Oxygen atom transfer in models for molybdenum enzymes: isolation and structural, spectroscopic, and computational studies of intermediates in oxygen atom transfer from molybdenum(VI) to phosphorus(III)

Intermediates in the oxygen atom transfer from Mo(VI) to P(III), [Tp(iPr)MoOX(OPR3)] (Tp(iPr) = hydrotris(3-isopropylpyrazol-1-yl)borate; X = Cl-, phenolates, thiolates), have been isolated from the reactions of [Tp(iPr)MoO2X] with phosphines (PEt3, PMePh2, PPh3). The green, diamagnetic oxomolybdenum(IV) complexes possess local C(1) symmetry (by NMR spectroscopy) and exhibit IR bands assigned to nu(Mo==O) (approximately 950 cm(-1)) and nu(P==O) (1140-1083 cm(-1)) vibrations. The X-ray crystal structures of [Tp(iPr)MoOX(OPEt3)] (X = OC6H4-2-sBu, SnBu), [Tp(iPr)MoO(OPh)(OPMePh2)], and [Tp(iPr)MoOCl(OPPh3)] have been determined. The monomeric complexes exhibit distorted octahedral geometries, with coordination spheres composed of tridentate fac-Tp(iPr) and mutually cis monodentate terminal oxo, phosphoryl (phosphine oxide), and monoanionic X ligands. The electronic structures and stabilities of the complexes have been probed by computational methods, with the three-dimensional energy surfaces confirming the existence of a low-energy steric pocket that restricts the conformational freedom of the phosphoryl ligand and inhibits complete oxygen atom transfer. The reactivity of the complexes is also briefly described.     

Finding the Homology of Submanifolds with High Confidence from Random Samples

Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high-dimensional spaces. We consider the case where data are drawn from sampling a probability distribution that has support on or near a submanifold of Euclidean space. We show how to “learn” the homology of the submanifold with high confidence. We discuss an algorithm to do this and provide learning-theoretic complexity bounds. Our bounds are obtained in terms of a condition number that limits the curvature and nearness to self-intersection of the submanifold. We are also able to treat the situation where the data are “noisy” and lie near rather than on the submanifold in question. The main results of this paper were first presented at a conference in honor of John Franks and Clark Robinson at Northwestern University in April 2003. These results were formally written as Technical Report No. TR-2004-08, Department of Computer Science, University of Chicago.     

Number-theoretic interpretation and construction of a digital circle

This paper presents a new interpretation of a digital circle in terms of the distribution of square numbers in discrete intervals. The number-theoretic analysis that leads to many important properties of a digital circle succinctly captures the original perspectives of digital calculus and digital geometry for its visualization and characterization. To demonstrate the capability and efficacy of the proposed method, two simple algorithms for the construction of digital circles, based on simple number-theoretic concepts, have been reported. Both the algorithms require only a few primitive operations and are completely devoid of any floating-point computation. To speed up the computation, especially for circular arcs of high radii, a hybridized version of these two algorithms has been given. Experimental results have been furnished to elucidate the analytical power and algorithmic efficiency of the proposed approach. It has been also shown, how and why, for sufficiently high radius, the number-theoretic technique can expedite a circle construction algorithm.     

A tandem mass spectrometric approach to the identification of O‐glycosylated glargine glycoforms in active pharmaceutical ingredient expressed in Pichia pastoris

Glycoforms of glargine expressed in Pichia pastoris were isolated by high‐performance liquid chromatography and analyzed by a series of chemical and mass spectrometric methods for the identification of various glycoforms, glycosylation position, nature and structure of glycans. Reduction and alkylation, peptide mapping techniques were used to decipher the amino acid site at which glycosylation had taken place. Chemical methods were coupled with mass spectrometry techniques such as electrospray ionization and matrix‐assisted laser desorption/ionization for identification of the glycosylation site. Copyright © 2009 John Wiley & Sons, Ltd.     

On further application of r as a metric for validation of QSAR models

Validation is a crucial aspect for quantitative structure–activity relationship (QSAR) model development. External validation is considered, in general, as the most conclusive proof of predictive capacity of a QSAR model. In the absence of truly external data set, external validation is usually performed on test set compounds, which are members of the original data set but not used in model development exercise. In the case of small data sets, QSAR researchers experience problem in model development due to the fact that the developed models may be less reliable on account of the small number of training set compounds and such models may also show poor external predictability because the models may not have captured all necessary features required for the particular structure–activity relationships. The present paper attempts to show that ‘true r_(LOO)’ statistic calculated based on the model derived from the undivided data set with application of variable selection strategy at each cycle of leave‐one‐out (LOO) validation may reflect external validation characteristics of the developed model thus obviating the requirement of splitting of the data set into training and test sets. This approach may be helpful in the case of small data sets as it uses all available data for model development and validation thus making the resulting model more reliable. Copyright © 2009 John Wiley & Sons, Ltd.     

A series of Cu(II)-azide polymers of Cu6 building units and the role of chelating diamine in controlling their dimensionality: synthesis, structures, and magnetic behavior

Four new neutral copper-azido polymers [Cu(6)(N(3))(12)(aem)(2)](n)(1), [Cu(6)(N(3))(12)(dmeen)(2)(H(2)O)(2)](n) (2), [Cu(6)(N(3))(12)(N,N'-dmen)(2)](n) (3), and [Cu(6)(N(3))(12)(hmpz)(2)](n) (4) [aem = 4-(2-aminoethyl)morpholine; dmeen = N,N-dimethyl-N'-ethylethylenediamine; N,N'-dmen = N,N'-dimethylethylenediamine and hmpz = homopiperazine] have been synthesized by using 0.33 mol equiv of the chelating diamine ligands with Cu(NO(3))(2)·3H(2)O/CuCl(2)·2H(2)O and an excess of NaN(3). Single crystal X-ray structures show that the basic unit of these complexes, especially 1-3, contains very similar Cu(II)(6) building blocks. But the overall structures of these complexes vary widely in dimensionality. While 1 is three-dimensional (3D) in nature, 2 and 3 have a two-dimensional (2D) arrangement (with different connectivity) and 4 has a one-dimensional (1D) structure. Cryomagnetic susceptibility measurements over a wide range of temperature exhibit dominant ferromagnetic behavior in all the four complexes. The experimental susceptibility data have been analyzed by some theoretical model equations.     

Syntheses,characterization, X-ray crystal structures and emission properties of copper(II), zinc(II) and cadmium(II) complexes of pyridyl–pyrazole derived Schiff base ligand – Metal selective ligand binding modes

The varying coordination modes of the title ligand, L [5-methyl-1-(pyridin-2-yl)-N′-[pyridin-2-ylmethylidene]pyrazole-3-carbohydrazide] towards the different metal centers is reported by preparation and characterization of Cu(II), Zn(II) and Cd(II) complexes, [Cu(L)NO₃.H₂O](NO₃) (1) [Zn(L)₂](ClO₄)₂·2DMF (2) and [Cd(L)(I)₂] (3) respectively. In 1, the neutral ligand serves as tetradentate 4 N donor where both pyridine and pyrazole nitrogen atoms of pyridyl–pyrazole part are coordinatively active, leaving the carbonyl oxygen of the carbohydrazide part inactive. The same pyridine and pyrazole N atoms remain abstained from the coordination process towards the Zn(II) and Cd(II) metal centers. For 2 and 3 the ligand behaves as a tridentate NNO donor where the two nitrogen atoms come from azomethine, pyridine of pyridine-2-carbaldehyde parts and O from carbonyl oxygen atoms (carbohydrazide part). The complex 1 and 2 are distorted octahedral while complex 3 adopts distorted square pyramidal geometry. All the complexes are X-ray crystallographically characterized.     

Finite frames,P-frames and basically disconnected frames

Let \({\mathcal{P}}\) be an ideal of closed quotients of a completely regular frame L and \({\mathcal{R}_{\mathcal{P}}(L)}\) the collection of all functions in the ring \({\mathcal{R}(L)}\) whose support belong to \({\mathcal{P}}\) . We show that \({\mathcal{R}(L)}\) is a Noetherian ring if and only if \({\mathcal{R}(L)}\) is an Artinian ring if and only if L is a finite frame. Using this result, we next show that if \({\mathcal{P}}\) is the ideal of all compact closed quotients of L and L is \({\mathcal{P}}\) -continuous, then \({\mathcal{R}_{\mathcal{P}}(L)}\) is a Noetherian ring if and only if L is finite. Moreover, we show that L is a P-frame if and only if each ideal of \({\mathcal{R}(L)}\) is of the form \({\mathcal{R}_{\mathcal{P}}(L)}\) for some choice of \({\mathcal{P}}\) . We furnish equivalent conditions for \({\mathcal{R}_{\mathcal{P}}(L)}\) to be a prime ideal, a free ideal, and an essential ideal of \({\mathcal{R}(L)}\) separately in terms of the cozero elements of L. Finally, we show that L is basically disconnected if and only if \({\mathcal{R}(L)}\) is a coherent ring.