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).     

Experimental investigation on seam geometry,microstructure evolution and microhardness profile of laser welded martensitic stainless steels

This paper investigates the effects of energy density on geometry of the weld seam and development of microstructures at various weld zones. Energy-based local microhardness profiles are made and linked with the formation of the microstructures. Weld resistance at the interface is energy-limited and seam profile only changes from conical to cylindrical after a certain limit of energy input. Microstructures in the fusion zone changes from cellular to columnar dendritic and equiaxed dendritic with increasing energy input. Variation in morphology of microstructures across the fusion zone is evident within the weld. A distinct region exists in between fusion and heat affected zones due to retention of the primary ferrite. Local microhardness reaches its peak in the fusion zone and decreases gradually from fusion zone to base metal of the outer shell. In the inner shell, peak microhardness occurs in HAZ and the local softening relative to fusion zone and HAZ is visible at the fusion boundary.     

Parabens Permeation through Biological Membranes: A Comparative Study Using Franz Cell Diffusion System and Biomimetic Liquid Chromatography

Parabens (PBs) are used as preservatives to extend the shelf life of various foodstuffs, and pharmaceutical and cosmetic preparations. In this work, the membrane barrier passage potential of a subset of seven parabens, i.e., methyl-, ethyl-, propyl- isopropyl, butyl, isobutyl, and benzyl paraben, along with their parent compound, p-hydroxy benzoic acid, were studied. Thus, the Franz cell diffusion (FDC) method, biomimetic liquid chromatography (BLC), and in silico prediction were performed to evaluate the soundness of both describing their permeation through the skin. While BLC allowed the achievement of a full scale of affinity for membrane phospholipids of the PBs under research, the permeation of parabens through Franz diffusion cells having a carbon chain > ethyl could not be measured in a fully aqueous medium, i.e., permeation enhancer-free conditions. Our results support that BLC and in silico prediction alone can occasionally be misleading in the permeability potential assessment of these preservatives, emphasizing the need for a multi-technique and integrated experimental approach.     

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.     

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.