A minimax theorem in the presence of unbounded Palais-Smale sequences

In a reflexive Banach space we consider a family of functionals that may admit unbounded Palais-Smale sequences. Under some structural conditions we provide a suitable Deformation Lemma that is obtained by modifying the classical pseudo-gradient flow. This leads to a variant of the minimax principle in the Lusternik-Schnirelman Theory.     

The submillimeter: A spectroscopist’s view

The submillimeter spectral region has undergone an explosive growth in the last decade, not only in its impact on the larger scientific and technological world, but also in the high resolution laboratory spectroscopy that makes much of this success possible. Major astronomical and atmospheric instruments are the most visible evidence, but the impact is much broader. This breadth lays the foundation for the impact of submillimeter spectroscopy to extend beyond the scientific community. In this paper we consider the scientific and technical foundations of submillimeter spectroscopy and show how the underlying physics has made possible current successes and shows the path forward to even greater opportunities.     

Probabilistic Study of the Speed of Approach to Equilibrium for an Inelastic Kac Model

This paper deals with a one-dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter p>0. In particular, the paper provides bounds for certain distances—such as specific weighted χ-distances and the Kolmogorov distance—between the solution of that equation and the limit. It is assumed that the even part of the initial datum (which determines the asymptotic properties of the solution) belongs to the domain of normal attraction of a symmetric stable distribution with characteristic exponent α=2/(1+p). With such initial data, it turns out that the limit exists and is just the aforementioned stable distribution. A necessary condition for the relaxation to equilibrium is also proved. Some bounds are obtained without introducing any extra condition. Sharper bounds, of an exponential type, are exhibited in the presence of additional assumptions concerning either the behaviour, close to the origin, of the initial characteristic function, or the behaviour, at infinity, of the initial probability distribution function. Research partially supported by Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR grant 2006/134526).     

Liposomes-entrapped chondroitin sulphate: ultrastructural characterization and in vitro biocompatibility

The purpose of this study was ultrastructural characterization of liposomes-entrapped chondroitin sulphate and to prove their in vitro biocompatibility in a human dermal fibroblast culture system, in order to use liposome-entrapped chondroitin sulphate in the treatment of inflammatory disorders. Chondroitin sulphate entrapped in liposomes appears as electron-dense particles in ultra-thin section. Comparative studies using chondroitin sulphate, empty liposomes and liposome-chondroitin sulphate systems were performed in order to evaluate their effect on growth and morphology of fibroblasts after 48 h of culture. Light microscopy indicated that chondroitin sulphate, empty liposomes and liposome-chondroitin sulphate systems do not induce appreciable cytotoxic effects, and cells maintain normal morphology when compared to control fibroblasts.     

Meet-irreducible congruence lattices

The system of all congruences of an algebra (A, F) forms a lattice, denoted \({{\mathrm{Con}}}(A, F)\). Further, the system of all congruence lattices of all algebras with the base set A forms a lattice \(\mathcal {E}_A\). We deal with meet-irreducibility in \(\mathcal {E}_A\) for a given finite set A. All meet-irreducible elements of \(\mathcal {E}_A\) are congruence lattices of monounary algebras. Some types of meet-irreducible congruence lattices were described in Jakubíková-Studenovská et al. (2017). In this paper, we prove necessary and sufficient conditions under which \({{\mathrm{Con}}}(A, f)\) is meet-irreducible in the case when (A, f) is an algebra with short tails (i.e., f(x) is cyclic for each \(x \in A\)) and in the case when (A, f) is an algebra with small cycles (every cycle contains at most two elements).     

An Introduction to Entropically-driven Ring-opening Polymerizations

Summary: This mini-review outlines the principles of entropically-driven ring-opening polymerizations (ED-ROPs), a relatively new approach to the synthesis of condensation polymers. The various features of ED-ROPs are noted and examples of applications to polymer synthesis, polymer processing and polymer recycling are discussed.     

Influence of deposition conditions for bottom cell on micromorph tandem device performance

We have realized micromorph tandem solar cells on Asahi U-type TCO-covered glass substrates. The intrinsic layers of both amorphous top cell and microcrystalline bottom cell are grown by very high frequency plasma enhanced chemical vapour deposition (VHF-PECVD) at 100 MHz at low substrate temperature (150 °C). For the bottom cell different growth regimes have been explored by changing both chamber pressure and plasma power. The effect of the structural composition of the microcrystalline absorber layer on the electrical parameters of the device has been investigated. High short circuit current density and constant FF in a wide silane concentration range are obtained when using large power to pressure ratio (0.5 W/Pa). However, low open circuit voltage is generally found in this regime. The largest V_OC values are found at 67 Pa and power to pressure ratio of 0.3 W/Pa, where the highest efficiency (11.1%) is reached. An evaluation of device stability has been done by exposing the tandem solar cells to white light (AM 1.5-like spectrum) for 200 h.     

Spectroscopic investigation of modern pigments on purportedly medieval miniatures by the ‘Spanish Forger’

Five miniatures by the so‐called ‘Spanish Forger’ were acquired by the Victoria and Albert Museum in 2008. Believed to be authentic medieval miniatures until the mid‐twentieth century, they are now considered to have been painted around the end of the nineteenth and the beginning of the twentieth century. To investigate this attribution and to gather detailed knowledge about the materials used by the artist, a comprehensive pigment analysis by Raman microscopy and X‐ray fluorescence was carried out. Although traditional materials such as vermilion, carbon black, red lead, lead white and indigo were identified, many others (chrome yellow, Scheele's green, emerald green and ultramarine blue) are modern and synthetic pigments, a result which provides a firm scientific basis for stating that the miniatures are forgeries. Copyright © 2009 John Wiley & Sons, Ltd.     

Precise measurement of Γ(K→e ν(γ))/Γ(K→μ ν(γ)) and study of K→e ν γ

We present a precise measurement of the ratio R _K =Γ(K→e ν(γ))/Γ(K→μ ν(γ)) and a study of the radiative process K→e ν γ, performed with the KLOE detector. The results are based on data collected at the Frascati e ⁺ e ^? collider DAΦNE for an integrated luminosity of 2.2 fb^?1. We find R _K =(2.493±0.025_stat±0.019_syst)×10^?5, in agreement with the Standard Model expectation. This result is used to improve constraints on parameters of the Minimal Supersymmetric Standard Model with lepton flavor violation. We also measured the differential decay rate dΓ(K→e ν γ)/dE _γ for photon energies 10<E _γ < 250 MeV. Results are compared with predictions from theory.     

Total chemical synthesis by native chemical ligation of the all-D immunoglobulin-like domain 2 of Axl

Axl is a tyrosine kinases receptor playing crucial role in several cellular responses. The deregulation of Axl signaling has been associated to many high impact diseases ranging from cancer to multiple sclerosis. We report the successful procedure for the chemical synthesis of the Ig2 domain of Axl, one of the key extracellular regions of the receptor involved in ligand binding. The protein was synthesized in its d-enantiomeric form (D-Axl-2), opening the way to the selection of D-peptides selectively targeting Axl receptor through the mirror-image phage display peptide library screening approach.