Proofs of the Parisi and Coppersmith‐Sorkin random assignment conjectures

Suppose that there are n jobs and n machines and it costs c_ij to execute job i on machine j. The assignment problem concerns the determination of a one‐to‐one assignment of jobs onto machines so as to minimize the cost of executing all the jobs. When the c_ij are independent and identically distributed exponentials of mean 1, Parisi [Technical Report cond‐mat/9801176, xxx LANL Archive, 1998] made the beautiful conjecture that the expected cost of the minimum assignment equals . Coppersmith and Sorkin [Random Structures Algorithms 15 ( 6 ), 113–144] generalized Parisi's conjecture to the average value of the smallest k‐assignment when there are n jobs and m machines. Building on the previous work of Sharma and Prabhakar [Proc 40th Annu Allerton Conf Communication Control and Computing, 20 , 657–666] and Nair [Proc 40th Annu Allerton Conf Communication Control and Computing, 17 , 667–673], we resolve the Parisi and Coppersmith‐Sorkin conjectures. In the process we obtain a number of combinatorial results which may be of general interest.© 2005 Wiley Periodicals, Inc. Random Struct. Alg. 2005     

The origins of phase stability in ordered and disordered Ni-Pt alloys

Using the atomic-sphere approximation formulation of the Korringa-Kohn-Rostoker coherent potential approximation (KKR CPA) method, we have studied the effects of relativity on the electronic structure of ordered and substitutionally disordered Ni-Pt alloys. The inclusion of mass-velocity and Darwin terms are found to be essential for describing the experimentally observed ground-state properties. For the stability of disordered Ni-Pt alloys we find that, in addition to relativity, the minimization of charge-transfer effects are important. We also find that the treatment of ordering tendencies based on the band energy term alone is not sufficiently accurate for alloys with charge-transfer effects. Further analysis, in terms of basis functions, densities of states and non-spherically averaged charge densities, indicate the importance ofs- andd-electrons of Pt for the stability of both ordered and disordered Ni-Pt alloys.     

Green synthesis of pyranopyrazoles via biocatalytic one-pot Knoevenagel condensation–Michael-type addition–heterocyclization cascade in non-aqueous media

Research on Chemical Intermediates - An efficient, green and facile route for the one-pot four-component synthesis of pyranopyrazole derivatives through the condensation of the aromatic aldehydes,...     

Phase holdups in three-phase fluidized beds in the presence of disc promoter

Three-phase fluidized beds are found to have wide applications in process industries. The present investigation essentially comprises of the studies on gas holdup, liquid holdup and bed porosity in three-phase fluidized beds with coaxially placed disc promoter. Holdup data were obtained from bed expansion and pressure drop measurements. Analysis of the data was done to elucidate the effects of dynamic and geometric parameters on gas holdup, liquid holdup and bed porosity. Data were correlated and useful equations were obtained from empirical modeling.     

Chiral discrimination of drugs by DNA tetranucleotides under electrospray ionisation conditions

The DNA tetranucleotides, extended versions of GCA at the 3'-end or 5'-end, were used as chiral selectors for the chiral discrimination of atenolol, DOPA, tamsulosin, valacyclovir and zolmitriptan. Chiral discrimination was achieved by investigating the collision-induced dissociation spectra of the [X+Y-2H](2-) ion generated by electrospraying a solution mixture of tetranucleotide (X) and R- or S-analyte drug (Y). The relative abundances of the precursor ion and the product ion, resulting from the loss of drug, were considered for measuring the degree of chiral discrimination. Among all the tetranucleotides studied, AGCA showed the highest chiral discrimination. The present study emphasised the position of an adenine base in the tetranucleotide in chiral discrimination. The suitability of the method for the measurement of optical purity was also demonstrated in the case of zolmitriptan.     

Restricted rotation due to the lack of free space within a capsule translates into product selectivity: photochemistry of cyclohexyl phenyl ketones within a water-soluble organic capsule

The rotational mobility of organic guest molecules when included within a confined capsule is restricted and this feature could be translated into product selectivity as established with the photochemical behavior of cyclohexyl phenyl ketones.     

Convenient and Efficient Synthesis of Some Novel Fused Thieno Pyrimidines Using Gewald's Reaction

Abstract

Several functionalized thienopyrimidines were synthesized by a facile synthetic method, which includes Gewald's reaction, and were characterized by spectral and analytical data. These functionalized thienopyrimidines were converted to various new chemical entities of biological importance, such as 2-piperazinymethyl thienopyrimidines (6, 8), 4-dimethylaminoethoxy thienopyrimidines (11), and 3-dimethylaminoethyl thienopyrimidines (12). All the compounds thus synthesized were screened for their invitro biological activities. Some of the compounds displayed promising serotonin 5-HT₆ receptor antagonist activities.

Biocompatibility studies on polyaniline and polyaniline-silver nanoparticle coated polyurethane composite

Biocompatibility of medical grade polyurethane coated with polyaniline (PANi) and polyaniline-silver nanoparticle composite (PANi-AgNp) is reported here. These modified films showed 23 and 18% of 3T3 L1 cell death when compared to 41% with virgin polyurethane (PU) after 48h of incubation, respectively. All the surfaces elucidated inflammatory response in the form of enhanced expressions of the proinflammatory cytokines genes, TNF-α and IL-6. But these values were less (by 20%) on modified films than on the bare PU. Attachment of Pseudomonas and Bacillus were markedly less on PANi-AgNp coated surface (by 90.6 and 50.5%, respectively) when compared to the uncoated PU. As the CFU counts decreases on the nanoparticle coated PU, the adsorbed carbohydrate as well as protein content on to the surface of polymer decreases accordingly, indicating less attachment. A 20% reduction in the thickness of biofilm was observed in PANi-AgNp coated PU surface. A very strong positive correlation is observed between the contact angles of the polymers and the various biological parameters (namely colony forming units, protein, carbohydrate, cell death and inflammatory response), indicating hydrophilic surfaces prevent bacterial biofilm as well as are compatible to cells when compared to hydrophobic surfaces. Coating PU with PANi and PANi+AgNp renders the surface conductive, suggesting potential application in electrochemical biosensors. In addition, these modifications make the surface more biocompatible than the original PU.     

Oxygen atom transfer promoted nitrate to nitric oxide transformation: a step-wise reduction of nitrate → nitrite → nitric oxide

Nitrate reductases (NRs) are molybdoenzymes that reduce nitrate (NO₃⁻) to nitrite (NO₂⁻) in both mammals and plants. In mammals, the salival microbes take part in the generation of the NO₂⁻ from NO₃⁻, which further produces nitric oxide (NO) either in acid-induced NO₂⁻ reduction or in the presence of nitrite reductases (NiRs). Here, we report a new approach of VCl₃ (V³⁺ ion source) induced step-wise reduction of NO₃⁻ in a Co^II-nitrato complex, [(12-TMC)Co^II(NO₃⁻)]⁺ (2,{Co^II–NO₃⁻}), to a Co^III–nitrosyl complex, [(12-TMC)Co^III(NO)]²⁺ (4,{CoNO}⁸), bearing an N-tetramethylated cyclam (TMC) ligand. The VCl₃ inspired reduction of NO₃⁻ to NO is believed to occur in two consecutive oxygen atom transfer (OAT) reactions, i.e., OAT-1 = NO₃⁻ → NO₂⁻ (r₁) and OAT-2 = NO₂⁻ → NO (r₂). In these OAT reactions, VCl₃ functions as an O-atom abstracting species, and the reaction of 2 with VCl₃ produces a Co^III-nitrosyl ({CoNO}⁸) with V^V-Oxo ({V^V O}³⁺) species, via a proposed Co^II-nitrito (3, {Co^II–NO₂⁻}) intermediate species. Further, in a separate experiment, we explored the reaction of isolated complex 3 with VCl₃, which showed the generation of 4 with V^V-Oxo, validating our proposed reaction sequences of OAT reactions. We ensured and characterized 3 using VCl₃ as a limiting reagent, as the second-order rate constant of OAT-2 (k₂^/) is found to be ∼1420 times faster than that of the OAT-1 (k₂) reaction. Binding constant (K_b) calculations also support our proposition of NO₃⁻ to NO transformation in two successive OAT reactions, as K_{b(Co^II–NO2⁻)} is higher than K_{b(Co^II–NO3⁻)}, hence the reaction moves in the forward direction (OAT-1). However, K_{b(Co^II–NO2⁻)} is comparable to K_b{CoNO}⁸, and therefore sequenced the second OAT reaction (OAT-2). Mechanistic investigations of these reactions using ¹⁵N-labeled-¹⁵NO₃⁻ and ¹⁵NO₂⁻ revealed that the N-atom in the {CoNO}⁸ is derived from NO₃⁻ ligand. This work highlights the first-ever report of VCl₃ induced step-wise NO₃⁻ reduction (NRs activity) followed by the OAT induced NO₂⁻ reduction and then the generation of Co-nitrosyl species {CoNO}⁸.

Single metal-induced reduction of NO₃⁻ → {NO₂⁻} → NO via oxygen atom transfer reaction.