Synthesis and structural characterization of two nostoclide analogues

The vinylogous aldol reaction between appropriate aldehydes and furan-based silyloxy diene synthon generated from 3-benzyl-5H-furan-2-one (3) afforded two truncated lactone analogues [compounds (4) and (5)] of nostoclides (2). The compounds were fully characterized by IR, NMR (H-1 and C-13), 2D NMR spectroscopy experiments (HMBC, HSQC and NOESY), MS spectrometry and X-ray crystallography. Compounds (4) and (5) crystallized in the space group P2(1)2(1)2(1) and P2(1)/c, respectively. Although expected correlations between hydrogen atoms in spatial close proximity were not observed for compound (5) using NMR, the stereochemistry of the exocyclic double bond of both (4) and (5) was unambiguously determined to be Z and E, respectively, using X-ray crystallography. The packing of both compounds within the crystal are stabilized by non-classical inter-molecular hydrogen bonds. DFT calculations (B3LYP/6-31+G* level) confirmed that the crystal structures possessed the lowest energies in the gas phase when compared to their geometric isomers. (c) 2006 Elsevier B.V. All rights reserved.

Transreal arithmetic as a consistent basis for paraconsistent logics

Paraconsistent logics are non-classical logics which allow non-trivial and consistent reasoning about inconsistent axioms. They have been pro- posed as a formal basis for handling inconsistent data, as commonly arise in human enterprises, and as methods for fuzzy reasoning, with applica- tions in Artificial Intelligence and the control of complex systems. Formalisations of paraconsistent logics usually require heroic mathe- matical efforts to provide a consistent axiomatisation of an inconsistent system. Here we use transreal arithmetic, which is known to be consis- tent, to arithmetise a paraconsistent logic. This is theoretically simple and should lead to efficient computer implementations. We introduce the metalogical principle of monotonicity which is a very simple way of making logics paraconsistent. Our logic has dialetheaic truth values which are both False and True. It allows contradictory propositions, allows variable contradictions, but blocks literal contradictions. Thus literal reasoning, in this logic, forms an on-the- y, syntactic partition of the propositions into internally consistent sets. We show how the set of all paraconsistent, possible worlds can be represented in a transreal space. During the development of our logic we discuss how other paraconsistent logics could be arithmetised in transreal arithmetic.

Evolution PDEs and augmented eigenfunctions. half line.

The solution of an initial-boundary value problem for a linear evolution partial differential equation posed on the half-line can be represented in terms of an integral in the complex (spectral) plane. This representation is obtained by the unified transform introduced by Fokas in the 90's. On the other hand, it is known that many initial-boundary value problems can be solved via a classical transform pair, constructed via the spectral analysis of the associated spatial operator. For example, the Dirichlet problem for the heat equation can be solved by applying the Fourier sine transform pair. However, for many other initial-boundary value problems there is no suitable transform pair in the classical literature. Here we pose and answer two related questions: Given any well-posed initial-boundary value problem, does there exist a (non-classical) transform pair suitable for solving that problem? If so, can this transform pair be constructed via the spectral analysis of a differential operator? The answer to both of these questions is positive and given in terms of augmented eigenfunctions, a novel class of spectral functionals. These are eigenfunctions of a suitable differential operator in a certain generalised sense, they provide an effective spectral representation of the operator, and are associated with a transform pair suitable to solve the given initial-boundary value problem.

Non-commutative symbolic coding

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Non-genomic actions of estrogens and their interaction with genomic actions in the brain

Ligands for the nuclear receptor superfamily have at least two mechanisms of action: (a) classical transcriptional regulation of target genes (genomic mechanisms); and (b) non-genomic actions, which are initiated at the cell membrane, which could also impact transcription. Though transcriptional mechanisms are increasingly well understood, membrane-initiated actions of these ligands are incompletely understood. This has led to considerable debate over the physiological relevance of membrane-initiated actions of hormones versus genomic actions of hormones, with genomic actions predominating in the endocrine field. There is good evidence that the membrane-limited actions of hormones, particularly estrogens, involve the rapid activation of kinases and the release of calcium and that these are linked to physiologically relevant scenarios in the brain. We show evidence in this review, that membrane actions of estrogens, which activate these rapid signaling cascades, can also potentiate nuclear transcription in both the central nervous system and in non-neuronal cell lines. We present a theoretical scenario which can be used to understand this phenomenon. These signaling cascades may occur in parallel or in series but subsequently, converge at the modification of transcriptionally relevant molecules such as nuclear receptors and/or coactivators. In addition, other non-cognate hormones or neurotransmitters may also activate cascades to crosstalk with estrogen receptor-mediated transcription, though the relevance of this is less clear. The idea that coupling between membrane-initiated and genomic actions of hormones is a novel idea in neuroendocrinology and provides us with a unified view of hormone action in the central nervous system.

Membrane-initiated non-genomic signaling by estrogens in the hypothalamus: cross-talk with glucocorticoids with implications for behavior

The estrogen receptor and glucocorticoid receptor are members of the nuclear receptor superfamily that can signal using both non-genomic and genomic transcriptional modes. Though genomic modes of signaling have been well characterized and several behaviors attributed to this signaling mechanism, the physiological significance of non-genomic modes of signaling has not been well understood. This has partly been due to the controversy regarding the identity of the membrane ER (mER) or membrane GR (mGR) that may mediate rapid, non-genomic signaling and the downstream signaling cascades that may result as a consequence of steroid ligands binding the mER or the mGR. Both estrogens and glucocorticoids exert a number of actions on the hypothalamus, including feedback. This review focuses on the various candidates for the mER or mGR in the hypothalamus and the contribution of non-genomic signaling to classical hypothalamically driven behaviors and changes in neuronal morphology. It also attempts to categorize some of the possible functions of non-genomic signaling at both the cellular level and at the organismal level that are relevant for behavior, including some behaviors that are regulated by both estrogens and glucocorticoids in a potentially synergistic manner. Lastly, it attempts to show that steroid signaling via non-genomic modes may provide the organism with rapid behavioral responses to stimuli.