The mixed vertex packing problem

We study a generalization of the vertex packing problem having both binary and bounded continuous variables, called the mixed vertex packing problem (MVPP). The well-known vertex packing model arises as a subproblem or relaxation of many 0-1 integer problems, whereas the mixed vertex packing model arises as a natural counterpart of vertex packing in the context of mixed 0-1 integer programming. We describe strong valid inequalities for the convex hull of solutions to the MVPP and separation algorithms for these inequalities. We give a summary of computational results with a branch-and-cut algorithm for solving the MVPP and using it to solve general mixed-integer problems. Received: June 1998 / Accepted: February 2000?Published online September 20, 2000     

Rhodium(I) catalyzed carbonylation reactions of halides and ethers

Benzylic bromides and methyl iodide react with ethers, carbon monoxide, potassium iodide, and the dimer of chloro(1,5-hexadiene)rhodium($\text{I}$) to give esters in good yields.     

Preparation,Characterization and Thermal Energy Storage Properties of Micro/Nano Encapsulated Phase Change Material with Acrylic-Based Polymer

The eutectic mixture of octacosane (C28)–heptadecane (C17) as core material was successfully encapsulated with an acrylic-based polymer (polymethylmethacrylate; PMMA) as shell material through emulsion polymerization. The polymeric reaction occurred around the core material was characterized by FTIR spectroscopy analysis. The polarized optical microscopy, scanning electron microscopy and particle size distribution investigations showed that the most of the prepared capsules had almost spherical shape with non-unimodal size distribution in micro-nano range. The differential scanning calorimetry analysis results exhibited that the capsules including highest amount of the eutectic PCM had a melting temperature of about 21°C and a latent heat capacity of about 98 J/g. The high thermal durability of the prepared capsules was confirmed by thermogravimetric analysis. The thermal cycling test designated that the synthesized capsules had good long-term usage latent heat thermal energy storage (LHTES) performance and chemical stability. Furthermore; the fabricated capsules with (1: 2) shell/core ratio had a reasonable thermal conductivity. It can be drawn a conclusion from all results that the prepared capsules especially PMMA/(C28–C17) (1: 2) product is a hopeful PCM that can be evaluated for low-temperature LHTES applications.     

Photoinduced Rearrangement of Dienones and Santonin Rerouted by Amines

The photoinduced rearrangement pathways of simple 2,5‐dienones and the natural product santonin were found to be effectively rerouted by amines, giving rise to unprecedented products. Either cis olefins or cyclobutenes were obtained from 4,4‐disubstituted 2,5‐dienone upon irradiation (365 nm) in the presence of various amines depending on the solvent. Previously undescribed [4.4.0] and [5.3.0] fused‐ring‐containing products were obtained when santonin was irradiated (365 nm) in the presence of methylamine. The amines present in these reactions were incorporated into the products by means of amide‐group formation.     

An efficient synthesis of propargylamines via C-H activation catalyzed by copper(I) in ionic liquids

A readily available copper(I) catalyst, in an ionic liquid, can effect three-component coupling of aldehydes, amines and alkynes to generate propargylamines in high yields.     

Synthesis and characterization of well‐defined ABC‐type triblock copolymers via atom transfer radical polymerization and stable free‐radical polymerization

An asymmetric difunctional initiator 2‐phenyl‐2‐[(2,2,6,6 tetramethylpiperidino)oxy] ethyl 2‐bromo propanoate ( 1 ) was used for the synthesis of ABC‐type methyl methacrylate (MMA)‐tert‐butylacrylate (tBA)‐styrene (St) triblock copolymers via a combination of atom transfer radical polymerization (ATRP) and stable free‐radical polymerization (SFRP). The ATRP‐ATRP‐SFRP or SFRP‐ATRP‐ATRP route led to ABC‐type triblock copolymers with controlled molecular weight and moderate polydispersity (M_w/M_n < 1.35). The block copolymers were characterized by gel permeation chromatography and ¹H NMR. The retaining chain‐end functionality and the applying halide exchange afforded high blocking efficiency as well as maintained control over entire routes. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2025–2032, 2002     

Novel rhodium-catalyzed reaction of thiazolidine derivatives with carbodiimides

A new, simple, and regioselective synthesis of thiazolidinimine derivatives based on the rhodium-catalyzed reaction of readily available thiazolidines with carbodiimides is described. This methodology provides direct access to a large variety of thiazolidinimine derivatives, possibly via a novel regiospecific insertion of carbodiimides into one of two ring carbon-nitrogen bonds, as well as a metal-catalyzed imine elimination process.     

Traveling waves in rational expressions of exponential functions to the conformable time fractional Jimbo–Miwa and Zakharov–Kuznetsov equations

The conformable time fractional Jimbo–Miwa and Zakharov–Kuznetsov equations are solved by the generalized form of the Kudryashov method. A simple compatible wave transformation is employed to reduce the dimension of the equations to one. The predicted solution is of the form of a rational expression of two finite series at both the numerator and the denominator. The terms of both series are of the powers of some functions having exponential expressions satisfying a particular ODE. The exact solutions are expressed explicitly in terms of powers of some exponential functions in form of rational expressions.