Algebras of Convolution Type Operators with Piecewise Slowly Oscillating Data. II: Local Spectra and Fredholmness

Let ${\mathcal{B}_{p,w}}$ be the Banach algebra of all bounded linear operators acting on the weighted Lebesgue space ${L^p(\mathbb{R},w)}$ , where ${p\in(1,\infty)}$ and w is a Muckenhoupt weight. We study the Banach subalgebra ${\mathfrak{U}_{p,w}}$ of ${\mathcal{B}_{p,w}}$ generated by all multiplication operators aI ( ${a\in PSO^\diamond}$ ) and all convolution operators W ⁰(b) ( ${b\in PSO_{p,w}^\diamond}$ ), where ${PSO^\diamond\subset L^\infty(\mathbb{R})}$ and ${PSO_{p,w}^\diamond\subset M_{p,w}}$ are algebras of piecewise slowly oscillating functions that admit piecewise slowly oscillating discontinuities at arbitrary points of ${\mathbb{R}\cup\{\infty\}}$ , and M _p,w is the Banach algebra of Fourier multipliers on ${L^p(\mathbb{R},w)}$ . Under some conditions on the Muckenhoupt weight w, using results of the local study of ${\mathfrak{U}_{p,w}}$ obtained in the first part of the paper and applying the theory of Mellin pseudodifferential operators and the two idempotents theorem, we now construct a Fredholm symbol calculus for the Banach algebra ${\mathfrak{U}_{p,w}}$ and establish a Fredholm criterion for the operators ${A\in\mathfrak{U}_{p,w}}$ in terms of their Fredholm symbols. In four partial cases we obtain for ${\mathfrak{U}_{p,w}}$ more effective results.     

Study of the first-order transition in the spin-1 Blume–Capel model by using effective-field theory

The spin-1 Blume–Capel model on a square lattice is studied by using an effective-field theory (EFT) with correlation. We propose an expression for the free energy within the EFT. The phase diagram is constructed in the temperature (T) and single-ion anisotropy amplitude (D) plane. The first-order transition line is obtained by Maxwell construction (comparison between free energies). Our results predict first-order transitions at low temperatures and large anisotropy strengths, which correspond in the phase diagram to the existence of a tricritical point (TCP). We compare our results with mean-field approximation (MFA), that show a qualitative correct behavior for the phase diagram.     

Electroactive copper(II) bimetallic self-assembled multilayers on Si(100)

Silicon (100) surfaces were modified by reacting 4-aminopyridine and Si–Cl bond. These surfaces were further used for tethering copper bimetallic complexes and growing monolayers and multilayers by changing the axial position via Lewis acid–base reactions. In this way, coordination chemistry approach can be used as building blocks for controlling the design of functional surfaces. Furthermore, the outcomes of the several characterization techniques indicate that the complex is spatially oriented suggesting that this simple strategy allows the preparation of three dimensional molecular structures exhibiting spatial order. The structures on surface show interesting electroactive behaviors leading two cathodic signals, that can be related to Cu(II)/Cu(I) and Cu(I)/Cu(0) electro-reduction species (signals at ? 0.15 V and ? 0.50 V) and one peak in the anodic region (? 0.15 V) ascribed to the Cu(0)/Cu(II) electro-oxidation reaction, using an Ag/AgCl saturated electrode and platinum wire as reference and counter electrodes, respectively.     

Effects of therapeutic pulsed ultrasound and dimethylsulfoxide phonophoresis on oxidative stress parameters after injury induced by eccentric exercise

Introduction

The aim of the study was to evaluate the effects of TPU together with DMSO on oxidative stress parameters after eccentric exercise.

Methods

Thirty and six animals were divided in control; eccentric exercise (EE); EE + saline gel 0.9%; EE + TPU 0.8 W/cm²; EE + DMSO gel; EE + TPU + DMSO gel and submitted to one 90-min downhill run (1.0 km h⁻¹). TPU was used 2, 12, 24, 46 h after exercise session and 48 h after the animals were killed and the gastrocnemius muscles were surgically removed. Production of superoxide anion, creatine kinase (CK) levels, lipoperoxidation, carbonylation, and antioxidants enzymes were analyzed.

Results

Showed that TPU and gel-DMSO improved muscle healing. Moreover, superoxide anion production, TBARS level and protein carbonyls levels, superoxide dismutase and catalase activity were all decreased in the group TPU plus gel-DMSO.

Discussion

Our results show that DMSO is effective in the reduction of the muscular lesion and in the oxidative stress after eccentric exercise only when used with TPU.     

Implicit differential equations with impasse singularities and singular perturbation problems

This paper concerns families of constrained differential systems having the form {fx1-1} where h: ? ⁿ → ? is a C ^r -function, (α ₁, …, α _n ) is a C ^r vector field on ? ⁿ , r ≥ 1, x ∈ ? ⁿ and λ is a real parameter. Using singular perturbation techniques we present some results on the dynamics of the system around a point (x, λ) of the impasse set λ = h(x). In addition, planar constrained systems with non-regular impasse surfaces are considered.     

Dependence of the Lifetime upon the Excitation Energy and Intramolecular Energy Transfer Rates: The (5) D(0) Eu(III) Emission Case

In many Eu(III) -based materials, the presence of an intermediate energy level, such as ligand-to-metal charge transfer (LMCT) states or defects, that mediates the energy transfer mechanisms can strongly affect the lifetime of the (5) D(0) state, mainly at near-resonance (large transfer rates). We present results for the dependence of the (5) D(0) lifetime on the excitation wavelength for a wide class of Eu(III) -based compounds: ionic salts, polyoxometalates (POMs), core/shell inorganic nanoparticles (NPs) and nanotubes, coordination polymers, β-diketonate complexes, organic-inorganic hybrids, macro-mesocellular foams, functionalized mesoporous silica, and layered double hydroxides (LDHs). This yet unexplained behavior is successfully modelled by a coupled set of rate equations with seven states, in which the wavelength dependence is simulated by varying the intramolecular energy transfer rates. In addition, the simulations of the rate equations for four- and three-level systems show a strong dependence of the emission lifetime upon the excitation wavelength if near-resonant non-radiative energy transfer processes are present, indicating that the proposed scheme can be generalized to other trivalent lanthanide ions, as observed for Tb(III) /Ce(III) . Finally, the proper use of lifetime definition in the presence of energy transfer is emphasized.     

Raman characterization of bulk ferromagnetic nanostructured graphite

Raman spectroscopy was used to characterize bulk ferromagnetic graphite samples prepared by controlled oxidation of commercial pristine graphite powder. The G:D band intensity ratio, the shape and position of the 2D band and the presence of a band around 2950 cm⁻¹ showed a high degree of disorder in the modified graphite sample, with a significant presence of exposed edges of graphitic planes as well as a high degree of attached hydrogen atoms.     

Magnetism in multivacancy graphene systems

Ab initio calculations using density functional theory (DFT) have been performed in order to study defects in graphene. The structural distortions that can be observed when multi-atom vacancies are created in graphene and the net magnetic moment that can eventually appear are characterized for a variety of vacancy sizes and shapes. We conclude that the configuration arising in the construction of multivacancies in graphene can unambiguously indicate whether a magnetic response of the defected system is to be expected. Making use of the shape of the complementary figure-i.e.?the geometric figure of the atomic arrangement that is extracted from graphene when the multivacancy is created-it is possible to construct a set of rules by means of which the optimized structural and magnetic behavior can be predicted. The validity of the rules is determined through DFT calculations.     

Spectrophotometric study of competitive complexation equilibria involving overlapped spectral responding species: Determination of the stability constant of bismuth-pyrophosphate complex

Spectrophotometric study of competitive complex formation equilibria involving overlapped spectral responding species applying a simple and versatile algorithm was carried out. The algorithm involves multivariable regression for calculation of equilibrium concentrations from multiwavelength data and mass action law for the stability constant calculation. The used regression functions are part of common statistical software. Stability constants and complex stoichiometry of competing equilibria were simultaneously determined. The species concentration profiles at several spectral overlapping and ??-coefficient of competing reaction were obtained. Non-absorbing bismuth ?? pyrophosphate (PPh) system was studied as a competitive reaction of bismuth ?? 4-(2-Pyridylazo) resorcinol (PAR) complex. The formation of Bi-PPh complex with 1:1 stoichiometry was proved in the studied concentration region (C_Bi = 1×10^?5 mol L^?1; C_PPh = 5×10^?6 ? 1×10^?4 mol L^?1). The stability constant of the complex at pH 1 and ?? = 1.0 have been determined: log?? = 4.2±0.2.