Rh(III)-Catalyzed One-Step Synthesis of ortho-Alkynylated Perylene Imide Dyes: Optical and Electrochemical Properties of New Derivatives

A one-step Rh-catalyzed site-selective ortho-C−H alkynylation of perylene as well as naphthalene mono- and diimides is reported. A single step regioselective access to ortho-C−H alkynylated derivatives of these ryleneimides not only increases the step economy of the ortho-functionalization on these dyes but also provides a quick access route towards highly functionalized dyes that have potential optoelectronic applications. Increased solubility of tetra(triisopropylsilyl)acetylenyl PDIs in organic solvents greatly enhances their utility for further derivatization.     

Scheduling data transfers in a network and the set scheduling problem

In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as max-stretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum max-stretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the max-stretch and total flow time for the case where online and offline algorithms are using same-capacity edges. Moreover, we also give polylogarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and max-stretch within a constant factor of optimum.     

Deciding confluence of certain term rewriting systems in polynomial time

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a constant.     

Degree-regular triangulations of torus and Klein bottle

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In [8], Lutz has classified all the weakly regular triangulations on at most 15 vertices. In [5], Datta and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices. In this article, we have proved that any degree-regular triangulation of the torus is weakly regular. We have shown that there exists ann-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. We have constructed two distinctn-vertex weakly regular triangulations of the torus for eachn ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for eachm ≥ 2. For 12 ≤n ≤ 15, we have classified all then-vertex degree-regular triangulations of the torus and the Klein bottle. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly regular.     

Constructing ‘hair’ for the three charge hole

It has been found that the states of the 2-charge extremal D1–D5 system are given by smooth geometries that have no singularity and no horizon individually, but a ‘horizon’ does arise after ‘coarse-graining’. To see how this concept extends to the 3-charge extremal system, we construct a perturbation on the D1–D5 geometry that carries one unit of momentum charge P. The perturbation is found to be regular everywhere and normalizable, so we conclude that at least this state of the 3-charge system behaves like the 2-charge states. The solution is constructed by matching (to several orders) solutions in the inner and outer regions of the geometry. We conjecture the general form of ‘hair’ expected for the 3-charge system, and the nature of the interior of black holes in general.     

Mössbauer studies of iron stabilised polymethacrylates

Polymethyl methacrylate (PMMA), polyethyl methacrylate (PEMA) and polybutyl methacrylate (PBuMA) containing ferric chloride and ferrous sulphate as stabilisers, were prepared by free radical polymerization. Mössbauer spactra of ferrous sulphate stabilised polymers don't show any change in the value of isomer shift (1.30 mm/s) while quadrupole splitting values are quite different from those for pure ferrous sulphate. This indicates that environment of Fe²⁺ moiety changes in polymers and thus stabilises the polymers. In case of ferric chloride stabilised polymers the isomer shift values don't differ significantly for different polymethacrylates but quadrupole splitting values increase from polymethyl methacrylate to polybutyl methacrylate. The TGA analysis shows that the inclusion of iron salts stabilises the polymers by 40°C (approx.) and at higher temperatures α-Fe₂O₃ is formed.     

Free-radical polymerization of methyl methacrylate in presence of the Cr(C5H7O2)3–Al(i-C4H9)3 catalyst system

Polymerization of methyl methacrylate has been studied with the chromium acetylacetonate–triisobutyl aluminum catalyst system in benzene medium at 40°C. These studies have been carried out at an Al/Cr ratio of 12 to compare the behavior with the previously studied chromium acetyl acetonate–triethyl aluminum catalyst system. The enhanced yield and gelling of polymer suggests a free-radical mechanism of polymerization. Further, the kinetics of polymerization and the heterotactic structure of polymer as determined by NMR examination have led to confirmation of the freeradical mechanism of polymerization of methyl methacrylate by an excess of triisobutylaluminum in the presence of catalyst complex.     

Kinetics and mechanism of polymerization yielding stereoblock poly(methyl methacrylate) with VCl4-Al(C2H5)3 catalyst system

Methyl methacrylate was polymerized at 40°C with the VCl₄–AlEt₃ catalyst system in n-hexane. The rate of polymerization was proportional to the catalyst and monomer concentration at Al/V ratio of 2, indicating a coordinate anionic mechanism of polymerization. NMR spectra were further used to confirm the mechanism of polymerization and stability of active sites responsible for isotacticity.