ZrCl4-mediated regio- and chemoselective Friedel-Crafts acylation of indole

An efficient method for regio- and chemoselective Friedel-Crafts acylation of indole using acyl chlorides in the presence of ZrCl(4) has been discovered. It minimizes/eliminates common competing reactions that occur due to high and multiatom-nucleophilic character of indole. In this method, a wide range of aroyl, heteroaroyl alkenoyl, and alkanoyl chlorides undergo smooth acylation with various indoles without NH protection and afford 3-acylindoles in good to high yields.     

A Morita theorem for dual operator algebras

We prove that two dual operator algebras are weak^∗ Morita equivalent in the sense of [D.P. Blecher, U. Kashyap, Morita equivalence of dual operator algebras, J. Pure Appl. Algebra 212 (2008) 2401-2412] if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak^∗-continuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case, we characterize such functors as the module normal Haagerup tensor product with an appropriate weak^∗ Morita equivalence bimodule. We also develop the theory of the W^∗-dilation, which connects the non-selfadjoint dual operator algebra with the W^∗-algebraic framework. In the case of weak^∗ Morita equivalence, this W^∗-dilation is a W^∗-module over a von Neumann algebra generated by the non-selfadjoint dual operator algebra. The theory of the W^∗-dilation is a key part of the proof of our main theorem.     

The service system M/M R /∞ with impatient customers

An infinite server queue is considered where customers have a choice of individual service or batch service. Transient results have been obtained for the first two moments of the system size distribution. Waiting time distribution is important in system evaluation and steady state results are obtained.     

Morita equivalence of dual operator algebras

We consider notions of Morita equivalence appropriate to weak* closed algebras of Hilbert space operators. We obtain new variants, appropriate to the dual algebra setting, of the basic theory of strong Morita equivalence, and new nonselfadjoint analogues of aspects of Rieffel’s W^∗-algebraic Morita equivalence.     

Rigged modules I: Modules over dual operator algebras and the Picard group

In a previous paper we generalized the theory of $W^{?}$-modules to the setting of modules over nonselfadjoint dual operator algebras, obtaining the class of weak^?-rigged modules. At that time we promised a forthcoming paper devoted to other aspects of the theory. We fulfill this promise in the present work and its sequel “Rigged modules II”, giving many new results about weak^?-rigged modules and their tensor products. We also discuss the Picard group of weak* closed subalgebras of a commutative algebra. For example, we compute the weak Picard group of $H^{\infty }(\mathbb{D})$, and prove that for a weak* closed function algebra A, the weak Picard group is a semidirect product of the automorphism group of A, and the subgroup consisting of symmetric equivalence bimodules.     

Examining the mechanism of action of a kinesin inhibitor using stable isotope labeled inhibitors for cross-linking (SILIC)

It is difficult to determine a chemical inhibitor's binding site in multiprotein mixtures, particularly when high-resolution structural studies are not straightforward. Building upon previous research involving photo-cross-linking and the use of mixtures of stable isotopes, we report a method, Stable Isotope Labeled Inhibitors for Cross-linking (SILIC), for mapping a small molecule inhibitor's binding site in its target protein. In SILIC, structure-activity relationship data is used to design inhibitor analogues that incorporate a photo-cross-linking group along with either natural or 'heavy' stable isotopes. An equimolar mixture of these inhibitor analogues is cross-linked to the target protein to yield a robust signature for identifying inhibitor-modified peptide fragments in complex mass spectrometry data. As a proof of concept, we applied this approach to an ATP-competitive inhibitor of kinesin-5, a widely conserved motor protein required for cell division and an anticancer drug target. This analysis, along with mutagenesis studies, suggests that the inhibitor binds at an allosteric site in the motor protein.     

Algorithms for non-uniform size data placement on parallel disks

We study an optimization problem that arises in the context of data placement in a multimedia storage system. We are given a collection of M multimedia objects (data items) that need to be assigned to a storage system consisting of N disks d₁,d₂,…,d_N. We are also given sets U₁,U₂,…,U_M such that U_i is the set of clients seeking the ith data item. Data item i has size s_i. Each disk d_j is characterized by two parameters, namely, its storage capacity C_j which indicates the maximum total size of data items that may be assigned to it, and a load capacity L_j which indicates the maximum number of clients that it can serve. The goal is to find a placement of data items to disks and an assignment of clients to disks so as to maximize the total number of clients served, subject to the capacity constraints of the storage system.We study this data placement problem for homogeneous storage systems where all the disks are identical. We assume that all disks have a storage capacity of k and a load capacity of L. Previous work on this problem has assumed that all data items have unit size, in other words s_i=1 for all i. Even for this case, the problem is NP-hard. For the case where s_i{1,…,Δ} for some constant Δ, we develop a polynomial time approximation scheme (PTAS). This result is obtained by developing two algorithms, one that works for constant k and one that works for arbitrary k. The algorithm for arbitrary k guarantees that a solution where at least -fraction of all clients are assigned to a disk (under certain assumptions). In addition we develop an algorithm for which we can prove tight bounds when s_i{1,2}. In fact, we can show that a -fraction of all clients can be assigned (under certain natural assumptions), regardless of the input distribution.