Extended Grassmann and Clifford Algebras

This paper is intended to investigate Grassmann and Clifford algebras over Peano spaces, introducing their respective associated extended algebras, and to explore these concepts also from the counterspace viewpoint. The presented formalism explains how the concept of chirality stems from the bracket, as defined by Rota et all [1]. The exterior (regressive) algebra is shown to share the exterior (progressive) algebra in the direct sum of chiral and achiral subspaces. The duality between scalars and volume elements, respectively under the progressive and the regressive products is shown to have chirality, in the case when the dimension n of the Peano space is even. In other words, the counterspace volume element is shown to be a scalar or a pseudoscalar, depending on the dimension of the vector space to be respectively odd or even. The de Rham cochain associated with the differential operator is constituted by a sequence of exterior algebra homogeneous subspaces subsequently chiral and achiral. Thus we prove that the exterior algebra over the space and the exterior algebra constructed on the counterspace are only pseudoduals each other, if we introduce chirality. The extended Clifford algebra is introduced in the light of the periodicity theorem of Clifford algebras context, wherein the Clifford and extended Clifford algebras can be embedded in which is shown to be exactly the extended Clifford algebra. We present the essential character of the Rota’s bracket, relating it to the formalism exposed by Conradt [25], introducing the regressive product and subsequently the counterspace. Clifford algebras are constructed over the counterspace, and the duality between progressive and regressive products is presented using the dual Hodge star operator. The differential and codifferential operators are also defined for the extended exterior algebras from the regressive product viewpoint, and it is shown they uniquely tumble right out progressive and regressive exterior products of 1-forms. R. da Rocha is supported by CAPES     

Air pollution control with semi-infinite programming

Environment issues are more than ever important in a modern society. Complying with stricter legal thresholds on pollution emissions raises an important economic issue. This paper presents some ideas in the use of optimization tools to help in the planning and control of stationary pollution sources.     

Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization

In this paper, we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) functions programming to solve the resulting subproblems which consist of the minimization of the RBF models subject to simple bounds on the variables. Extensive numerical results are reported with a test set of bound and linearly constrained problems.     

A study on structural and electrical properties of low dielectric constant SiOC(–H) thin films deposited via PECVD

Low-dielectric constant SiOC(–H) films were deposited on p-type Si(100) substrates using plasma enhanced chemical vapor deposition (PECVD) at different radio frequency (rf) powers. The structural characteristics of the SiOC(–H) films were characterized using Fourier transform infrared spectroscopy (FTIR) in the absorbance mode. The bonding configurations of the SiOC(–H) films remained unchanged upon annealing, showing their good thermal stability. Electrical characteristics of the SiOC(–H) thin films with Al/SiOC(–H)/p-Si(100)/Al metal-insulator-semiconductor (MIS) structures were analyzed using capacitance–voltage (C–V) and conductance–voltage (G/ω–V) at different frequencies. The conductance and the capacitance measurements were used to extract the interface state density in the MIS structures. From the experimental data and the subsequent quasi-static C–V analysis, the energy distribution of interface state density was obtained. The interface state density of the as-deposited and 400 °C annealed MIS structures increased with increasing rf powers, whereas the fixed charge density decreased with increasing rf powers. The interface state densities and their electrical properties of the SiOC(–H) films strongly affected by the radio frequency power.     

Colored Texture Analysis Fuzzy Entropy Methods with a Dermoscopic Application

Texture analysis is a subject of intensive focus in research due to its significant role in the field of image processing. However, few studies focus on colored texture analysis and even fewer use information theory concepts. Entropy measures have been proven competent for gray scale images. However, to the best of our knowledge, there are no well-established entropy methods that deal with colored images yet. Therefore, we propose the recent colored bidimensional fuzzy entropy measure, FuzEnC2D, and introduce its new multi-channel approaches, FuzEnV2D and FuzEnM2D, for the analysis of colored images. We investigate their sensitivity to parameters and ability to identify images with different irregularity degrees, and therefore different textures. Moreover, we study their behavior with colored Brodatz images in different color spaces. After verifying the results with test images, we employ the three methods for analyzing dermoscopic images of malignant melanoma and benign melanocytic nevi. FuzEnC2D, FuzEnV2D, and FuzEnM2D illustrate a good differentiation ability between the two—similar in appearance—pigmented skin lesions. The results outperform those of a well-known texture analysis measure. Our work provides the first entropy measure studying colored images using both single and multi-channel approaches.     

Delving into the Variability of Supramolecular Affinity: Self-Ion Pairing as a Central Player in Aqueous Host-Guest Chemistry

The determination of binding constants is a key matter in evaluating the strength of host–guest interactions. However, the profound impact of self-ion pairing on this parameter is often underrated in aqueous solution, leading in some cases to a misinterpretation of the true potential of supramolecular assemblies. In the present study, we aim to shed further light on this critical factor by exploring the concentration-dependent behavior of a multicharged pillararene in water. Our observations reveal an extraordinary 1-million-fold variability in the affinity of this macrocycle toward a given anion, showcasing the highly dynamic character of electrostatic interactions. We argue that these findings bring to the forefront the inherent determinism that underlies the estimation of affinity constants, a factor profoundly shaped by both the sensitivity of the instrumental technique in use and the intricacies of the experimental design itself. In terms of applications, these results may provide the opportunity to optimize the operational concentrations of multicharged hosts in different scenarios, aiming to achieve their maximum efficiency based on the intended application. Unlocking the potential of this hidden variability may pave the way for the creation of novel molecular materials with advanced functionalities.     

Metallocenes for polypropylene: Polymerization performance and computer modeling

The structures of eleven different metallocenes substituted with either methyl and/or t-butyl groups were minimized by computer molecular modeling. Using Comparative Molecular Field Analysis (CoMFA), a computer model was generated from the minimized metallocene structures and actual polymerization performance. When the model was tested, a statistically valid correlation of the model's predicted DSC melting point with the observed DSC melting point was found. The model indicates the extent of the steric effect of these alkyl substituents and their influence on the DSC melting point.