Random Copolymers of 1,5-Dioxepan-2-one

ABSTRACT

Copolymers of 1,5-dioxepan-2-one (DXO) and e-caprolactone (?-CL), δ-valerolactone (δ-VL) or L-lactide (LLA) have been synthesized and characterized. High molecular weight copolymers were obtained using stannous-2-ethyl hexanoate as catalyst in bulk. Reactivity ratios for the copolymerization of DXO and δ-VL were determined at 110°C as r_VL=0.5 and r_DXO=2.3. At high conversion, depolymerization of δ-VL occurred, resulting in lower molecular weight and variations in the copolymer composition.

Physical properties, such as crystallinity and melting temperature of the DXO-copolymers proved to be strongly dependent on the choice of comonomer and on the molar composition of the copolymers. DXO appears to be incorporated into the poly-?-caprolactone (PCL) crystals and to some extent into the poly-δ-valerolactone (PVL) crystals, resulting in a more gradual decrease in crystallinity with increasing amount of DXO.     

Selective Cleavage of β-Keto and Vinylogous β-Keto Esters by 3-Quinuclidinol

As a result of a continuing study utilizing nitrogenous bases^2–6, we now wish to report that the base 3-quinuclidinol (13) is useful for the cleavage of β-keto and vinylogous β-keto esters.     

Total Synthesis of (6R,10R,13R,14R,16R,17R,19S,20R,21R,24S, 25S,28S,30S,32R,33R,34R,36S,37S,39R)‐Azaspiracid‐3 Reveals Non‐Identity with the Natural Product

A convergent and stereoselective total synthesis of the previously assigned structure of azaspiracid‐3 has been achieved by a late‐stage Nozaki–Hiyama–Kishi coupling to form the C21?C22 bond with the C20 configuration unambiguously established from l ‐(+)‐tartaric acid. Postcoupling steps involved oxidation to an ynone, modified Stryker reduction of the alkyne, global deprotection, and oxidation of the resulting C1 primary alcohol to the carboxylic acid. The synthetic product matched naturally occurring azaspiracid‐3 by mass spectrometry, but differed both chromatographically and spectroscopically.     

Parametric excitation of an internally resonant double pendulum

Summary A system of two weakly damped, nonlinearly coupled pendulums with (uncoupled) natural frequencies of ₁ and ₂ 2 ₁ is subjected to a small, vertical oscillation of frequency 22 ₁. The resulting motion (after transients have decayed) may be either a simple (rigid-body) translation of the entire system or coupled oscillations of the pendulums superimposed on such a translation. The stability of these two types of motion is examined and their parametric domains established. There are no Hopf bifurcations, in consequence of which neither periodically modulated nor chaotic motions appear to be possible (for weak excitation). The corresponding problem for a symmetric triple pendulum is shown to be isomorphic to that for the double pendulum.

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Zusammenfassung Ein System von schwach gedämpften, nichtlinear gekoppelten Pendeln mit den (ungekoppelten) natürlichen Frequenzen ₁ und ₂2 ₁ wird vertikalen erzwungenen Schwingungen mit der Frequenz 22 ₁ unterworfen. Die entstehende Bewegung ist (nach dem Abklingen von temporären Bewegungsanteilen) entweder eine einfache Translation des (starren) Systems oder aber eine solche Translation mit überlagerten gekoppelten Schwingungen der Pendel. Die Stabilität dieser beiden Bewegungstypen wird untersucht, und ihr parametrischer Gültigkeitsbereich wird bestimmt. Es gibt keine Hopf-Bifurkationen, so daß weder periodisch modulierte noch chaotische Bewegungen möglich erscheinen (für schwache Erregungen). Das entsprechende Problem für ein symmetrisches Dreifach-Pendel ergibt sich isomorph zu dem des Doppel-Pendels.

     

Scheduling Production in a Heavily Constrained Plant – Anode Manufacture in an Aluminium Smelter

In this paper a mathematical model of an anode manufacturing plant is developed with the objective of assisting in the planning and scheduling of production for up to a month ahead. A model of the overall smelter already exists and is based on a monthly time frame. The anode plant is a part of this model but is a very heavily constrained area and it is necessary to have a daily planning model that will help to achieve the optimal level of operations as dictated by the overall model of the smelter. The anode area is responsible for the production of carbon blocks (called anodes) which are an integral part of the aluminium smelting process. The plant is also responsible for the delivery of all raw materials within the smelter. The model developed is a daily one replicated for up to a month ahead, interconnected by opening and closing stocks.     

Support Varieties for Selfinjective Algebras

Support varieties for any finite dimensional algebra over a field were introduced in (Proc. London Math. Soc. 88 (3) (2004) 705–732) using graded subalgebras of the Hochschild cohomology ring. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, the variety of periodic modules are lines and for symmetric algebras a generalization of Webbs theorem is true. As a corollary of a more general result we show that Webbs theorem generalizes to finite dimensional cocommutative Hopf algebras.Received November 2003Mathematics Subject Classifications (2000) Primary: 16E40, 16G10, 16P10, 16P20; Secondary: 16G70.     

Simulations of radiative effects on the Rayleigh–Taylor instability using the CRASH code

Future experiments at the National Ignition Facility will be able to generate diagnosable Rayleigh–Taylor instability growth in the presence of locally generated, high radiation fluxes. This interplay of radiative energy transfer and hydrodynamic instability is relevant to many astrophysical systems, such as core-collapse red supergiant supernovae. Previous simulations of high-energy-density Rayleigh–Taylor instabilities in the presence of a hot environment near a radiative shock demonstrate behavior that differs from that found in non-radiative cases. However, these simulations considered only 1D or single wavelength cases. Here we report simulations of an entire experimental system using the CRASH code. These simulations lead to modified predictions, attributed to the effects of radial energy losses.     

Parallel distributed-memory simplex for large-scale stochastic LP problems

We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal basic solutions, which allow for efficient hot-starts (e.g., in a branch-and-bound context) and can provide important sensitivity information. Our approach exploits the dual block-angular structure of these problems inside the linear algebra of the revised simplex method in a manner suitable for high-performance distributed-memory clusters or supercomputers. While this paper focuses on stochastic LPs, the work is applicable to all problems with a dual block-angular structure. Our implementation is competitive in serial with highly efficient sparsity-exploiting simplex codes and achieves significant relative speed-ups when run in parallel. Additionally, very large problems with hundreds of millions of variables have been successfully solved to optimality. This is the largest-scale parallel sparsity-exploiting revised simplex implementation that has been developed to date and the first truly distributed solver. It is built on novel analysis of the linear algebra for dual block-angular LP problems when solved by using the revised simplex method and a novel parallel scheme for applying product-form updates.