关于广义三项指数和的四次幂均值

The main purpose of this paper is using estimates for trigonometric sums and properties of congruence to study the computation of one kind of fourth power mean of a generalized three-term exponential sum, and give an interesting identity for it.     

Cyclic (ALN)n Compounds as Precursors to Aluminum Nitride: Synthesis and Structure of [(CH3)2AlNH2]3 and the Planar Species [(t-C4H9)2AlNH2]3

Abstract

The crystal and molecular structures of the title compounds, [(CH₃)₂AlNH₂]₃ 1 and [(t-C₄H₉)₂AlNH₂]₃ 2, have been determined in connection with their investigation as possible precursors to aluminum nitride. Both compounds have an (AlN)₃ ring-structure with distorted tetrahedral geometries for the ring Al and N atoms. The distortion from tetrahedral geometry is most pronounced for the N atoms where the endocyclic Al-N-Al bond angles average 125.3 for 1 and 134.2 for 2. The (AlN)₃ ring in 1 is in a skew-boat conformation with no unusual intra- or intermolecular contacts. Compound 2 on the other hand exhibits an unprecedented planar (AlN)₃ ring as required by a crystallographic three-fold symmetry axis. The effects of the Al and N substituents on the (AlN)₃ ring size and conformation, as well as on the endocyclic Al-N-Al bond angles, are discussed in the context of the structural results obtained for these and other (AlN)_n ring compounds.     

Viscosity-Temperature Behavior of Hydroxypropyl Cellulose Solution in Presence of an Electrolyte or a Surfactant: A Convenient Method to Determine the Cloud Point of Polymer Solutions

The viscosity of hydroxypropyl cellulose (HPC) solution with or without an additive has been measured continuously as a function of temperature with the help of a vibro-viscometer. The viscosity of the polymer solution showed a gradual decrease initially with increase in temperature until a particular point beyond which there was a sharp decrease in the viscosity, which coincided with the clouding of the solution. The cloud point temperature (CP) of the polymer solution was determined from the first derivative plot of viscosity vs. temperature. Effect of addition of an electrolyte or a surfactant on the CP of HPC solution has also been studied. While a decrease in CP of HPC solution in presence of fluoride, chloride, or bromide ions was observed, presence of iodide or thiocyanide ions led to an increase in the CP. However, presence of an ionic surfactant initially lowered the CP but beyond a particular surfactant concentration a sharp increase in cloud point was observed due to interaction of the surfactant with the polymer. The results suggest that surfactants with longer hydrophobic tail or more hydrophobic groups have more affinity for HPC.     

Solubility of novel open-chain crown ether bridged diphosphates in supercritical carbon dioxide

The solubility of newly synthesized chelating agents, i.e., tetraethylene glycol bis (2-ethylhexyl) dimethyl diphosphate (EG4EH), tetraethylene glycol bis (n-octyl) dimethyl diphosphate (EG4Oct), and tetraethylene glycol bis (2-butoxyethyl) dimethyl diphosphate (EG4BOE) in supercritical carbon dioxide (scCO₂) were determined at temperatures ranging from (318.15 to 333.15) K and pressures ranging from (12 to 21) MPa. Solubility increases in the order of EG4Oct (MW = 606.33) < EG4BOE (MW = 582.26) < EG4EH (MW = 606.33), indicating that branched side chains of the ligands play an important part in increasing solubility in scCO₂. Semi empirical density-based models proposed by Bartle and Chrastil were used to correlate the experimental data, and AARD values were calculated to be (1.2 to 2.9)% and (0.40 to 0.93)% for Bartle and Chrastil model, respectively. Additionally, the partial molar volumes of those compounds were estimated following the theory developed by Kumar and Johnston.     

Fluorescent azophenol-quinazoline dyad as multichannel reversible pH indicator in aqueous media: an innovative concept on diazo based dyads

A novel azophenol-quinazoline dyad 1 has been designed, synthesized and demonstrated as an efficient reversible multichannel pH indicator through distinct signalling in aqueous media. Owing to the competence between highly fluorescent quinazoline moiety and a well known fluorescence quencher diazo group, dyad 1 is moderately fluorescent in nature. Under acidic conditions 1 displays diverse fluorogenic changes (blue emission at pH 4.25; green at pH 1.80) while under basic condition (pH 11.80) chromogenic changes were observed.     

FEW: A workflow tool for free energy calculations of ligand binding

In the later stages of drug design projects, accurately predicting relative binding affinities of chemically similar compounds to a biomolecular target is of utmost importance for making decisions based on the ranking of such compounds. So far, the extensive application of binding free energy approaches has been hampered by the complex and time‐consuming setup of such calculations. We introduce the free energy workflow (FEW) tool that facilitates setup and execution of binding free energy calculations with the AMBER suite for multiple ligands. FEW allows performing free energy calculations according to the implicit solvent molecular mechanics (MM‐PB(GB)SA), the linear interaction energy, and the thermodynamic integration approaches. We describe the tool's architecture and functionality and demonstrate in a show case study on Factor Xa inhibitors that the time needed for the preparation and analysis of free energy calculations is considerably reduced with FEW compared to a fully manual procedure. © 2013 Wiley Periodicals, Inc.     

Comparative assessment of computational methods for the determination of solvation free energies in alcohol‐based molecules

The determination of differences in solvation free energies between related drug molecules remains an important challenge in computational drug optimization, when fast and accurate calculation of differences in binding free energy are required. In this study, we have evaluated the performance of five commonly used polarized continuum model (PCM) methodologies in the determination of solvation free energies for 53 typical alcohol and alkane small molecules. In addition, the performance of these PCM methods, of a thermodynamic integration (TI) protocol and of the Poisson–Boltzmann (PB) and generalized Born (GB) methods, were tested in the determination of solvation free energies changes for 28 common alkane‐alcohol transformations, by the substitution of an hydrogen atom for a hydroxyl substituent. The results show that the solvation model D (SMD) performs better among the PCM‐based approaches in estimating solvation free energies for alcohol molecules, and solvation free energy changes for alkane‐alcohol transformations, with an average error below 1 kcal/mol for both quantities. However, for the determination of solvation free energy changes on alkane‐alcohol transformation, PB and TI yielded better results. TI was particularly accurate in the treatment of hydroxyl groups additions to aromatic rings (0.53 kcal/mol), a common transformation when optimizing drug‐binding in computer‐aided drug design. © 2013 Wiley Periodicals, Inc.