Structure-activity relationship between the 3D distribution of the electrophilicity of sugar derivatives and their cytotoxic and antiviral properties

Summary The cytotoxic activities of a series of sugar derivatives bearing electrophilic groups (1-cyanovinyl, 4-cyanochromen-2-yl and 3-nitrochromen-2-yl) have been correlated with their electrophilic properties. To this end, an electrophilic index was defined as an isovalue surface where the interaction energy with an incoming model nucelophile (H^–) was equal to a predefined value. This index, calculated from extended Hückel wave functions, allows one to quantify the electrophilic character of the substrates and to describe its spatial localization within the molecular volume (at Michael acceptor sites or on other parts of the molecules). Only sugars for which Michael acceptor reactivity was predicted were retained, and they were subdivided into two groups: those showing antiviral activity against a retrovirus and those devoid of such activity. Under these conditions, good correlations between cytotoxic activity and electrophilic reactivity-positive for the first group, negative for the second-were found. In addition, the ratio electrophilicity/sum of the absolute value of the dipole plus its projection along the principal axis of inertia, Z, of the molecule allows one to predict to which of these groups a sugar derivative belongs.     

Logical structures and genus of proofs

Any arbitrarily complicated non-oriented graph, that is a graph of arbitrarily large genus, can be encoded in a cut-free proof. This unpublished result of Statman was shown in the early seventies. We provide a proof of it, and of a number of other related facts.     

Justifying and Proving in the Cabri Environment

This paper describes a long term teaching experiment carried out with students from the 9th–10th grades. Geometrical constructions in the Cabri environment were selected as a specific field of experience, within which the sense of theory may emerge. The idea of construction constitutes the key to accessing the idea of theorem, moving from a generic idea of justification towards the idea of validating within a geometrical system. The study aims at clarifying the role of the Cabri environment in this teaching-learning processes: analysis of protocols shows the possible evolution of a justification into a proof but at the same time indicates that this evolution is not expected to be simple and spontaneous.This revised version was published online in September 2005 with corrections to the Cover Date.     

Quadratic Hedging Methods for Defaultable Claims

We apply the local risk-minimization approach to defaultable claims and we compare it with intensity-based evaluation formulas and the mean-variance hedging. We solve analytically the problem of finding respectively the hedging strategy and the associated portfolio for the three methods in the case of a default put option with random recovery at maturity.     

KAM Stability for a three-body problem of the Solar system

A new (iso-energetic) KAM method is tested on a specific three-body problem “extracted” from the Solar system (Sun-Jupiter + asteroid 12 Victoria). Analytical results in agreement with the observed data are established. This paper is a concise presentation of [2]. Supported by the MIUR projects: “Dynamical Systems: Classical, Quantum, Stochastic” and “Variational Methods and Nonlinear Differential Equations” Received: February 3, 2004     

A computationally efficient finite element model with perfectly matched layers applied to scattering from axially symmetric objects

A frequency-domain finite-element (FE) technique for computing the radiation and scattering from axially symmetric fluid-loaded structures subject to a nonsymmetric forcing field is presented. The Berenger perfectly matched layer (PML), applied directly at the fluid-structure interface, makes it possible to emulate the Sommerfeld radiation condition using FE meshes of minimal size. For those cases where the acoustic field is computed over a band of frequencies, the meshing process is simplified by the use of a wavelength-dependent rescaling of the PML coordinates. Quantitative geometry discretization guidelines are obtained from a priori estimates of small-scale structural wavelengths, which dominate the acoustic field at low to mid frequencies. One particularly useful feature of the PML is that it can be applied across the interface between different fluids. This makes it possible to use the present tool to solve problems where the radiating or scattering objects are located inside a layered fluid medium. The proposed technique is verified by comparison with analytical solutions and with validated numerical models. The solutions presented show close agreement for a set of test problems ranging from scattering to underwater propagation.     

Structural Revision and Elucidation of the Biosynthesis of Hypodoratoxide by 13C,13C COSY NMR Spectroscopy

Feeding of (2,3,4,5,6‐¹³C₅)mevalonolactone to the fungus Hypomyces odoratus resulted in a completely labeled sesquiterpene ether. The connectivity of the carbon atoms was easily deduced from a ¹³C,¹³C COSY spectrum, revealing a structure that was different from the previously reported structure of hypodoratoxide, even though the reported ¹³C NMR data matched. A structural revision of hypodoratoxide is thus presented. Its absolute configuration was tentatively assigned from its co‐metabolite cis‐dihydroagarofuran. Its biosynthesis was investigated by feeding of (3‐¹³C)‐ and (4,6‐¹³C₂)mevalonolactone, which gave insights into the complex rearrangement of the carbon skeleton during terpene cyclization by analysis of the ¹³C,¹³C couplings.