Solid-state and solution structures of hetero-aggregates formed between nBuLi and NCN pincer aryl lithium

The reaction of NCNLi pincers (NCN = [2,6-(R(2)NCH(2))(2)C(6)H(3)](-), R = Me (), Et ()) with various equivalents of nBuLi in non-polar solvent results in the generation of novel mixed alkyl-aryl organolithium hetero-aggregates. The identification (variable temperature (1)H, (13)C, (7)Li and 2D NMR spectroscopy and X-ray crystallography) of multiple, equilibrating mixed-aggregates that form in these reactions has been achieved. Fluxional processes in the parent [NCNLi](2) dimeric homo-aggregates were re-evaluated and Li-N bond rupture was found to be in operation, a prerequisite towards further aggregation chemistry. The crystallized aggregates, with the formula (2).[nBuLi](2) or (2).[nBuLi](2), shows one amine arm from each NCNLi fragment stabilizing a [nBuLi](2) dimer. The core of the aggregates exhibit a roughly cubic Li(4)C(4) configuration with each aryl carbanion eta(3) coordinated to Li(3) triangular faces. Dissolution of microcrystalline powders of (2).[nBuLi](2) or (2).[nBuLi](2) regenerates the observed equilibria. Based on the NMR data, the remaining mixed aggregates are proposed to have the formula .[nBuLi](3) and .[nBuLi](3), respectively; the solution structure is again based on a Li(4)C(4) cluster. The relative concentration of the constituents in these equilibria was found to vary depending on the steric size of the amine groups. In the case of , the predominant species is the (2).[nBuLi](2) aggregate while for , the dimer (2) is favoured.     

How O-substitution of sialyl donors affects their stereoselectivity

The profound effect of substituents at C-5 of glycosyl sialosides on their stereoselectivity is well-known although the exact nature of this effect is somewhat less understood. Presented herein is a comparative study of a range of novel sialyl donors with various O-substituents. It is demonstrated that O-substituents at C-4 and C-7 may also have a significant effect on the reactivity of sialyl donors and on the stereoselectivity of chemical sialylation.     

Deep-UV Raman spectroscopic analysis of structure and dissolution rates of silica-rich sodium borosilicate glasses

As part of ongoing studies to evaluate relationships between structure and rates of dissolution of silicate glasses in aqueous media, sodium borosilicate glasses of composition Na₂O·xB₂O₃·(3 − x)SiO₂, with x ≤ 1 (Na₂O/B₂O₃ ratio ≥ 1), were analyzed using deep-UV Raman spectroscopy. Results were quantified in terms of the fraction of SiO₄ tetrahedra with one non-bridging oxygen (Q³) and then correlated with Na₂O and B₂O₃ content. The Q³ fraction was found to increase with increasing Na₂O content, in agreement with studies on related glasses, and, as long as the value of x was not too high, this contributed to higher rates of dissolution in single pass flow-through testing. In contrast, dissolution rates were less strongly determined by the Q³ fraction when the value of x was near unity, and appeared to grow larger upon further reduction of the Q³ fraction. Results were interpreted to indicate the increasingly important role of network hydrolysis in the glass dissolution mechanism as the BO₄ tetrahedron replaces the Q³ unit as the charge-compensating structure for Na⁺ ions. Finally, the use of deep-UV Raman spectroscopy was found to be advantageous in studying finely powdered glasses in cases where visible Raman spectroscopy suffered from weak Raman scattering and fluorescence interference.     

On the Homological Dimension of Algebras of Differential Operators

Let A be a commutative algebra over a field k, and V_A be the k-subalgebra of End_k(A) generated by End_A(A) = A and all k-derivations of A. A study of the homological properties of V_A was initiated by Hochschild, Kostant, and Rosenberg in [5], and continued by Rinehart [8], [9], Roos [11], Björk [1], Rinehart and Rosenberg [10], and others. It was proved in [5] that, if k is perfect and A is a regular affine algebra of dimension r, then the global dimension of V_A is between r and 2r. Moreover, if k has positive characteristic, then gl.dim V_A = 2r [8]. By a recent celebrated theorem of Roos [11], gl.dim V_A = r if k has characteristic zero and A = k[x₁, …, x_r]; in this case V_A is the so-called “Weyl algebra on 2r variables”.     

Fourier transform Raman spectroscopy

The basic experimental aspects of Fourier transform Raman Spectroscopy are reviewed with an emphasis on detector technology. The sensitivity is comparable to dispersive Raman Spectroscopy using visible lasers. The ease of spectral subtraction is demonstrated and examples are given showing the elimination of fluorescence.     

Raman spectra of CrO2 and MoO2 single Crystals

The Raman spectra of single crystals of CrO₂ and MoO₂ have been studied from 77°K to 500°K for a comparison with the heavily damped phonon features in metallic VO₂. The spectrum of MoO₂ is very similar to that of monoclinic VO₂ whereas CrO₂ exhibits phonon spectra similar to rutile with no appreciable change at the ferromagnetic c curie temperature. The results are discussed with respect to the various models proposed for the semiconductor-to-metal transition in VO₂.     

Explicit volume-preserving splitting methods for polynomial divergence-free vector fields

We present new, explicit, volume-preserving splitting methods for polynomial divergence-free vector fields of arbitrary degree (both positive and negative). The main idea is to decompose the divergence polynomial by means of an appropriate basis for polynomials: the monomial basis. For each monomial basis function, the split fields are then identified by collecting the appropriate terms in the vector field so that each split vector field is volume preserving. We show that each split field can be integrated exactly by analytical methods. Thus, the composition yields a volume preserving numerical method. Our numerical tests indicate that the methods compare favorably to standard integrators both in the quality of the numerical solution and the computational effort.     

Symmetric spaces and Lie triple systems in numerical analysis of differential equations

A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature and their tangents. This theory can be used to unify a range of different topics, such as polar-type matrix decompositions, splitting methods for computation of the matrix exponential, composition of selfadjoint numerical integrators and dynamical systems with symmetries and reversing symmetries. The thread of this paper is the following: involutive automorphisms on groups induce a factorization at a group level, and a splitting at the algebra level. In this paper we will give an introduction to the mathematical theory behind these constructions, and review recent results. Furthermore, we present a new Yoshida-like technique, for self-adjoint numerical schemes, that allows to increase the order of preservation of symmetries by two units. The proposed techniques has the property that all the time-steps are positive.