The Local Structure of Graded Representations

In this article we show that the local structure of the projective representation space of a graded algebra can locally be described by quivers with an automorphism of their path algebra, a weighted twist. We describe the quotient spaces of these weighted twisted quiver settings and determine which of them are smooth.     

Multicomponent Self‐Assembly with a Shape‐Persistent N‐Heterotriangulene Macrocycle on Au(111)

Multicomponent network formation by using a shape‐persistent macrocycle ( MC6 ) at the interface between an organic liquid and Au(111) surface is demonstrated. MC6 serves as a versatile building block that can be coadsorbed with a variety of organic molecules based on different types of noncovalent interactions at the liquid–solid interface. Scanning tunneling microscopy (STM) reveals the formation of crystalline bicomponent networks upon codeposition of MC6 with aromatic molecules, such as fullerene (C₆₀) and coronene. Tetracyanoquinodimethane, on the other hand, was found to induce disorder into the MC6 networks by adsorbing on the rim of the macrocycle. Immobilization of MC6 itself was studied in two different noncovalently assembled host networks. MC6 assumed a rather passive role as a guest and simply occupied the host cavities in one network, whereas it induced a structural transition in the other. Finally, the central cavity of MC6 was used to capture C₆₀ in a complex three‐component system. Precise immobilization of organic molecules at discrete locations within multicomponent networks, as demonstrated here, constitutes an important step towards bottom‐up fabrication of functional surface‐based nanostructures.     

A temperature dependence kinetic study of O(1D) + CH4: overall rate coefficient and product yields

Using a recently-developed chemiluminescence technique for monitoring O(1D), the rate coefficient, k1, of the important atmospheric reaction O(1D) + CH4 --> products has been determined over a wide temperature range, 227 to 450 K. The rate coefficient was shown to be independent of temperature, having a value of (1.91 +/- 0.08) x 10(-10) cm3 s(-1); the quoted uncertainties are with 95% confidence. This highly precise value, based on an extended set of determinations with very low scatter, is significantly greater, 26%, than current recommended values. Secondly, the fraction of O(1D) quenched to O(3P) by CH4, k(1q)/k1, was precisely determined from chemiluminescence decays over the temperature range 236 to 340 K. A temperature independent value for k(1q)/k1 of 0.002 +/- 0.003 was found. Finally, LIF detection of OH has been applied to accurately determine the product branching fraction to OH of O(1D) + CH4 at room temperature. Our value, k(1a)/k1 = 0.76 +/- 0.08 (95% confidence), is in line with recent determinations by other groups.     

Reactivity of N-(omega-haloalkyl)-beta-lactams with regard to lithium aluminium hydride: novel synthesis of 1-(1-aryl-3-hydroxypropyl)aziridines and 3-aryl-3-(N-propylamino)propan-1-ols

The reactivity of 4-aryl-1-(2-chloroethyl)azetidin-2-ones and 4-aryl-1-(3-bromopropyl)azetidin-2-ones with regard to lithium aluminium hydride has been evaluated for the first time. 4-Aryl-1-(2-chloroethyl)azetidin-2-ones were transformed into novel 1-(1-aryl-3-hydroxypropyl)aziridines through an unprecedented conversion of beta-lactams into 2,3-unsubstituted aziridine derivatives. Unexpectedly, 4-aryl-1-(3-bromopropyl)azetidin-2-ones underwent dehalogenation towards 3-aryl-3-(N-propylamino)propan-1-ols upon treatment with LiAlH(4). 1-(1-Aryl-3-hydroxypropyl)aziridines were further elaborated by means of ring opening reactions using benzyl bromide in acetonitrile towards 3-aryl-3-[N-benzyl-N-(2-bromoethyl)amino]propan-1-ols and using aluminium(iii) chloride in diethyl ether, affording 3-aryl-3-[N-(2-chloroethyl)amino]propan-1-ols.     

On the optimization of two-class work-conserving parameterized scheduling policies

Numerous scheduling policies are designed to differentiate quality of service for different applications. Service differentiation can in fact be formulated as a generalized resource allocation optimization towards the minimization of some important system characteristics. For complex scheduling policies, however, optimization can be a demanding task, due to the difficult analytical analysis of the system at hand. In this paper, we study the optimization problem in a queueing system with two traffic classes, a work-conserving parameterized scheduling policy, and an objective function that is a convex combination of either linear, convex or concave increasing functions of given performance measures of both classes. In case of linear and concave functions, we show that the optimum is always in an extreme value of the parameter. Furthermore, we prove that this is not necessarily the case for convex functions; in this case, a unique local minimum exists. This information greatly simplifies the optimization problem. We apply the framework to some interesting scheduling policies, such as Generalized Processor Sharing and semi-preemptive priority scheduling. We also show that the well-documented \(c\mu \)-rule is a special case of our framework.     

Packet loss characteristics for <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/1/<Emphasis Type="Italic">N</Emphasis> queueing systems

In this contribution we investigate higher-order loss characteristics for M/G/1/N queueing systems. We focus on the lengths of the loss and non-loss periods as well as on the number of arrivals during these periods. For the analysis, we extend the Markovian state of the queueing system with the time and number of admitted arrivals since the instant where the last loss occurred. By combining transform and matrix techniques, expressions for the various moments of these loss characteristics are found. The approach also yields expressions for the loss probability and the conditional loss probability. Some numerical examples then illustrate our results.     

Woodward-Hoffmann rules in density functional theory: initial hardness response

The Woodward-Hoffmann rules for pericyclic reactions, a fundamental set of reactivity rules in organic chemistry, are formulated in the language of conceptual density functional theory (DFT). DFT provides an elegant framework to introduce chemical concepts and principles in a quantitative manner, partly because it is formulated without explicit reference to a wave function, on whose symmetry properties the Woodward-Hoffmann [J. Am. Chem. Soc. 87, 395 (1965)] rules are based. We have studied the initial chemical hardness response using a model reaction profile for two prototypical pericyclic reactions, the Diels-Alder cycloaddition of 1,3-butadiene to ethylene and the addition of ethylene to ethylene, both in the singlet ground state and in the first triplet excited state. For the reaction that is thermally allowed but photochemically forbidden, the initial hardness response is positive along the singlet reaction profile. (By contrast, for the triplet reaction profile, a negative hardness response is observed.) For the photochemically allowed, thermally forbidden reaction, the behavior of the chemical hardness along the initial stages of the singlet and triplet reaction profiles is reversed. This constitutes a first step in showing that chemical concepts from DFT can be invoked to explain results that would otherwise require invoking the phase of the wave function.     

Local aromaticity in polycyclic aromatic hydrocarbons: electron delocalization versus magnetic indices

The local aromaticity of benzenoid rings is examined by means of the Polansky index (P) and generalized population analysis (GPA). The results are found to agree very well with recently published circuit-condensed ring currents and magnetic-energetic aromaticity indices, but no correlation is found with nucleus independent chemical shifts (NICS). This is usually seen as a manifestation of the more general multidimensional nature of aromaticity. This paper examines the sources for the observed correlations, showing that some indices give conflicting results because they inherently reflect different phenomena.     

Heteroleptic silver-containing ionic liquids

The first examples of structurally characterised mixed-ligand metal-containing ionic liquids (ILs) are presented, synthesised by the use of different N-alkylimidazoles. The cations consist of two-coordinate silver(i) centres ligated by two different N-alkylimidazole ligands. It is shown that the resulting ionic liquids have lower melting points than the single ligand ILs.