Lanthanide SMMs Based on Belt Macrocycles: Recent Advances and General Trends

Enhancement of axial magnetic anisotropy is the central objective to push forward the performance of Single-Molecule Magnet (SMM) complexes. In the case of mononuclear lanthanide complexes, the chemical environment around the paramagnetic ion must be tuned to place strongly interacting ligands along either the axial positions or the equatorial plane, depending on the oblate or prolate preference of the selected lanthanide. One classical strategy to achieve a precise chemical environment for a metal centre is using highly structured, chelating ligands. A natural approach for axial-equatorial control is the employment of macrocycles acting in a belt conformation, providing the equatorial coordination environment, and leaving room for axial ligands. In this review, we present a survey of SMMs based on the macrocycle belt motif. Literature systems are divided in three families (crown ether, Schiff-base and metallacrown) and their general properties in terms of structural stability and SMM performance are briefly discussed.     

PTML modeling for peptide discovery: in silico design of non-hemolytic peptides with antihypertensive activity

Molecular Diversity - Hypertension is a medical condition that affects millions of people worldwide. Despite the high efficacy of the current antihypertensive drugs, they are associated with...     

The “Essential Tension” at Work in Qualitative Analysis: A Case Study of the Opposite Points of View of Poincaré and Enriques on the Relationships between Analysis and Geometry

An analysis of the different philosophic and scientific visions of Henri Poincaré and Federigo Enriques relative to qualitative analysis provides us with a complex and interesting image of the “essential tension” between “tradition” and “innovation” within the history of science. In accordance with his scientific paradigm, Poincaré viewed qualitative analysis as a means for preserving the nucleus of the classical reductionist program, even though it meant “bending the rules” somewhat. To Enriques's mind, qualitative analysis represented the affirmation of a synthetic, geometrical vision that would supplant the analytical/quantitative conception characteristic of 19th-century mathematics and mathematical physics. Here, we examine the two different answers given at the turn of the century to the question of the relationship between geometry and analysis and between mathematics, on the one hand, and mechanics and physics, on the other.Copyright 1998 Academic Press.Un'analisi delle diverse posizioni filosofiche e scientifiche di Henri Poincaré e Federigo Enriques nei riguardi dell'analisi qualitativa fornisce un'immagine complessa e interessante della “tensione essenziale” tra “tradizione” e “innovazione” nell'ambito della storia della scienza. In linea con il proprio paradigma scientifico, Poincaré vedeva nell'analisi qualitativa un mezzo per preservare il nucleo del programma riduzionista calssico, anche se cio comportava una lieve “distorsione delle regole”. Nella mente di Enriques, l'analisi qualitativa rappresentava l'affermazione di un punto di vista sintetico e geometrico che avrebbe soppiantato la concezione analitico-quantitativa caratteristica della matematica e della fisica matematica del 19° secolo. Il nostro scopo principale è di esaminare due diverse risposte date a cavallo del secolo alla questione dei rapporti tra geometria e analisi e tra matematica da un lato e meccanica e fisica dall'altro.Copyright 1998 Academic Press.AMS subject classification: 01A55     

Prediction problem in quantum mechanics is intractable (NP-Hard)

It is proved that both the prediction problem and the problem of reconstructing the state from the observations in quantum mechanics are NP-hard.     

Some new topological cardinal inequalities

In this paper we make use of the Pol-Šapirovski?'s technique to prove several cardinal inequalities, which generalize other well-known inequalities.     

Risk-neutral valuation with infinitely many trading dates

The first Fundamental Theorem of Asset Pricing establishes the equivalence between the absence of arbitrage in financial markets and the existence of Equivalent Martingale Measures, if appropriate conditions hold. Since the theorem may fail when dealing with infinitely many trading dates, this paper draws on the A.A. Lyapunov Theorem in order to retrieve the equivalence for complete markets such that the Sharpe Ratio is adequately bounded.     

On the fast reduction of a quasiseparable matrix to Hessenberg and tridiagonal forms

In this paper we design a fast new algorithm for reducing an N × N quasiseparable matrix to upper Hessenberg form via a sequence of N − 2 unitary transformations. The new reduction is especially useful when it is followed by the QR algorithm to obtain a complete set of eigenvalues of the original matrix. In particular, it is shown that in a number of cases some recently devised fast adaptations of the QR method for quasiseparable matrices can benefit from using the proposed reduction as a preprocessing step, yielding lower cost and a simplification of implementation.