Nonlinear transmission of a tetrabrominated naphthalocyaninato indium chloride

The axially substituted complex chloro indium(III) 2-tetrabromo-3-tetra-(3,5-di-tert-butylphenyloxy)naphthalocyanine [Br4(tBu2PhO)4NcInCl (1); MW = 1996] has been synthesized for the first time, and its nonlinear transmission properties have been evaluated with the Z-scan technique in both open and closed aperture configurations at 532 nm for nanosecond pulsed radiation. The tetrabrominated complex 1 displayed a larger positive nonlinear absorption coefficient when compared to an analogous nonbrominated naphthalocyanine [(tBu2PhO)8NcInCl (2); MW = 2498]. The effect of the four Br atoms on the nonlinear optical behavior of 1 is evaluated, discussed, and compared with the nonlinear optical behavior of 2. It is shown that the bromination of the naphthalocyanine ring considerably improves the limiting properties of such a system when high-intensity radiations are produced by nanosecond laser pulses at 532 nm.     

The crossed product by a partial endomorphism and the covariance algebra

Given a local homeomorphism where U⊆X is clopen and X is a compact and Hausdorff topological space, we obtain the possible transfer operators Lρ which may occur for given by α(f)=f○σ. We obtain examples of partial dynamical systems (XA,σA) such that the construction of the covariance algebra C^∗(XA,σA), proposed by B.K. Kwasniewski, and the crossed product by a partial endomorphism O(XA,α,L), recently introduced by the author and R. Exel, associated to this system are not equivalent, in the sense that there does not exist an invertible function ρ∈C(U) such that O(XA,α,Lρ)≅C^∗(XA,σA).     

Multivariate Multiscale Cosine Similarity Entropy and Its Application to Examine Circularity Properties in Division Algebras

The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding multivariate methods, multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), were developed to explore the structural richness within signals at high scales. However, the requirement of high scale limits the selection of embedding dimension and thus, the performance is unavoidably restricted by the trade-off between the data size and the required high scale. More importantly, the scale of interest in different situations is varying, yet little is known about the optimal setting of the scale range in MMSE and MMFE. To this end, we extend the univariate cosine similarity entropy (CSE) method to the multivariate case, and show that the resulting multivariate multiscale cosine similarity entropy (MMCSE) is capable of quantifying structural complexity through the degree of self-correlation within signals. The proposed approach relaxes the prohibitive constraints between the embedding dimension and data length, and aims to quantify the structural complexity based on the degree of self-correlation at low scales. The proposed MMCSE is applied to the examination of the complex and quaternion circularity properties of signals with varying correlation behaviors, and simulations show the MMCSE outperforming the standard methods, MMSE and MMFE.     

TiO2 Synthesis by the Pechini’s Method and Application for Diclofenac Photodegradation†

In this work, the effect of the calcination temperature on the TiO₂ synthesis using Pechini’s method was reported. The adopted calcination temperatures were 500, 600, and 700°C. XRD measurements indicated the composition of crystalline phases, and from there, the conversion of the anatase phase to rutile. TiO₂ Evonik^® was used as a reference standard and sodium diclofenac as a standard for photodegradation assessment. The average crystalline size increased. In both cases, this trend accompanied the increase in calcination temperature. The optical properties were performed using diffuse UV‐Vis reflectance. Results obtained indicated maximum absorption wavelength values more intense and displaced to the visible region. Also, the estimated band gap energy values decreased. The photocatalytic performance of TiO₂ samples was superior to the reference catalyst (TiO₂ Evonik^®). Especially in the first 10 minutes, the comparative photodegradation was up to approximately 58% higher. The photodegradation kinetic constants were also higher, and by comparison, up to approximately 73% higher. Toxicity measurements, using Artemias salina, also indicated similar decay behavior in the first 10 minutes, with a performance of up to approximately 60%.     

Foliations by curves on threefolds

We study the conormal sheaves and singular schemes of one-dimensional foliations on smooth projective varieties X of dimension 3 and Picard rank 1. We prove that if the singular scheme has dimension 0, then the conormal sheaf is μ-stable whenever the tangent bundle $TX$ is stable, and apply this fact to the characterization of certain irreducible components of the moduli space of rank 2 reflexive sheaves on ${\mathbb{P}}^3$ and on a smooth quadric hypersurface $Q_3\subset {\mathbb{P}}^4$. Finally, we give a classification of local complete intersection foliations, that is, foliations with locally free conormal sheaves, of degree 0 and 1 on Q₃.     

On the convergence properties of sampling Durrmeyer-type operators in Orlicz spaces

Here, we provide a unifying treatment of the convergence of a general form of sampling-type operators, given by the so-called sampling Durrmeyer-type series. The main result consists of the study of a modular convergence theorem in the general setting of Orlicz spaces $L^{\phi }(\mathbb{R})$. From the latter theorem, the convergence in $L^p(\mathbb{R})$, in $L^{\alpha }{\log }^{\beta }L$, and in the exponential spaces can be obtained as particular cases. For the completeness of the theory, we provide a pointwise and uniform convergence theorem on $\mathbb{R}$, in case of bounded continuous and bounded uniformly continuous functions; in this context, we also furnish a quantitative estimate for the order of approximation, using the modulus of continuity of the function to be approximated. Finally, applications and examples with graphical representations are given for several sampling series with special kernels.