Necessary conditions and non-existence results for autonomous nonconvex variational problems

Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained.     

A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions

Comparison results of Talenti type for elliptic problems with Dirichlet boundary conditions have been widely investigated in recent decades. In this paper, we deal with Robin boundary conditions. Surprisingly, contrary to the Dirichlet case, Robin boundary conditions make the comparison sensitive to the dimension, and while the planar case seems to be completely settled, in higher dimensions some open problems are yet unsolved. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

The Role of Information in Managing Interactions from a Multifractal Perspective

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.     

A variational method for the calculation of spin-rovibronic energy levels of triatomic molecules with three interacting electronic states

A general method is presented for the evaluation of the spin rovibronic energy levels of triatomic molecules with up to three interacting potential energy surfaces. The full theory is outlined in detail, both for singlet and for doublet electronic states and the method is then applied to the benchmark example of C₂H. High quality multireference configuration interaction calculations have been carried out to generate the 3-dimensional near-equilibrium adiabatic potential energy surfaces of the three lowest 1²A'(X²Σ⁺), 2²A'(A²Π), 1²A''(A²Π) electronic states of C₂H, and the pair of interacting states of A 0 symmetry have then been diabatized. Results are presented for J up to 7/2 and compared with gas-phase high resolution experimental results for energies up to 5600 cm¹.     

Analysis of mural paintings using in situ non‐invasive XRF,FTIR spectroscopy and optical microscopy

An analytical protocol consisting of X‐ray fluorescence spectroscopy, optical microscopy and Fourier transform infrared spectroscopy was used to study the origin and the nature of the materials (pigments, binders and coating preparation) of the Fundenii Doamnei church mural paint from Bucharest. The main interest of the present study consisted in the original votive paint from narthex, painted in 1757 in a secco technique. During analysis, an unexpected pigment in the votive paint could be detected by the combined analytical techniques: ultramarine blue. Along with this pigment, the presence of gypsum binder based on egg and flax seed oil could also be evidenced. These results demonstrated a secco execution technique of the votive paint and also the presence of a restoration treatment. Moreover, during the present study, the components of the preparation layer and the constitutive pigments from both 1699 and 1757 years mural paints have been analyzed. Hence, the following pigments could be identified: vermilion, azurite, cinnabar, lead white, ochre, natural umber and gold, by using the combination of the analytical techniques. The novelty of our results consists in detecting the composition of the materials used in this church painting (fresco and a secco) during these 254 years since its first restoration. The results of these investigations pointed to the suitability of the non‐destructive and semi‐destructive analytical techniques in the complex characterization of the paints realized in different techniques, at different periods. Copyright © 2013 John Wiley & Sons, Ltd.     

Sample Preparation for the Determination of Metals in Food Samples Using Spectroanalytical Methods—A Review

Abstract

The present article gives an overview of recent publications and modern techniques of sample preparation for food analysis employing atomic and inorganic mass spectrometric techniques, such as flame atomic absorption spectrometry, chemical vapor generation atomic absorption and atomic fluorescence spectrometry, graphite furnace atomic absorption spectrometry, inductively coupled plasma optical emission spectrometry, and inductively coupled plasma mass spectrometry. Among the most frequently applied sample preparation techniques for food analysis are dry ashing, usually with the addition of an ashing aid, and acid digestion, preferably with the assistance of microwave energy. Slurry preparation, particularly with the assistance of ultrasound, is increasingly used to reduce acid consumption and sample preparation time. Direct analysis of solid samples is gaining importance in the field of food analysis as it offers the highest sensitivity, avoids the use of acids and other aggressive reagents, makes possible the analysis of micro‐samples, and can be applied for fast screening analysis, e.g., of fresh meat.     

Isoparametric submanifolds in two-dimensional complex space forms

We show that an isoparametric submanifold of a complex hyperbolic plane, according to the definition of Heintze, Liu and Olmos’, is an open part of a principal orbit of a polar action. We also show that there exists a non-isoparametric submanifold of the complex hyperbolic plane that is isoparametric according to the definition of Terng’s. Finally, we classify Terng-isoparametric submanifolds of two-dimensional complex space forms.     

Weakly <Emphasis Type="Italic">φ</Emphasis>-pairs and common fixed points in cone metric spaces

In this paper we introduce a weak contractive condition, called weakly φ-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which ensures existence and uniqueness of common fixed points for such mappings. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.