One catalyst for both enantiomers: uncovering the inversion of enantioselectivity in cinchona-mediated desymmetrization of glutaric meso-anhydrides

A puzzling inversion of enantioselectivity dependent on catalyst loading was observed during the quinine-mediated desymmetrization of glutaric meso-anhydrides. This study presents the improvement of the catalytic path by the inclusion of carboxylic acid additives up to synthetically useful levels. The novel protocol utilizing 0.1 equiv of alkaloid and xanthene-9-carboxylic acid at room temperature (rt) was found comparable to the protocol requiring 1.1 equiv of alkaloid at ?30 °C. Thus, by altering the protocol the same catalyst produces the opposite enantiomer.This occurrence was rationalized by an extensive computational study of the interactions governing the molecular complexes formed by quinine, methanol, 3-methylglutaric anhydride, and the acetic acid. It was found that in a quinine catalyzed reaction the alcohol and the anhydride were directly hydrogen bonded to the catalyst. On the other hand, in the reaction with additive the acid intercalates between the alcohol and quinine. Due to this insertion the alcohol approaches the anhydride from the opposite face, in agreement with the observed inversion of enantioselectivity     

On the Henry constant and isosteric heat at zero loading in gas phase adsorption

The Henry constant and the isosteric heat of adsorption at zero loading are commonly used as indicators of the strength of the affinity of an adsorbate for a solid adsorbent. It is assumed that (i) they are observable in practice, (ii) the Van Hoff's plot of the logarithm of the Henry constant versus the inverse of temperature is always linear and the slope is equal to the heat of adsorption, and (iii) the isosteric heat of adsorption at zero loading is either constant or weakly dependent on temperature. We show in this paper that none of these three points is necessarily correct, first because these variables might not be observable since they are outside the range of measurability; second that the linearity of the Van Hoff plot breaks down at very high temperature, and third that the isosteric heat versus loading is a strong function of temperature. We demonstrate these points using Monte Carlo integration and Monte Carlo simulation of adsorption of various gases on a graphite surface. Another issue concerning the Henry constant is related to the way the adsorption excess is defined. The most commonly used equation is the one that assumes that the void volume is the volume extended all the way to a boundary passing through the centres of the outermost solid atoms. With this definition the Henry constant can become negative at high temperatures. Although adsorption at these temperatures may not be practical because of the very low value of the Henry constant, it is more useful to define the Henry constant in such a way that it is always positive at all temperatures. Here we propose the use of the accessible volume; the volume probed by the adsorbate when it is in nonpositive regions of the potential, to calculate the Henry constant.     

Stability and the immediate acceptance rule when school priorities are weak

In a model of school choice, we allow school priorities to be weak and study the preference revelation game induced by the immediate acceptance (IA) rule (also known as the Boston rule), or the IA game. When school priorities can be weak and matches probabilistic, three stability notions—ex post stability, ex ante stability, and strong ex ante stability—and two ordinal equilibrium notions—sd equilibrium and strong sd equilibrium—become available (“sd” stands for stochastic dominance). We show that for no combination of stability and equilibrium notions does the set of stable matches coincide with the set of equilibrium matches of the IA game. This stands in contrast with the existing result that the two sets are equal when priorities are strict. We also show that in the presence of weak priorities, the transition from the IA rule to the deferred acceptance rule may, in fact, harm some students.     

Newsvendor characterizations for one-warehouse multi-retailer inventory systems with discrete demand under the balance assumption

This paper considers a one-warehouse multi-retailer inventory system that faces discrete stochastic demand of the customers. Under the so-called balance assumption (also known as the allocation assumption), base stock policies are optimal. Our main contribution is to show that the optimal base stock levels satisfy newsvendor characterizations, which are in terms of inequalities, and to extend the newsvendor equalities known for the continuous demand model. These characterizations are appealing because they (i) are easy to explain to nonmathematical oriented people like managers and MBA students, (ii) contribute to the understanding of optimal control, (iii) help intuition development by providing direct relation between cost and optimal policy parameters.     

Ergodic averages with vector-valued Besicovitch weights

For a von Neumann algebra ${\mathcal M}$ , we introduce ${\mathcal M}$ -valued Besicovitch sequences and study the norm and individual convergences of the corresponding weighted ergodic averages. The limits of the averages are examined under the condition that the contraction in question is weakly mixing.     

Strengthened invex and perturbations

If the strengthened invex property holds for a constrained minimization problem, then a Karush-Kuhn-Tucker point is a strict minimum. The strict minimum property is preserved under small perturbations of the problem. This allows sufficient conditions to be given for a minimax, starting from Karush-Kuhn-Tucker conditions. They extend to vector-valued minimax and to nonsmooth (Lipschitz) problems. An example is provided to illustrate the strengthened invex property, also a discussion of quadratic-linear (nonconvex) programming implications.     

Critical oscillation constant for half-linear differential equations with periodic coefficients

We compute explicitly the oscillation constant for certain half-linear second-order differential equations involving periodic coefficients. If these periodic functions are constants, our results reduce to the well-known oscillation constants for half-linear Euler and Riemann–Weber differential equations.     

Optimality and duality in constrained interval-valued optimization

Fritz John and Karush–Kuhn–Tucker necessary conditions for local LU-optimal solutions of the constrained interval-valued optimization problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators are established. Under suitable assumptions on the generalized convexity of objective and constraint functions, sufficient conditions for LU-optimal solutions are given. The dual problems of Mond–Weir and Wolfe types are studied together with weak and strong duality theorems for them.     

Single bubble growth in saturated pool boiling on a constant wall temperature surface

Nucleate pool boiling experiments with constant wall temperatures were performed using R11 and R113 for saturated pool boiling conditions. A microscale heater array and Wheatstone bridge circuits were used to maintain a constant wall temperature condition and to obtain measurements with high temporal and spatial resolution. Accurate heat flow rate data were obtained from microscale heater array by controlling the surface conditions at a high temporal resolution. Images of the bubble growth were captured using a high-speed CCD camera synchronized with the heat flow rate measurements. The geometry of the bubble was obtained from the images. In the asymptotic growth region, the bubble showed a growth rate that was proportional to t^1/5, which was slower than the growth rate proposed in previous analytical analyses. The bubble growth behavior was analyzed using a new dimensionless parameter to permit comparisons with previous results at the same scale. The comparisons showed good agreement in the asymptotic growth region. A non-dimensional correlation for the bubble radius that can predict the bubble growth and the heat flow rate simultaneously, was suggested. The required heat flow rate for the volume change of the observed bubble was estimated to be larger than the instantaneous heat flow rate measured from the wall. Heat, other than the instantaneous heat supplied from the wall, is estimated to be transferred through the interface between bubble and liquid, even with saturated pool conditions. This phenomenon under a saturated pool condition needs to be analyzed and the data from this study can supply the good experimental data with the precise boundary condition (constant wall temperature).