BECOOL: Ballooning eigensolver with COOL finite elements

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ballooning Eigensolver using COOL finite elements) with second order Legendre polynomials recovers precisely the eigenvalues computed by the VVBAL shooting code. Timing runs reveal the need to determine an optimal lower order case. Eigenvalue convergence runs show that cubic Legendre polynomials construct the optimal ballooning mode equation for intensive computations.     

A new interpretation of Problem 10 of the Moscow Mathematical Papyrus

Although much discussed, the original intent of Problem 10 of the Moscow Mathematical Papyrus continues to be an unresolved question. This essay proposes a possible solution to the issue by joining together aspects of two theories on the subject advanced in the 1930s by W. W. Struve and T. E. Peet. From this point of beginning it is shown that the problem’s “basket” may originally have been intended to be understood as being of a specific actual size, thus revealing a set of correlations and insights regarding early Middle Kingdom mathematical capabilities and grain measurement concerns.     

(Benzo[4, 5]cyclohepta[l, 2-b]thiophen-4-ylidene)acetic Acids: Novel Non-ulcerogenic Antiinflammatory Agents

Compound (Z)- 8a has been found to display interesting antiinflammatory activity. In order to prepare derivatives with a wide variety of substituents in the aromatic part of the molecule, a new synthesis of the key intermediates 9a-g was developed starting from thiophene-3-carboxylic acid ( 11 ) and substituted benzyl bromides. The conversion of 9a-g to 10a-g follows a known procedure. Ketones 10a-g , on reaction with alkyl (dialkoxy-phosphoryl)acetate, followed by isomer separation and alkaline ester hydrolysis, yielded the desired derivatives (Z)- 8a-g and (E)- 8a-g . The biologically most interesting compound (Z)- 8a is currently undergoing clinical trials.     

Sequential and localized grafting on aliphatic polyester diblock copolymers using alkyne deprotection and click cycloaddition

Diblock copolymers, in which both blocks are composed of aliphatic polyesters, were synthesized from two different alkyne‐functionalized δ‐valerolactone monomers by ring opening polymerization and subsequent click cycloaddition. Trimethylsilyl protection of the alkyne functionality of one block was instrumental to the success of the synthesis. These novel aliphatic polyester diblock copolymers were characterized by ¹H and ¹³C NMR spectroscopy, gel permeation chromatography (GPC), and infrared (IR) spectroscopy. Sequential functionalization of the diblock copolymers with hydrophobic groups on one block, and hydrophilic groups on the other block, provides access to amphiphilic structures. Micellar structures generated from these polyester amphiphiles were characterized by fluorescence spectroscopy and transition electron microscopy (TEM). © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2009     

On the scattering frequencies of time-dependent potentials

This paper discusses the scattering frequencies associated with the scalar wave equation and a time-periodic, real, potential. It is shown that the scattering frequencies form a discrete set in the complex plane and depend continuously on the potential. Existence of the scattering frequencies is proved for periodic potentials which are perturbations of a time independent, nonnegative, potential.     

High‐field asymmetric waveform ion mobility spectrometry (FAIMS) coupled with high‐resolution electron transfer dissociation mass spectrometry for the analysis of isobaric phosphopeptides

We have applied high‐field asymmetric waveform ion mobility spectrometry (FAIMS) to the analysis of the phosphopeptides APLpSFRGSLPKSYVK, APLSFRGpSLPKSYVK, and APLSFRGSLPKpSYVK. The peptides have identical amino acid sequences and differ only in the site of phosphorylation. The results show that FAIMS is capable of at least partially separating these species. Separation was confirmed by coupling FAIMS with high‐resolution electron transfer dissociation (ETD) mass spectrometry. Phosphorylation is retained on the ETD peptide fragments thereby allowing assignment of the site of the modification. Co‐eluting phosphopeptides which differ only in the site of modification are frequently observed in liquid chromatography/tandem mass spectrometry phosphoproteomics experiments, and therefore these proof‐of‐principle results have implications for the application of FAIMS in that field. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthetic neovibsanes and their ability to induce neuronal differentiation in PC12 cells

A series of neovibsanin A and B derivatives and lower homologues were synthesized to study their neurotrophic ability with PC12 cells. 4,5-Bis-epi-neovibsanin A displayed prominent ability to induce neurite outgrowth compared to control cultures. Herein we describe the total synthesis of 4,5-bis-epi-neovibsanin A and B as well as comparing the biological activity of several neovibsane derivatives.     

A linked electron pair functional

A modification of the variational configuration interaction functional in the first-order interacting space for molecular electronic structure is presented. The modified functional is a fully linked expression that by construction is extensive and invariant to transformations of the underlying orbital basis and is exact for an ensemble of separated two-electron subsystems. In addition, an approximation to variational coupled cluster is generated through truncation of the exponential cluster operator. When combined, these methods demonstrate accuracy that exceeds that of the standard coupled-cluster method, in particular in situations where the reference Slater determinant is not a good approximation.