Sparse inertially arbitrary patterns

An n-by-n sign pattern is a matrix with entries in {+,-,0}. An n-by-n nonzero pattern is a matrix with entries in {*,0} where * represents a nonzero entry. A pattern is inertially arbitrary if for every set of nonnegative integers n₁,n₂,n₃ with n₁+n₂+n₃=n there is a real matrix with pattern having inertia (n₁,n₂,n₃). We explore how the inertia of a matrix relates to the signs of the coefficients of its characteristic polynomial and describe the inertias allowed by certain sets of polynomials. This information is useful for describing the inertia of a pattern and can help show a pattern is inertially arbitrary. Britz et al. [T. Britz, J.J. McDonald, D.D. Olesky, P. van den Driessche, Minimal spectrally arbitrary sign patterns, SIAM J. Matrix Anal. Appl. 26 (2004) 257–271] conjectured that irreducible spectrally arbitrary patterns must have at least 2n nonzero entries; we demonstrate that irreducible inertially arbitrary patterns can have less than 2n nonzero entries.     

Resonances and O-curves in Hamiltonian systems

We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.      

Gas phase reaction of Cl atoms with a series of oxygenated organic species at 295 K

The relative rate technique has been used to determine the rate constants for the reaction of chlorine atoms with a series of oxygenated organic species. Experiments were performed at 295 ± 2 K and atmospheric pressure of synthetic air or nitrogen. The decay rates of the organic species were measured relative to that of ethane or n-butane. Using rate constants of 5.7 × 10^?11 cm³ molecule^?1 s^?1, and 2.25 × 10^?10 cm³ molecule^?1 s^?1 for the reaction of Cl with ethane and n-butane respectively the following rate constants were derived, in units of 10^?11 cm³ molecule^?1 s^?1: propane, (16.0 ± 0.4);i-butane, (15.1 ± 0.9) n-pentane, (31.0 ± 1.6); n-hexane, (34.5 ± 2.3); cyclohexane, (36.1 ± 1.5); methanol, (4.57 ± 0.40); ethanol, (8.45 ± 0.91); n-propanol, (14.4 ± 1.2); t-butylalcohol, (3.26 ± 0.19); acetaldehyde, (8.45 ± 0.79); propionaldehyde, (11.3 ± 0.9); dimethylether, (20.5 ± 0.8); diethylether, (35.6 ± 2.8); and methyl-t-butylether, (16.6 ± 1.2). Quoted errors represent 2σ, and do not include any errors due to uncertainties in the rate constants used to place our relative measurements on an absolute basis. The results are discussed with respect to the mechanisms of these reactions and to previous literature data.     

Covalent versus electrostatic nature of the strong hydrogen bond: discrimination among single, double, and asymmetric single-well hydrogen bonds by variable-temperature X-ray crystallographic methods in beta-diketone enol RAHB systems

Beta-diketone enols are known to form intramolecular...O=C-C=C-OH... resonance-assisted hydrogen bonds (RAHBs) with O...O distances as short as 2.39-2.44 A. However, even the most accurate diffraction studies have not been able to assess with certainty whether these very strong hydrogen bonds (H-bonds) are to be described as proton-centered O...H...O bonds in a single-well (SW) potential or as the dynamic or static mixing of two O-H...O <= => O...H-O tautomers in a double-well (DW) one. This contribution reexamines the problem and shows that diffraction methods are fairly able to assess the SW or DW nature of the H-bond formed and, in the second case, its dynamic or static nature, provided a Bayesian approach is used which associates a number of experimental techniques (X-ray crystallography at variable temperature, difference Fourier maps, least-squares refinement of proton populations, Hirshfeld's rigid-bond test) with a reasonable prior, that is the full set of possible proton-transfer (PT) pathways for the O-H...O system derived from theoretical calculations. The method is first applied to three beta-diketone enols, whose crystal structures were determined in the interval of temperatures 100-295 K and then generalized to the interpretation of a much wider set of beta-diketone enol structures derived from the literature, making it possible to establish a general relationship between chemical structure (symmetric or dissymmetric substitution, steric compression or stretching, increased pi-bond delocalizability), H-bond strength, and the shape of the PT-barrier. Final results are interpreted in terms of simplified VB theory and state-correlation (or avoided-crossing) diagrams.     

Quasi-invariant manifolds,stability, and generalized Hopf bifurcation

Sunto Viene compiuta un'analisi completa del problema della biforcazione di Hopf relativa ad arbitrarie piccole perturbazioni del secondo membro di un'equazione differenziale in Rⁿ, p=f₀(p). Gli autovalori di f₀(O) soddisfano una condizione di non risonanza. I risultati sono forniti in termini delle proprietá di stabilità di un sistema dinamico piano convenientemente associato all'equazione imperturbata.

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Research partially supported by U.S. Army Research Grant DAAG-29-80-C-0060 and by C.N.R. (Italian Council of Research) contr. 79.00696.01.

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Work performed under the auspices of the National Group of Math, Phys. of C.N.R.     

A structure-activity study of antibacterial diterpenoids

An analysis of the antibacterial activities of 15 terpenoids, eleven of which were previously described by us and four were extracted from the literature, suggested two structural requirements for activity of these and related compounds: a hydrophobic moiety,consisting of a substituted decalin skeleton, and a hydrophilic region possessing one hydrogen-bond-donor group. These structural requirements are responsible for an optimal insertion of these and related compounds into cell membranes, as suggested by the results of docking some of these compounds into a model phospholipid bilayer.     

Michael addition of Grignard reagents to tetraethyl ethenylidenebisphosphonate

Tetraethyl ethenylidenebisphosphonate can undergo facile Michael type addition reaction with simple Grignard reagents to give alkyl, arylalkyl, aryl C-substituted methylene bisphosphonates. This addition easily occurs even if funtionalised Grignard reagents are used.     

Biological applications of LbL multilayer capsules: From drug delivery to sensing

Polyelectrolyte multilayer (PEM) capsules engineered with active elements for targeting, labeling, sensing and delivery hold great promise for the controlled delivery of drugs and the development of new sensing platforms. PEM capsules composed of biodegradable polyelectrolytes are fabricated for intracellular delivery of encapsulated cargo (for example peptides, enzymes, DNA, and drugs) through gradual biodegradation of the shell components. PEM capsules with shells responsive to environmental or physical stimuli are exploited to control drug release. In the presence of appropriate triggers (e.g., pH variation or light irradiation) the pores of the multilayer shell are unlocked, leading to the controlled release of encapsulated cargos. By loading sensing elements in the capsules interior, PEM capsules sensitive to biological analytes, such as ions and metabolites, are assembled and used to detect analyte concentration changes in the surrounding environment. This Review aims to evaluate the current state of PEM capsules for drug delivery and sensing applications.     

Synthesis of Asymmetric Monomethine Cyanine Dyes with Red‐Shifted Optical Properties

Six novel asymmetrical monomethine cyanine dyes were synthesized via the condensation reaction of 1‐butyl‐2‐(methylthio)benzo[c,d]indol‐1‐ium iodide and various 1,5‐substituted indolenine salts under basic conditions. The dyes were characterized using UV–vis spectroscopy, fluorescence, ¹H NMR, ¹³C NMR, and mass spectrometry; furthermore, the purity of these compounds was observed using LC/ELSD/MS.     

The antiproton cell experiment—do antiprotons offer advantages over other particle beam modalities?

The use of heavy charged particles for cancer therapy has the potential for a significant improvement of the therapeutic window compared to standard X-ray treatments. This is due to the improved energy deposition profile, exhibiting a well-defined peak at a depth in target controllable by the initial energy of the beam. Particles heavier than protons in addition show an increase in biological effectiveness. Compared to protons or heavy ions, antiprotons deposit additional annihilation energy, mostly by low energy recoils, resulting in an increase of dose and also adding a component with high biological effectiveness in the target region. The relative magnitude of the physical energy deposition of antiprotons compared to protons was measured at Low Energy Antiproton Ring (LEAR) by A. Sullivan, but no study of the biological effect had been conducted prior to the Antiproton Cell Experiment (AD-4/ACE) experiment at CERN. The special conditions found at CERN present significant challenges, but also offer unique opportunities. 500?ns pulses of antiprotons are extracted from the Antiproton Decelerator (AD) at 500?MeV/c momentum. Biological cell samples are irradiated and clonogenic survival fractions are measured for various doses. To extract biological efficiency, the physical dose deposition is obtained by Monte-Carlo calculations in conjunction with shot-by-shot monitoring of the incoming beam intensity and profile using a silicon pixel detector. Also imaging of the pions resulting from antiproton annihilations in the target using silicon pixel detector technology to determine the actual range in more complex targets with strong variations in material densities was carried out. The feasibility of this technique using a novel arrangement of the detector was demonstrated. This paper describes the ACE experiment and focuses on the different detector activities within the AD-4/ACE collaboration, explaining the experimental set-up, physical and biological methods used, recent results, and future plans.