailed. An active set/Newton method permits to compute the minimum of the energy and tracks the presence or not of solid salts at the equilibrium. Numerical results show the efficiency of our algorithm for the prediction of multiphase multireaction chemical equilibria.Communicated by R. GlowinskiThis work has been partially supported by the United States Environmental Protection Agency through Cooperative Agreement X-83234201 to the University of Houston. The second author was supported by the Swiss National Science Foundation, Grant PBEL2-103152.     

The Almost Pasting Property of Digital Continuity

The pasting property plays a significant role in studying a continuous map in general topology. Unlike the pasting property, digital continuity has some intrinsic features. In this paper we prove that digital continuity has the almost pasting property instead of the pasting one. Furthermore, as a digital version of the straightness of a metric space, we introduce the notion of k-straightness of a digital space (X,k) and study its properties which can be used in image synthesis and digital image weaving.     

Efficient and stereoselective synthesis of threo-β-hydroxy-l-glutamic acid via a tandem (Z)-olefination-conjugate addition

threo-β-Hydroxy-l-glutamic acid 1 is an attractive target as a biologically active compound and as a chiral synthon. The required β-hydroxyl group in 1 was efficiently and stereoselectively introduced via an intramolecular conjugate addition of the N-hydroxymethyl group of γ-amino-α,β-unsaturated (Z)-ester 4. While the corresponding (E)-ester 3 gave a lower selectivity of ca. 5:1 in the intramolecular conjugate addition, a selectivity of up to 70:1 was shown with (Z)-ester 4. The tandem (Z)-olefination-conjugate addition could be achieved by simply changing the reaction conditions to give a selectivity of >20:1. Thus, the target compound 1 was obtained as its hydrochloride salt in 70% overall yield over four steps from lactol 2.     

Fluorescent studies of two new binaphthyl-azacrown-anthracene fluorophores with metal ions and chiral guests: dual fluorescent detection via binaphthyl and anthracene groups

Two new binaphthyl-azacrown-anthracene fluorophores were synthesized. These new fluorescent receptors exhibited large fluorescent changes with aqueous Hg²⁺, Cu²⁺ and Zn²⁺. Interestingly, the fluorescent emissions from the binaphthyl and anthracene groups using different excitation wavelengths showed different patterns in the presence of metal ions. The chiral recognitions of these receptors with chiral ammonium guests were also examined.     

Sufficient dimension reduction for the conditional mean with a categorical predictor in multivariate regression

Recent sufficient dimension reduction methodologies in multivariate regression do not have direct application to a categorical predictor. For this, we define the multivariate central partial mean subspace and propose two methodologies to estimate it. The first method uses the ordinary least squares. Chi-squared distributed statistics for dimension tests are constructed, and an estimate of the target subspace is consistent and efficient. Moreover, the effects of continuous predictors can be tested without assuming any model. The second method extends Iterative Hessian Transformation to this context. For dimension estimation, permutation tests are used. Simulated and real data examples for illustrating various properties of the proposed methods are presented.     

Robust memory state feedback model predictive control for discrete-time uncertain state delayed systems

In this paper, we propose a memory state feedback model predictive control (MPC) law for a discrete-time uncertain state delayed system with input constraints. The model uncertainty is assumed to be polytopic, and the delay is assumed to be unknown, but with a known upper bound. We derive a sufficient condition for cost monotonicity in terms of LMI, which can be easily solved by an efficient convex optimization algorithm. A delayed state dependent quadratic function with an estimated delay index is considered for incorporating MPC problem formulation. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Therefore, a less conservative sufficient conditions in terms of linear matrix inequality (LMI) can be derived to design a more robust MPC algorithm. A numerical example is included to illustrate the effectiveness of the proposed method.