The index of a plane curve and green’s formula

Rendiconti del Circolo Matematico di Palermo Series 2 - In this paper we compute the line integral of a complex function on a rectifiable cycle homologous to zero obtaining a Green’s formula...     

Experimental Validation of the Attenuation Properties in the Sonic Range of Metaconcrete Containing Two Types of Resonant Inclusions

Experimental Mechanics - Metaconcrete is a new concept of concrete, showing marked attenuation properties under impact and blast loading, where traditional aggregates are partially replaced by...     

Solving a problem proposed by T. Ogawa

This paper ascertains the sharp behavior of the first zero of the radially symmetric solution of a superlinear elliptic three-dimensional equation as a function of its value at the origin, and it establishes the strict monotonicity and asymptotic finitude of the underlying associated mass.     

Push–Pull (Iso)quinoline Chromophores: Synthesis,Photophysical Properties,and Use for White-Light Emission

The photophysical properties of a series of conjugated push–pull (iso)quinolines were studied. The compounds were synthesized by well-established and straightforward methodologies. The materials exhibited not only emission solvatochromism in a variety of nonpolar solvents, but also tunable halochromism. Some of the compounds remained moderately luminescent after protonation and had a red emissive form, which was used to obtain white-light emission, both in solution and in thin films, by controlled protonation of the initially blue–green-emitting materials. This methodology has potential applications in the fabrication of white organic light-emitting diodes with two forms of a single emitter in equilibrium.     

A 3.3 Å-Resolution Structure of Hyperthermophilic Respiratory Complex III Reveals the Mechanism of Its Thermal Stability

Respiratory chain complexes convert energy by coupling electron flow to transmembrane proton translocation. Owing to a lack of atomic structures of cytochrome bc₁ complex (Complex III) from thermophilic bacteria, little is known about the adaptations of this macromolecular machine to hyperthermophilic environments. In this study, we purified the cytochrome bc₁ complex of Aquifex aeolicus, one of the most extreme thermophilic bacteria known, and determined its structure with and without an inhibitor at 3.3 Å resolution. Several residues unique for thermophilic bacteria were detected that provide additional stabilization for the structure. An extra transmembrane helix at the N-terminus of cyt. c₁ was found to greatly enhance the interaction between cyt. b and cyt. c₁, and to bind a phospholipid molecule to stabilize the complex in the membrane. These results provide the structural basis for the hyperstability of the cytochrome bc₁ complex in an extreme thermal environment.     

Anion‐Responsive Diguanidinium‐Based Chiral Organogelators

The chiral bicyclic diguanidinium chloride 1 forms gels in aromatic apolar solvents. The gels were characterized at different levels of organization, from the macroscopic to the molecular level by using microscopy, spectroscopy, and powder X‐ray diffraction. The dependency on chirality has been highlighted by circular dichroism and electron microscopy. Furthermore, the gel has been shown to be effectively responsive to anionic stimuli, thus allowing the reversible control of the organic‐phase gelation in contact with different salted aqueous solutions.     

Cross‐Coupling Reactions of Organosilicon Compounds in the Stereocontrolled Synthesis of Retinoids

This paper presents a full account of the use of Hiyama cross‐coupling reactions in a highly convergent approach to retinoids in which the key step is construction of the central C10? C11 bond. Representatives of two families of oxygen‐activated dienyl silanes (ethoxysilanes and silanols) and of all reported families of “safety‐catch” silanols (siletanes, silyl hydrides, allyl‐, benzyl‐, aryl‐, 2‐pyridyl‐ and 2‐thienylsilanes) were regio‐ and stereoselectively prepared and stereospecifically coupled to an appropriate electrophile by treatment with a palladium catalyst and a nucleophilic activator. Both all‐trans and 11‐cis‐retinoids, and their chain‐demethylated analogues, were obtained in good yields regardless of the geometry (E/Z) and of the steric congestion in each fragment. This comprehensive study conclusively establishes the Hiyama cross‐coupling reaction, with its mild reaction conditions and stable, easily prepared, ecologically advantageous silicon‐based coupling partners, as the most effective route to retinoids reported to date.     

The calculation of the L 2-norm of the index of a plane curve and related formulas

We provide formulas for calculating the L ²-norm of the index function of a rectifiable closed curve in the complex plane. Some applications to isoperimetric inequalities are given. The main tool used is the decomposition of a rectifiable closed curve into a sequence of Jordan curves, curves with null index functions, and an exceptional set.