The chemistry and preparation of tantalum complexes with 2,3-dihydroxy benzoic acid: experimental and theoretical investigation

The effect of 2,3-dihydroxybenzoic acid (2,3DHBA, pyrocatechuic acid) on the chloro-alkoxo-species [TaCl(5-x)(OMe)(x)], formed by dissolving TaCl(5) in MeOH, has been studied. The coordination of 2,3DHBA-H(2)(-) on Ta (V) replacing MeO-terminal groups was monitored via NMR spectroscopy. The yellow solid 1 was isolated from the mixture of TaCl(5), with neutral 2,3-DHBA, in MeOH. From this solid the elemental (C, H and Ta), the thermogravimetric analyses, the IR, NMR, ESR and electronic spectra support the formula Ta(2)(2,3DHBA)(2)(O)(2)Cl(4)(MeO)(4). The ESR spectrum of solid 1, at 4.2 K, shows a half-field signal apart from a multiline signal around g=2, supporting evidence for semiquinone and Ta (IV) presence. The occurrence of superoxide radical, in the low temperature of ESR spectrum recording, cannot be ruled out. By heating the solid 1 at 500°C, an oxide phase showing porous character (SEM) and retaining CO(2) (IR), is evident. Solid 1 heated at 900°C, leads to the formation of β-Ta(2)O(5) orthorhombic phase, as the XRD pattern indicates. The hydrolytic process of solid 1, in aqueous solutions, has been studied; the presence of paramagnetic species generated in situ upon addition of base and the consequent degradative process of 2,3-DHBA, under aerobic conditions is obvious. In order to gain information for the structure of solid 1, DFT calculations have been performed for some theoretical models, based on the empirical formula of solid 1. The calculated structural and spectroscopic parameters have been correlated to experimental results. The energy optimized structures may give an idea about the way of MeCl and MeOMe formation as well some possible intermediates of the hydrolytic mechanism.     

On the equivalence of heat kernel estimates and logarithmic Sobolev inequalities for the Hodge Laplacian

In this paper we consider the Hodge Laplacian on differential k-forms over smooth open manifolds MN, not necessarily compact. We find sufficient conditions under which the existence of a family of logarithmic Sobolev inequalities for the Hodge Laplacian is equivalent to the ultracontractivity of its heat operator.We will also show how to obtain a logarithmic Sobolev inequality for the Hodge Laplacian when there exists one for the Laplacian on functions. In the particular case of Ricci curvature bounded below, we use the Gaussian type bound for the heat kernel of the Laplacian on functions in order to obtain a similar Gaussian type bound for the heat kernel of the Hodge Laplacian. This is done via logarithmic Sobolev inequalities and under the additional assumption that the volume of balls of radius one is uniformly bounded below.     

Talking mathematically: An analysis of discourse communities

Discourse has always been at the heart of teaching. In more recent years, the mathematics education community has also turned its attention towards understanding the role of discourse in mathematics teaching and learning. Using earlier classifications of discourse, in this paper, we looked at three types of classrooms: classrooms that engage in high discourse, low discourse and a hybrid of the two. We aimed to understand how the elements of each discourse affected classroom learning, relationships between teachers and students, and participatory structures for students. Overall, our findings highlight the important relationship between cognitively demanding tasks and mathematical talk, and the power of discourse as a “thinking device” as opposed to mere conduit of knowledge. Our work also points to the under-theorized nature of hybrid discourse in mathematics classrooms, thereby providing some directions for pedagogy and further research.     

On conditions for optimality of a class of nondifferentiable functions

The purpose of this paper is to derive first-order necessary conditions for optimality of a class of nondifferentiable functions. The first-order necessary conditions for optimality for the minimax function and thel ₁-function can be considered as special cases of the present method. Furthermore, the optimality conditions obtained are used to obtain threshold values for the controlling parameters of a class of exact penalty functions.     

Use of Adsorptive Transfer Stripping Voltammetry for Analyzing Variations of Cytosine Methylation in DNA

The electrochemical behavior and thermal stability of double stranded oligonucleotides containing 5‐methyl‐cytosine and 7‐deaza‐guanosine as nucleotide analogues, as well as of Jurkat genomic DNAs methylated to different degree were studied by ACV and SWV and by thernal denaturation analysis. ACV and SWV combined with thermal denaturation analysis of the natural and modified oligonucleotides gave information regarding the presence of methylation and the concomitant conformational changes. ACV and SWV of Jurkat DNA mixtures methylated to different degrees revealed a decrease of the peak heights with increasing methylation, indicating an increase of structural rigidity, in agreement with the thermal denaturation data. These results verify the, possibly local, conformational changes introduced by DNA methylation. The results obtained in all cases were reproducible.     

Direct Constructions of the Paracompact Coreflections of Frames

We present a general construction from which one can derive in a unified manner (i) the Stone–ech compactification of a frame, (ii) the Lindelöf coreflection for both frames and nearness frames and (iii) the paracompact coreflection in the category of frames.     

Vanadium reactions with 3,4–dihydroxyphenylethanoic acid in alcohol solutions. Aromatic ring degradation

The reaction of Vv with 3,4–dihydroxyphenylethanoic acid (3,4–DHPE) was studied by various spectroscopic techniques. Vanadium-catechol complexation is the first step, and is followed by stepwise ligand degradation, leading to several products, including AcOH. The mechanism of this degradation is investigated.