Multiple periodic solutions of scalar second order differential equations

We prove multiplicity of periodic solutions for a scalar second order differential equation with an asymmetric nonlinearity, thus generalizing previous results by Lazer and McKenna (1987) [1] and Del Pino, Manasevich and Murua (1992) [2]. The main improvement lies in the fact that we do not require any differentiability condition on the nonlinearity. The proof is based on the use of the Poincaré-Birkhoff Fixed Point Theorem.     

Water absorption kinetics in different wettability conditions studied at pore and sample scales in porous media by NMR with portable single-sided and laboratory imaging devices

NMR relaxation time distributions of water (1)H obtained by a portable single-sided surface device have been compared with MRI internal images obtained with a laboratory imaging apparatus on the same biocalcarenite (Lecce Stone) samples during capillary water uptake. The aim of this work was to check the ability of NMR methods to quantitatively follow the absorption phenomenon under different wettability conditions of the internal pore surfaces. Stone wettability changes were obtained by capillary absorption of a chloroform solution of Paraloid PB72, a hydrophobic acrylic resin frequently used to protect monuments and buildings, through one face of each sample. Both relaxation and imaging data have been found in good quantitative agreement each other and with masses of water determined by weighing the samples. In particular the Washburn model of water capillary rise applied to the imaging data allowed us to quantify the sorptivity in both treated and untreated samples. Combining relaxation and imaging data, a synergetic improvement of our understanding of the water absorption kinetics at both pore and sample scales is obtained. Since relaxation data have been taken over the course of time without interrupting the absorption process, simply by keeping the portable device on the surface opposite to the absorption, the results show that the single-sided NMR technique is a powerful tool for in situ evaluation of water-repellent treatments frequently used for consolidation and/or protection of stone artifacts.     

Electronic Transitions in Different Redox States of Trinuclear 5,6,11,12,17,18-Hexaazatrinaphthylene-Bridged Titanium Complexes: Spectroelectrochemistry and Quantum Chemistry

Multinuclear transition metal complexes bridged by ligands with extended π-electronic systems show a variety of complex electronic transitions and electron transfer reactions. While a systematic understanding of the photochemistry and electrochemistry has been attained for binuclear complexes, much less is known about trinuclear complexes such as hexaphenyl-5,6,11,12,17,18-hexaazatrinaphthylene-tristitanocene [(Cp₂Ti)₃HATN(Ph)₆]. The voltammogram of [(Cp₂Ti)₃HATN(Ph)₆] shows six oxidation and three reduction waves. Solution spectra of [(Cp₂Ti)₃HATN(Ph)₆] and of the electrochemically formed oxidation products show electronic transitions in the UV, visible and the NIR ranges. Density functional theory (DFT) and linear response time-dependent DFT show that the three formally titanium(II) centers transfer an electron to the HATN ligand in the ground state. The optically excited transitions occur exclusively between ligand-centered orbitals. The charged titanium centers only provide an electrostatic frame to the extended π-electronic system. Complete active self-consistent field (CASSCF) calculation on a structurally simplified model compound, which considers the multi-reference character imposed by the three titanium centers, can provide an interpretation of the experimentally observed temperature-dependent magnetic behavior of the different redox states of the title compound in full consistency with the interpretation of the electronic spectra.     

Short interval asymptotics for a class of arithmetic functions

Summary We provide a general asymptotic formula which permits applications to sums like <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation> \sum_{x< n\le x+y} \big(d(n)\big)^2, \quad \sum_{x< n\le x+y} d(n^3),\quad \sum_{x< n\le x+y}\big(r(n)\big)^2, \quad \sum_{x< n\le x+y}r(n^3), $$ where $d(n)$ and $r(n)$ are the usual arithmetic functions (number of divisors, sums of two squares), and $y$ is small compared to~$x$.     

Regularity for minimizers of functionals with p – q growth

We prove higher integrability for the gradient of vector-valued minimizers of some integral functionals with p – q growth. Received February 9, 1998     

C imaging by double resonance scalar-coupling editing

The two-dimensional FT Imaging of ¹³C-glucose obtained with twin spin-echo double resonance sequence is presented. The images have been obtained by a doubly tuned surface coil on samples containing water and ¹³C-enriched glucose in water. It is shown, both theoretically and experimentally, that the whole editing capability of the twin spin-echo double resonance imaging sequence is also preserved in the presence of the radiofrequency field inhomogeneity produced by the surface coil. As in an efficient selective irradiation method, the enhancement in the signal-to-noise ratio with respect to the direct ¹³C detection, depends on the number of protons J-coupled to ¹³C.     

The use of Raman microscopy and laser desorption ionization mass spectrometry in the examination of synthetic organic pigments in modern works of art

Synthetic organic pigments are widely used in modern and contemporary works of art. They have been examined by a variety of techniques including spectroscopic methods such as Fourier transform infrared spectroscopy, Raman, and X‐ray powder diffraction as well as chromatographic or mass spectrometric techniques such as pyrolysis‐gas chromatography/mass spectrometry and laser desorption ionization mass spectrometry (LDI–MS). Often, a combination of techniques has been used to examine these pigments. This paper describes use of Raman spectroscopy to create a database of colorants including two pigments not previously reported, PO1 and PO2. Then, using Raman spectroscopy in combination with LDI–MS, samples from modern works of art by artists including Mark Rothko, Barnett Newman, and José de Rivera were examined in order to identify the pigments present. One finding was that Rothko used a variety of red pigments over the course of his career including PR11 which has not been previously reported in artwork, and PO2 found with its positional isomer PR1. Knowledge of the colorants serves to inform conservators about display and treatment decisions. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

The modified bordering method to evaluate eigenvalues and eigenvectors of normal matrices

A bordering procedure is here proposed to evaluate the eigensystem of hermitian matrices, and more in general of normal matrices, when the spectral decomposition is known of then–1×n–1 principal minor. The procedure is also applicable to special real and nonsymmetric matrices here named quasi-symmetric. The computational cost to write the characteristic polynomial isO(n ²), using a new set of recursive formulas. A modified Brent algorithm is used to find the roots of the polynomial. The eigenvectors are evaluated in a direct way with a computational cost ofO(n ²) for each one. Some numerical considerations indicate where numerical difficulties may occur. Numerical results are given comparing this method with the Givens-Householder one.