Shadow price of information in discrete time stochastic optimization

Mathematical Programming - The shadow price of information has played a central role in stochastic optimization ever since its introduction by Rockafellar and Wets in the mid-seventies. This...     

Application of enriched stable 196Hg isotope for monitoring the stability of total mercury in water samples

A novel tool for the investigation of stability of total mercury in water samples is presented. The study focuses on the application of enriched ¹⁹⁶Hg stable isotopic reagent for the stability studies. Natural abundance of ¹⁹⁶Hg in water samples is only 0.15%. Thus, the use of the ¹⁹⁶Hg isotope spike represents a major advantage, when it can be assumed that all the measured isotope is the same as is accurately added by the analyst, and the change in its mass concentration can be followed simply and reliably. Tests were carried out with industrial waste water and two type of the natural water. Cold vapour (CV) inductively coupled plasma mass spectrometer (ICP-MS) technique was applied for the mercury measurements. Monitoring was continued for approximately 100 days. It is commonly advised that the measurement for total mercury in water samples should be carried out within 14 days. In this study the samples were observed to be stable for more than three months, if they were stored at a temperature of 4–6°C. The results of this stability study were in line with the guidance presented in EPA standard 1631. However, the samples were noticed to be stable for a much longer time than is presented in the standard method ISO 17852.     

Heat Transport in Unsaturated Zone Thermal Energy Storage – Analysis with Two-Phase and Single-Phase Models

We analyze a field experiment where ambient air is injected into the soil during the summer and extracted again during the winter. A multiphase model accounting for the conductive transport as well as the convective transport with the moving liquid and gas phases is used along with a more simplified single-phase model where the convective transport is due to the gas alone. The latter model also accounts for subzero wintertime temperatures. The multiphase model captures well both the seasonal variations and the actual test sequence, the main calibration being in the adjustment of medium permeabilities based on the observed pressure responses. The effect of the injection pump on the temperature and humidity of the injection air needs to be known accurately. Taking into account the humidity of the injection air explicitly instead of using humidity-corrected enthalpy values also has an effect. The effect of various humidity and specific enthalpy assumptions is of the order of 1–1.5°C, while ignoring the wintertime subzero temperatures has an effect of 1–2°C. These differences are of the same order of magnitude as the heterogeneity-introduced differences in field data. Using the simplified single-phase model typically appears to cause a difference of 1–2°C, but can yield an even higher deviation of the order of 3–4°C.     

A One‐Pot Synthesis of N‐Aryl‐2‐Oxazolidinones and Cyclic Urethanes by the Lewis Base Catalyzed Fixation of Carbon Dioxide into Anilines and Bromoalkanes

The multicomponent assembly of pharmaceutically relevant N‐aryl‐oxazolidinones through the direct insertion of carbon dioxide into readily available anilines and dibromoalkanes is described. The addition of catalytic amounts of an organosuperbase such as Barton's base enables this transformation to proceed with high yields and exquisite substrate functional‐group tolerance under ambient CO₂ pressure and mild temperature. This report also provides the first proof‐of‐principle for the single‐operation synthesis of elusive seven‐membered ring cyclic urethanes.     

Alnumycins A2 and A3: new inverse-epimeric pairs stereoisomeric to alnumycin A1

Two new pairs of stereoisomeric alnumycin As, A2 {(2)-(1R,1′RS,4′SR,5′SR)} and A3 {(2)-(1R,1′RS,4′SR,5′RS)}, are described. Similar to alnumycin A1 {(2)-(1R,1′RS,4′RS,5′SR)}, each of these naturally occurring compounds is also a pair of C-1 inverse epimers. The relative configurations of the dioxane ring sidechains were assigned on the basis of ¹H NMR NOE contacts and molecular modeling using density functional theory (DFT) at the M06-2X/6-31G(d) level of theory. The absolute configurations of C-1 and the determination of inverse epimeric relationships were achieved by experimental electronic circular dichroism (ECD) measurements, with both aspects confirmed by using the chiral derivatizing agent (CDA) Mosher′s acid chloride {α-methoxy-α-trifluorophenylacetyl chloride (MTPACl)} to effect enantiodifferentiation. The absolute configurations of the dioxane ring using the CDA could only be effected in the case of alnumycin A1, the results of which were in agreement with previous assignments. The dioxane ring conformational mobility and the likely interaction between the MTPA groups coupled with the structural novelty of the diols in the dioxane ring with respect to CDA analysis precluded an absolute configuration assignment for alnumycins A2 and A3 based on empirical comparisons or by computational analysis of through-space NMR shieldings (TSNMRS) emanating from the phenyl groups of the MTPA moieties.     

Stochastic programs without duality gaps

This paper studies dynamic stochastic optimization problems parameterized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programming equations, whose validity is established under new relaxed conditions that generalize certain no-arbitrage conditions from mathematical finance.     

Multivariate Association of Graph-Theoretic Variables and Physicochemical Properties

Abstract

We used canonical correlation analysis to examine the multivariate association between two distinct data sets commonly measured or calculated for approximately 600 chemicals: (1) measured or calculated values of select physieochemical properties (i.e., K _ow, boiling point, heat of vaporization, molecular weight, water solubility, molecular volume, hydrogen bonding potential, and vapor pressure) and (2) calculated algorithmically-derived variables (i.e., topological and neighborhood indices derived from graph theory). Canonical correlation analysis identified eight highly significant associations between linear combinations of graph-theoretic variables and linear combinations of physicochemical properties. The set of graph theoretic variables was significantly related to all physieochemical properties, explaining 55% to 99% of the variation in these properties.     

Direct Evidence of Significantly Different Chemical Behavior and Excited‐State Dynamics of 1,7‐ and 1,6‐Regioisomers of Pyrrolidinyl‐Substituted Perylene Diimide

Novel bay‐functionalized perylene diimides with additional substitution sites close to the perylene core have been prepared by the reaction between 1,7(6)‐dibromoperylene diimide 6 (dibromo‐PDI) and 2‐(benzyloxymethyl)pyrrolidine 5 . Distinct differences in the chemical behaviors of the 1,7‐ and 1,6‐regioisomers have been discerned. While the 1,6‐dibromo‐PDI produced the corresponding 1,6‐bis‐substituted derivative more efficiently, the 1,7‐dibromo‐PDI underwent predominant mono‐debromination, yielding a mono‐substituted PDI along with a small amount of the corresponding 1,7‐bis‐substituted compound. By varying the reaction conditions, a controlled stepwise bis‐substitution of the bromo substituents was also achieved, allowing the direct synthesis of asymmetrical 1,6‐ and 1,7‐PDIs. The compounds were isolated as individual regioisomers. Fullerene (C₆₀) was then covalently linked at the bay region of the newly prepared PDIs. In this way, two separate sets of perylene diimide–fullerene dyads, namely single‐bridged (SB‐1,7‐PDI‐C₆₀ and SB‐1,6‐PDI‐C₆₀) and double‐bridged (DB‐1,7‐PDI‐C₆₀ and DB‐1,6‐PDI‐C₆₀), were synthesized. The fullerene was intentionally attached at the bay region of the PDI to achieve close proximity of the two chromophores and to ensure an efficient photoinduced electron transfer. A detailed study of the photodynamics has revealed that photoinduced electron transfer from the perylene diimide chromophore to the fullerene occurs in all four dyads in polar benzonitrile, and also occurs in the single‐bridged dyads in nonpolar toluene. The process was found to be substantially faster and more efficient in the dyads containing the 1,7‐regioisomer, both for the singly‐ and double‐bridged molecules. In the case of the single‐bridged dyads, SB‐1,7‐PDI‐C₆₀ and SB‐1,6‐PDI‐C₆₀, different relaxation pathways of their charge‐separated states have been discovered. To the best of our knowledge, this is the first observation of photoinduced electron transfer in PDI‐C₆₀ dyads in a nonpolar medium.     

Graph-distance convergence and uniform local boundedness of monotone mappings

In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uniformly locally bounded around any point from the interior of the domain of the limit mapping. The result is an extension of a similar one from finite dimensions. As an application we give a simplified condition for the stability (under graph-distance convergence) of the sum of maximal monotone mappings in Hilbert spaces.