Cutting and Surrogate Constraint Analysis for Improved Multidimensional Knapsack Solutions

We use surrogate analysis and constraint pairing in multidimensional knapsack problems to fix some variables to zero and to separate the rest into two groups – those that tend to be zero and those that tend to be one, in an optimal integer solution. Using an initial feasible integer solution, we generate logic cuts based on our analysis before solving the problem with branch and bound. Computational testing, including the set of problems in the OR-library and our own set of difficult problems, shows our approach helps to solve difficult problems in a reasonable amount of time and, in most cases, with a fewer number of nodes in the search tree than leading commercial software.     

Enantio- and diastereoselective synthesis of (E)-1,5-syn-diols: application to the synthesis of the C(23)-C(40) fragment of tetrafibricin

A highly stereoselective synthesis of (E)-1,5-syn-diols 6 is described. The kinetically controlled hydroboration of allenyltrifluoroborate 8 with Soderquist borane 2 provides the (Z)-allylic trifluoroborate 9, which undergoes sequential allylboration with two different aldehydes to provide (E)-1,5-syn-diols 6 in 72-98% yields with >95% ee and >20:1 dr. Application of this method to the synthesis of the tetrafibricin C(23)-C(40) fragment 19 is described.     

'Non-covalent synthesis' of a chiral host of calix[6]arene and enantiomeric discrimination

'Non-covalent synthesis' of novel chiral hosts (calix[6]arene-chiral amine complexes) and its application to enantiomeric discrimination was investigated by (1)H NMR spectroscopy. The topology of a ternary complex was proposed for the calix[6]arene-amine-sulfoxide to rationalize the chiral recognition.     

The heat semigroup on sectorial domains,highly singular initial values and applications

We show that the heat semigroup is well defined on the Banach space \({\mathcal{X}_{m,\gamma} = \{ \psi:\Omega_m \to \mathbb{R} ;\; |x|^{\gamma +2m}(\prod_{i=1}^m x_i)^{-1}\psi(x) \in L^\infty(\Omega_m)\},}\) \({0 < \gamma < N}\), where \({\Omega_m=\{(x_1,\, x_2,\, \ldots,\, x_N) \in \mathbb{R}^{N};\; x_i > 0,\, 1\leq i\leq m\},}\) \({1\leq m\leq N}\). We then investigate the large time behavior of solutions of the heat equation \({u_{t}-\Delta u=0}\) for t > 0 and \({x \in \Omega_m.}\) Using certain notions from dynamical systems, we show that the large time behavior is related to the spatial asymptotic behavior of its initial value. Since the space \({\mathcal{X}_{m, \gamma}}\) contains highly singular initial data, which can be extended to all of \({\mathbb{R}^{N}}\) by antisymmetry, we also obtain new results on the complexity in the asymptotic behavior of solutions for the heat equation on the whole space.     

Early gas chromatography/mass spectrometry

Spectroscopy Laboratory, The Dow Chemical Company, Midland, Michigan, USA In December 1955 or thereabouts, the authors coupled a homemade gas chromatograph to a research time-of-flight mass spectrometer constructed by W. C. Wiley, I. H. McLaren, and D. B. Harrington. This unique gas chromatography/mass spectrometry (GC/MS) instrument generated mass spectra at a lo-kHz rate for display on an oscilloscope; eluted gas chromate graphic components, such as methanol, acetone, benzene, toluene, and carbon tetrachloride, could be visually identified immediately from the oscilloscope display. Many years of further research and development in many laboratories worldwide were necessary, however, to make continuous on-line GC/MS the uniquely valuable analytical tool that it is today.     

Enhancement of the Catalytic Activity of a Macrocyclic Cobalt(II) Complex for the Electroreduction of O(2) by Adsorption on Graphite

In solution, the [(tim)Co](2+) complex (tim = 2,3,9,10-tetramethyl-1,4,8,11-tetraazacyclotetradeca-1,3,8,10-tetraene) reacts only slowly with O(2), but upon adsorption on graphite electrodes, it becomes an active catalyst for the reduction of O(2) to H(2)O(2). The electroreduction of O(2) proceeds in a single voltammetric step at close to the diffusion-controlled rate at a relatively positive potential (0.25 V vs SCE). The remarkable enhancement in catalytic activity is attributed to a higher affinity for O(2) of the adsorbed complex as a result of its interactions with functional groups on the surface of roughened or oxidized graphite. A possible mechanism for the catalytic reduction of O(2) is proposed. It differs from the one employed by the analogous [(hmc)Co](2+) complex (hmc = C-meso-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane) which operates at less positive potentials and exhibits two separated voltammetric steps in the reduction of O(2), via [(hmc)CoOOH](2+), to H(2)O(2).     

The determination of aluminum by atomic absorption spectroscopy

A study of the determination of aluminum by atomic absorption spectroscopy has been made using a solution of aluminum cupferrate in 4-methyl-2-pentanone to feed oxy-acetylene or oxy-hydrogen flames. Investigations were made on the effect of the variables, viz., slit-width, flow rates, flow ratios and flame positions, on the intensity of aluminum absorption. The data were studied to determine the optimum conditions. These investigations brought out the comparative merits of the two flames for the determination of aluminum, and also elucidated the mechanism of aluminum absorption in an oxy-acetylene flame.     

C*-algebras associated with interval maps

For each piecewise monotonic map of , we associate a pair of C*-algebras and and calculate their K-groups. The algebra is an AI-algebra. We characterize when and are simple. In those cases, has a unique trace, and is purely infinite with a unique KMS state. In the case that is Markov, these algebras include the Cuntz-Krieger algebras , and the associated AF-algebras . Other examples for which the K-groups are computed include tent maps, quadratic maps, multimodal maps, interval exchange maps, and -transformations. For the case of interval exchange maps and of -transformations, the C*-algebra coincides with the algebras defined by Putnam and Katayama-Matsumoto-Watatani, respectively.

     

Cyclodimerization versus Polymerization of Methyl Methacrylate Induced by N‐Heterocyclic Carbenes: A Combined Experimental and Theoretical Study

The activation behavior of two N‐heterocyclic carbenes (NHCs), namely, 1,3‐bis(isopropyl)imidazol‐2‐ylidene(NHCiPr) and 1,3‐bis(tert‐butyl) imidazol‐2‐ylidene (NHCtBu), as organic nucleophiles in the reaction with methyl methacrylate (MMA) is described. NHCtBu allows the polymerization of MMA in DMF at room temperature and in toluene at 50 °C, whereas NHCiPr reacts with two molecules of MMA, forming an unprecedented imidazolium–enolate cyclodimer (NHCiPr/MMA=1:2). It is proposed that the reaction mechanism occurs by initial 1,4‐nucleophilic addition of NHCiPr to MMA, generating a zwitterionic enolate 2 , followed by addition of 2 to a second MMA molecule, forming a linear imidazolium–enolate 3 (NHCiPr/MMA=1:2). Proton transfer, generating intermediate 5 , followed by cyclization and release of methanol yielded the aforementioned zwitterionic cyclodimer 1:2 adduct 7 , the molecular structure of which has been established by NMR spectroscopy, X‐ray diffraction, and mass spectrometry. This unexpected difference between NHCtBu and NHCiPr in the reaction with MMA (polymerization and cyclodimerization, respectively) can be rationalized by using DFT calculations. In particular, the nature of the NHC strongly influences the cyclodimerization pathway, the cyclization of 5 and the release of methanol are the discriminating step and limiting step, respectively. In the case of NHCtBu, both steps are strongly disfavoured compared with that of NHCiPr (energetic difference of around 14 and 9 kcal mol^?1, respectively), preventing the cyclization mechanism from a kinetic viewpoint. Moreover, addition of a third molecule of MMA in the polymerization pathway results in a lower activation barrier than that of the limiting step in the cyclodimerization pathway (difference of around 14 kcal mol^?1), in agreement with the formation of polymethyl methacrylate (PMMA) by using NHCtBu as nucleophile.     

From the N‐Heterocyclic Carbene‐Catalyzed Conjugate Addition of Alcohols to the Controlled Polymerization of (Meth)acrylates

Among various N‐heterocyclic carbenes (NHCs) tested, only 1,3‐bis(tert‐butyl)imidazol‐2‐ylidene (NHC^tBu) proved to selectively promote the catalytic conjugate addition of alcohols onto (meth)acrylate substrates. This rather rare example of NHC‐catalyzed 1,4‐addition of alcohols was investigated as a simple means to trigger the polymerization of both methyl methacrylate and methyl acrylate (MMA and MA, respectively). Well‐defined α‐alkoxy poly(methyl (meth)acrylate) (PM(M)A) chains, the molar masses of which could be controlled by the initial [(meth)acrylate]₀/[ROH]₀ molar ratio, were ultimately obtained in N,N‐dimethylformamide at 25 °C. A hydroxyl‐terminated poly(ethylene oxide) (PEO‐OH) macro‐initiator was also employed to directly access PEO‐b‐PMMA amphiphilic block copolymers. Investigations into the reaction mechanism by DFT calculations revealed the occurrence of two competitive concerted pathways, involving either the activation of the alcohol or that of the monomer by NHC^tBu.