Full potential calculation of electronic properties of rutile RO2 (R=Si, Ge, Sn and Pb) compounds via modified Becke Johnson potential

The electronic properties of RO₂ (R=Si, Ge, Sn and Pb; a group IVA element) compounds in rutile structure have been calculated using WIEN2k implementation of full potential linearized augmented plane wave (FPLAPW) method. The exchange and correlation (XC) effects are taken into account by an orbital independent modified Becke Johnson (MBJ) potential as coupled with Local Density Approximation (LDA) for all the compounds except for PbO₂ where only Generalized Gradient Approximation (GGA) is considered for the same. We predict a direct band gap in all these compounds with continuous decrease as the atomic size of IVA element increases such that there is an appearance of semimetallic band structure for the last compound, PbO₂. The largest band gap (7.66 eV) has been found for SiO₂, which governs its insulating nature. We observe that MBJLDA results for band gaps of these compounds are far better than those obtained using GGA and Engel-Vosko's GGA (EV-GGA). A very good agreement is observed between MBJLDA band gaps with corresponding experimental values as compared to other calculations. The electronic band structures are also analyzed in terms of contributions from various electrons.     

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.     

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.     

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.     

Exploiting silver trifluoromethanesulfonate as efficient and reusable catalyst for the synthesis of dihydropyrimidine derivatives under different reaction environments

Different results were generated under different reaction conditions for the multicomponent reactions. Herein, an efficiently improved and mild protocol for the synthesis of dihydropyrimidine derivatives using cheap silver trifluoromethanesulfonate (CF₃SO₃Ag) as reusable catalyst is explained. With conventional heating and microwave irradiation method, the synthesis of substituted 3,4‐dihydropyrimidine‐2(1H)‐one and 3,4‐dihydropyrimidine‐2(1H)‐thione was achieved in different solvent environments like acetonitrile, water, and under solvent free neat condition. Moreover, the solvents (CH₃CN and H₂O) containing the CF₃SO₃Ag were reused for several times without loss of much catalytic activity after separation from the desired products. Thus, the method provides much improved and efficient alternative pathway to the original Biginelli reaction.