Multivariate holomorphic Hermite polynomials

The Ramanujan Journal - We introduce holomorphic Hermite polynomials in n complex variables that generalize the Hermite polynomials in n real variables introduced by Hermite in the late 19th...     

Covariance mapping in matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

A novel method for acquisition and numerical analysis of matrix-assisted laser desorption/ionization (MALDI) time-of-flight mass spectral data is described. The digitized ion current transient from each consecutive laser shot is first acquired and stored independently. Subsequently, statistical correlation parameters between all stored transients are computed. We illustrate the uses of this event-by-event analysis method for studies of sample surface heterogeneity as well as for elucidating the mechanisms of ion formation in MALDI. Other potential applications of the method are also outlined.     

Synthesis and antibacterial activity of hydroxylated 2-arylbenzothiazole derivatives

Abstract

N-acyliminium reagents formed in situ from benzothiazole and alkyl chloroformates react with hydroxyarenes in a Friedel-Crafts manner, providing access to 2-(hydroxyaryl)-benzothiazolines with antibacterial properties.     

1,1,1‐Trichloro‐3‐(1‐phenethylamino‐ethylidene)‐ pentane‐2,4‐dione—synthesis,spectroscopic, theoretical and structural elucidation

1,1,1‐Trichloro‐3‐(1‐phenethylamino‐ethylidene)‐pentane‐2,4‐dione is spectroscopically and structurally elucidated by means of linear‐polarized IR spectroscopy (IR‐LD) of oriented solids as a colloidal suspension in nematic liquid crystal. Structural information and IR‐spectroscopic assignment are supported by quantum chemical calculations at MP2 and B3LYP level of theory and 6‐311++G** basis set. The geometry is characterized with an inramolecular hydrogen bond of NH^…O?C with length of 2.526 Å and a NHO angle of 140.5(1)°. The NH? C(CH₃)C?C? C?O(CH₃) fragment is nearly flat with a maximal deviation of total planarity of 10.4°. Copyright © 2007 John Wiley & Sons, Ltd.     

Non-random fluctuations and multi-scale dynamics regulation of human activity

We investigate if known extrinsic and intrinsic factors fully account for the complex features observed in recordings of human activity as measured from forearm motion in subjects undergoing their regular daily routine. We demonstrate that the apparently random forearm motion possesses dynamic patterns characterized by robust scale-invariant and nonlinear features. These patterns remain stable from one subject to another and are unaffected by changes in the average activity level that occur within individual subjects throughout the day and on different days of the week, since they persist during daily routine and when the same subjects undergo time-isolation laboratory experiments designed to account for the circadian phase and to control the known extrinsic factors. Further, by modeling the scheduled events imposed throughout the laboratory protocols, we demonstrate that they cannot account for the observed scaling patterns in activity fluctuations. We attribute these patterns to a previously unrecognized intrinsic nonlinear multi-scale control mechanism of human activity that is independent of known extrinsic factors such as random and scheduled events, as well as the known intrinsic factors which possess a single characteristic time scale such as circadian and ultradian rhythms.     

Boundary rigidity and stability for generic simple metrics

We study the boundary rigidity problem for compact Riemannian manifolds with boundary : is the Riemannian metric uniquely determined, up to an action of diffeomorphism fixing the boundary, by the distance function known for all boundary points and ? We prove in this paper local and global uniqueness and stability for the boundary rigidity problem for generic simple metrics. More specifically, we show that there exists a generic set of simple Riemannian metrics such that for any , any two Riemannian metrics in some neighborhood of having the same distance function, must be isometric. Similarly, there is a generic set of pairs of simple metrics with the same property. We also prove Hölder type stability estimates for this problem for metrics which are close to a given one in .     

Synthesis of some novel 11b-substituted pyrimido[6,1-a]-isoquinoline derivatives

A series of novel 11b-substituted 1,6,7,11b-tetrahydropyrimido[6,1-a]- isoquinoline-2,4-diones and 4-thioxo-1,3,4,6,7,11b-hexahydropyrimido[6,1-a]isoquinolin-2- ones were synthesized, utilizing two alternative strategies for ring closure of tetrahydroisoquinoline intermediates obtained from N-phenethyl enaminones.     

On the identities of the Grassmann algebras in characteristicp>0

In this note we exhibit bases of the polynomial identities satisfied by the Grassmann algebras over a field of positive characteristic. This allows us to answer the following question of Kemer: Does the infinite dimensional Grassmann algebra with 1, over an infinite fieldK of characteristic 3, satisfy all identities of the algebraM ₂(K) of all 2×2 matrices overK? We give a negative answer to this question. Further, we show that certain finite dimensional Grassmann algebras do give a positive answer to Kemer's question. All this allows us to obtain some information about the identities satisfied by the algebraM ₂(K) over an infinite fieldK of positive odd characteristic, and to conjecture bases of theidentities ofM ₂(K).     

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized‐gradient approximation (GGA), nonlocal correlation, meta‐GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised‐RPBE, vdW‐DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW‐DF and meta‐GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of ?2.62 and ?1.1% for the N? N stretching and Rh? H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh? H and N? N stretching modes from the bulk phonons and by solving one‐ and two‐dimensional Schrödinger equation associated with the Rh? H, Rh? N, and N? N potential energy we calculated the anharmonic correction for N? N and Rh? H stretching modes as ?31 cm^?1 and ?77 cm^?1 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. © 2014 Wiley Periodicals, Inc.