Development and validation of LC‐MS/MS method for the estimation of β‐hydroxy‐β‐methylbutyrate in rat plasma and its application to pharmacokinetic studies

A simple, sensitive and specific high‐performance liquid chromatography mass spectrometry (LC‐MS/MS) method was developed and validated for the quantification of β‐hydroxy‐β‐methyl butyrate (HMB) in small volumes of rat plasma using warfarin as an internal standard (IS). The API‐4000 LC‐MS/MS was operated under the multiple reaction‐monitoring mode using the electrospray ionization technique. A simple liquid–liquid extraction process was used to extract HMB and IS from rat plasma. The total run time was 3 min and the elution of HMB and IS occurred at 1.48 and 1.75 min respectively; this was achieved with a mobile phase consisting of 0.1% formic acid in a water–acetonitrile mixture (15:85, v/v) at a flow rate of 1.0 mL/min on a Agilent Eclipse XDB C₈ (150 × 4.6, 5 µm) column. The developed method was validated in rat plasma with a lower limit of quantitation of 30.0 ng/mL for HMB. A linear response function was established for the range of concentrations 30–4600 ng/mL (r > 0.998) for HMB. The intra‐ and inter‐day precision values for HMB were acceptable as per Food and Drug Administration guidelines. HMB was stable in the battery of stability studies, viz. bench‐top, autosampler freeze–thaw cycles and long‐term stability for 30 days in plasma. The developed assay method was applied to a bioavailability study in rats. Copyright © 2012 John Wiley & Sons, Ltd.     

Bivariate factorizations connecting Dickson polynomials and Galois theory

In his Ph.D. Thesis of 1897, Dickson introduced certain permutation polynomials whose Galois groups are essentially the dihedral groups. These are now called Dickson polynomials of the first kind, to distinguish them from their variations introduced by Schur in 1923, which are now called Dickson polynomials of the second kind. In the last few decades there have been extensive investigations of both of these types, which are related to the classical Chebyshev polynomials. We give new bivariate factorizations involving both types of Dickson polynomials. These factorizations demonstrate certain isomorphisms between dihedral groups and orthogonal groups, and lead to the construction of explicit equations with orthogonal groups as Galois groups.

     

Semilinear transformations

In previous papers, nice trinomial equations were given for unramified coverings of the once punctured affine line in nonzero characteristic with the projective general group and the general linear group as Galois groups where is any integer and is any power of . These Galois groups were calculated over an algebraically closed ground field. Here we show that, when calculated over the prime field, as Galois groups we get the projective general semilinear group and the general semilinear group . We also obtain the semilinear versions of the local coverings considered in previous papers.

     

Latex-mediated synthesis of ZnS nanoparticles: green synthesis approach

A low-cost, green synthesis of ZnS nanoparticles is reported using 0.3 % latex solution prepared from Jatropha curcas L. ZnS nanoparticles were characterized by X-ray diffraction, selected area electron diffraction, transmission electron microscopy, energy dispersive analysis of X-rays, UV–vis optical absorption and photoluminescence techniques. Fourier Transform Infrared Spectroscopy was performed to find the role of cyclic peptides namely curcacycline A (an octapeptide), curcacycline B (a nonapeptide) and curcain (an enzyme) as a possible reducing and stabilizing agents present in the latex of J. curcas L. The average size of ZnS nanoparticles was found to be 10 nm. Latex of J. curcas L. itself acts as a source of sulphide (S⁻²) ions that are donated to Zn ions under present experimental conditions. Source of sulphide (S⁻²) ions is still unclear, but we speculate that cysteine or thiol residues present in enzyme curcain may be donating these sulphide (S⁻²) ions.     

Dicritical divisors and Jacobian problem

The dicritical divisor coming out of integrable holonomic systems gets miraculously married to the jacobian problem of algebraic geometry.     

Cross‐Platform DNA Encoding for Single‐Cell Imaging of Gene Expression

Integration of imaging data across different molecular target types can provide in‐depth insight into cell physiology and pathology, but remains challenging owing to poor compatibility between target‐type‐specific labeling methods. We show that cross‐platform imaging analysis can be readily achieved through DNA encoding of molecular targets, which translates the molecular identity of various target types into a uniform in situ array of ssDNA tags for subsequent labeling with complementary imaging probes. The concept was demonstrated through multiplexed imaging of mRNAs and their corresponding proteins with multicolor quantum dots. The results reveal heterogeneity of cell transfection with siRNA and outline disparity in RNA interference (RNAi) kinetics at the level of both the mRNA and the encoded protein.     

Equations of similitude

A general technique is developed to enlarge the Galois group of an equation from a subgroup of a finite classical isometry group towards the corresponding similitude group. Abhyankar’s work was partly supported by NSF grant DMS 97-32592 and NSA grant MDA 904-97-1-0010, and Loomis’s work was partly supported by a Sloan Doctoral Dissertation Fellowship.     

Projective polynomials

Certain nice trinomials have the projective linear groups as their Galois groups. This was proved using considerable group theory. Here is an easier proof based on the observation that the said trinomials are what may be called projective polynomials. It extends the results to a local situation.

     

Polynomial expansion

The idea of initial form is refined into the concept of polyform. This can be used to streamline desingularization.