Solving mixed-integer robust optimization problems with interval uncertainty using Benders decomposition

Uncertainty and integer variables often exist together in economics and engineering design problems. The goal of robust optimization problems is to find an optimal solution that has acceptable sensitivity with respect to uncertain factors. Including integer variables with or without uncertainty can lead to formulations that are computationally expensive to solve. Previous approaches for robust optimization problems under interval uncertainty involve nested optimization or are not applicable to mixed-integer problems where the objective or constraint functions are neither quadratic, nor linear. The overall objective in this paper is to present an efficient robust optimization method that does not contain nested optimization and is applicable to mixed-integer problems with quasiconvex constraints (? type) and convex objective funtion. The proposed method is applied to a variety of numerical examples to test its applicability and numerical evidence is provided for convergence in general as well as some theoretical results for problems with linear constraints.     

Homogeneous and unimolecular gas‐phase thermal decomposition kinetics of methyl benzoylformate: experimental and theoretical study

The kinetics of the gas‐phase thermal decomposition of the α‐ketoester methyl benzoylformate was carried out in a static system with reaction vessel deactivated with allyl bromide, and in the presence of the free radical inhibitor propene. The rate coefficients were determined over the temperature range of 440–481 °C and pressures from 32 to 80 Torr. The reaction was found to be homogenous, unimolecular and obey a first‐order rate law. The products are methyl benzoate and CO. The temperature dependence of the rate coefficient gives the following Arrhenius parameters: log₁₀ k (s^?1) = 13.56 ± 0.31 and E_a (kJ mol^?1) = 232.6 ± 4.4. Theoretical calculations of the kinetic and thermodynamic parameters are in good agreement with the experimental values using PBE1PBE/6‐311++g(d,p). A theoretical Arrhenius plot was constructed at this level of theory, and the good agreement with the experimental Arrhenius plot suggests that this model of transition state may describe reasonably the elimination process. These results suggest a concerted non‐synchronous semi‐polar three‐membered cyclic transition state type of mechanism. The most advanced coordinate is the bond breaking C^δ+‐‐‐^δ‐OCH₃ with an evolution of 66.7%, implying this as the limiting factor of the elimination process. Copyright © 2014 John Wiley & Sons, Ltd.     

Gas‐phase elimination kinetics of selected aliphatic α,β‐unsaturated aldehydes catalyzed by hydrogen chloride

The gas‐phase elimination of 2‐methyl‐2‐propenal catalyzed by HCl yields propene and CO gas, while E‐2‐pentenal with the same catalyst gives butene and CO gas. The kinetics determinations were carried out in a static system with the reaction vessels deactivated with allyl bromide and the presence of the free radical inhibitor toluene. Temperature and pressure ranges were 350.0–410.0 °C and 34–76 Torr. The elimination reactions are homogeneous and unimolecular, and follow a first‐order rate law. The rate coefficients for the reactions are expressible by the following Arrhenius equations: Data from the kinetic and thermodynamic parameters of these catalyzed elimination reactions implies a mechanism of a concerted five‐membered cyclic transition state structure for the formation of the corresponding olefin and carbon monoxide. Copyright © 2015 John Wiley & Sons, Ltd.     

Stereospecific Formal [3+2] Dipolar Cycloaddition of Cyclopropanes with Nitrosoarenes: An Approach to Isoxazolidines

The MgBr₂‐catalyzed formal [3+2] cycloaddition of donor–acceptor activated cyclopropanes with nitrosoarenes offers a novel approach to various structurally diverse isoxazolidines. The reactions, which are experimentally easy to conduct, occur with complete stereospecificity and perfect control of regioselectivity. Product isoxazolidines can be readily transformed into α‐amino lactones by reductive or decarboxylative N? O cleavage and subsequent lactonisation, and the N‐aryl bond cleavage is also possible under oxidative conditions.     

Ab Initio Study on the Stability of NgnBe2N2, NgnBe3N2 and NgBeSiN2 Clusters

The global minima of Be₂N₂, Be₃N₂ and BeSiN₂ clusters are identified using a modified stochastic kick methodology. The structure, stability and bonding nature of these clusters bound to noble gas (Ng) atoms are studied at the MP2/def2‐QZVPPD level of theory. Positive Be?Ng bond dissociation energy, which gradually increases down Group 18 from He to Rn, indicates the bound nature of Ng atoms. All of the Ng‐binding processes are exothermic in nature. The Xe and Rn binding to Be₂N₂ and Be₃N₂ clusters and Ar?Rn binding to BeSiN₂ are exergonic processes at room temperature; however, for the lighter Ng atoms, lower temperatures are needed. Natural population analysis, Wiberg bond index computations, electron density analysis, and energy decomposition analysis are performed to better understand the nature of Be?Ng bonds.     

A Pressure-Induced Inverse Order–Disorder Transition in Double Perovskites

Given the consensus that pressure improves cation ordering in most of known materials, a discovery of pressure-induced disordering could require recognition of an order–disorder transition in solid-state physics/chemistry and geophysics. Double perovskites Y₂CoIrO₆ and Y₂CoRuO₆ polymorphs synthesized at 0, 6, and 15 GPa show B-site ordering, partial ordering, and disordering, respectively, accompanied by lattice compression and crystal structure alteration from monoclinic to orthorhombic symmetry. Correspondingly, the long-range ferrimagnetic ordering in the B-site ordered samples are gradually overwhelmed by B-site disorder. Theoretical calculations suggest that unusual unit-cell compressions under external pressures unexpectedly stabilize the disordered phases of Y₂CoIrO₆ and Y₂CoRuO₆.     

Photocontrolled Release of the Anticancer Drug Chlorambucil with Caged Harmonic Nanoparticles

While chemotherapy is one of the most used treatments in oncology, the systemic administration of chemotherapeutics generally results in undesired damages to healthy tissues and cells, side effects such as severe nausea and leukopenia, and reduced efficacy due to multidrug resistance and poor target accessibility. The limitations of conventional chemotherapy formulation have prompted the development of alternative nanomaterials-based strategies to achieve targeted and stimuli sensitive payload delivery to reach optimal local drug concentration at tumor sites. In this study, the anticancer drug chlorambucil (Clb) was conjugated to the surface of silica coated lithium niobate (LNO) harmonic nanoparticles (HNPs) using a photocaging tether based on coumarin-4-yl methyl derivative. Upon laser pulsed femtosecond irradiation at 790 nm, the second harmonic emission from the metal oxide core induced the efficient release of Clb, with concomitant contribution from the nonlinear absorption of the coumarin (CM)-based moiety.