Multiplicative character sums of Fermat quotients and pseudorandom sequences

We prove a bound on sums of products of multiplicative characters of shifted Fermat quotients modulo p. From this bound we derive results on the pseudorandomness of sequences of modular discrete logarithms of Fermat quotients modulo p: bounds on the well-distribution measure, the correlation measure of order ?, and the linear complexity.     

Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in H [^(?)] _s,psH{H \hat{\otimes} _{s,\pi _{s}}H} is an infinite absolute convex combination of points of the form x?x{x\otimes x} with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of H [^(?)] _s,psH{H \hat{\otimes} _{s,\pi _{s}}H} .     

New Deposit of Mordenite–Clinoptilolite in the Eastern Region of Cuba: Uses as Pozzolans

This work describes the newly discovered zeolites in the eastern region of Cuba. In the researched area, there have been no previous studies of natural zeolite exploration. Therefore, the results shown here are new. The main object of this research is to analyse five samples of zeolites and demonstrate their pozzolanic capacity and the possibility of their usage in the industrial manufacturing of pozzolanic cements. The study of the samples was performed by X-ray diffraction (XRD), X-ray fluorescence (XRF) and scanning electron microscopy (SEM). A chemical analysis (CAQ) to determine the quality of the samples as pozzolans was performed, by determining the total SiO₂, reactive SiO₂, total CaO, reactive CaO, Al₂O₃, MgO and the insoluble residue (I.R.). Lastly, an eight-day pozzolanicity analysis (PA) was carried out to determine the pozzolanic reactivity of the samples. The results obtained by XRD, XRF and SEM established that the researched zeolite samples have two main zeolitic phases: mordenite and clinoptilolite. Altered volcanic glass, quartz and smectite (montmorillonite) are the secondary phases. The results of the chemical quality analysis (CAQ) showed that the samples contain a considerable amount of reactive SiO₂ and reactive CaO, as well as a low content of insoluble residue, which reinforces their properties as pozzolans. The results of the pozzolanicity analysis (PA) concluded that the analysed samples actively react with Ca(OH)₂ after eight days. Based on all the results mentioned above, it is established that both mordenite and clinoptilolite behave like pozzolans and can be recommended for the manufacture of pozzolanic cements, which have more effective properties than Portland cement, in terms of physical, chemical and mechanical strength, low heat of hydration, resistance to sulphates, low CO₂ emissions to the atmosphere and negligible impacts on the environment.     

Altered Volcanic Tuffs from Los Frailes Caldera. A Study of Their Pozzolanic Properties

This work presents the results of the study of the physical, chemical, mineralogical and pozzolanic properties of the altered volcanic tuffs (AVT) that lie in the Los Frailes caldera, south of the Iberian Peninsula, and demonstrates their qualities as pozzolans for the manufacturing of mortars and pozzolanic cements of high mechanical strength. The main objective of this research is to show to what extent the AVTs can replace portland cement (PC) in mortars, with standardised proportions of 75:25% and 70:30% (PC-AVT). To achieve these objectives, three AVT samples were studied by a petrographic analysis of thin section (PATS), DRX, FRX and MEB. The pozzolanic properties were determined by three methods: electrical conductivity (ECT), chemical pozzolanicity tests (CPT) at 8 and 15 days and mechanical strength tests (MS) of the specimens at 2, 7, 28 and 90 days. Studies of a PATS, DRX, FRX and MEB showed that the AVT samples’ constitutions are complex where smectite (montmorillonite), mordenite, quartz, halloysite, illite, kaolinite, volcanic glass and lithic fragments coexist. The results of the ECT and CPT tests confirmed the pozzolanic properties of the samples analysed and proved an increase in mechanical strength from 2 to 90 days of testing.     

Controlled Self‐Assembly of Mesoporous CuO Networks Guided by Organic Interlinking

The controlled aggregation of copper oxide nanoparticles (CuO NPs) induced by a multitopic carboxylic acid allows the formation of mesoporous structures with high surface area, in the order of 100 m² g^?1, as demonstrated herein. The main novelty in the designed process is the use, as a previous step, of a sacrificeable monotopic carboxylate ligand for capping the CuO NPs. This step avoids the often observed unwanted behavior of uncontrolled aggregation and material densification. The monotopic 3,6,9‐trioxadecanoate (HTODA) is used as the capping agent to prepare TODA@CuO, a starting material that forms colloidal dispersions in ethanol. For NPs self‐assembly, the bulky tricarboxylic acid 4,4′,4′′,‐benzene‐1,3,5‐triyl‐tris(benzoic acid) (H₃BTB) is chosen as an efficient interlinker in the controlled aggregation. The obtained mesoporous network shows a considerable thermal stability, retaining ≈70% of its specific surface area after annealing at 300 °C under vacuum. Thermal treatment involves TODA capping agent elimination, but not BTB linker. The simultaneous reduction of the CuO NPs to a Cu₂O/Cu mixture is observed.     

A self-contained progress variable space solution method for thermochemical variables and flame speed in freely-propagating premixed flamelets

Flamelet models for premixed combustion, which are based on equations formulated and solved in progress variable space, have been proposed in the past, but have not been adopted for chemistry reduction methods. This is due to one limitation of these models: they need a closure for both the magnitude and the shape of the gradient (or scalar dissipation rate) of the progress variable, which is essential for an accurate prediction of the flame displacement speed. So far, solution methods for the aforementioned models require gradient information as an input, which is either modelled and non-generic, or extracted from a previous physical space flame solution for the analogous problem. The objective of this work is to provide a self-contained solution method for freely-propagating premixed flamelets in progress variable space, by solving an additional flamelet equation for the gradient of the progress variable. With this, the novel method provides both magnitude and shape of the gradient. Studying hydrogen-air and methane-air configurations, it is demonstrated that an accurate prediction of the laminar flame speed without the necessity for further input parameters can be obtained.     

Exclusion Process with Slow Boundary

We study the hydrodynamic and the hydrostatic behavior of the simple symmetric exclusion process with slow boundary. The term slow boundary means that particles can be born or die at the boundary sites, at a rate proportional to \(N^{-\theta }\), where \(\theta > 0\) and N is the scaling parameter. In the bulk, the particles exchange rate is equal to 1. In the hydrostatic scenario, we obtain three different linear profiles, depending on the value of the parameter \(\theta \); in the hydrodynamic scenario, we obtain that the time evolution of the spatial density of particles, in the diffusive scaling, is given by the weak solution of the heat equation, with boundary conditions that depend on \( \theta \). If \(\theta \in (0,1)\), we get Dirichlet boundary conditions, (which is the same behavior if \(\theta =0\), see Farfán in Hydrostatics, statical and dynamical large deviations of boundary driven gradient symmetric exclusion processes, 2008); if \(\theta =1\), we get Robin boundary conditions; and, if \(\theta \in (1,\infty )\), we get Neumann boundary conditions.     

Understanding the mechanisms of [3+2] cycloaddition reactions. The pseudoradical versus the zwitterionic mechanism

Analysis of 12 three-atom-components (TACs) participating in [3+2] cycloaddition (32CA) reactions towards ethylene and acetylene allows establishing good correlations between the pseudodiradical character, the hardness η, and the nucleophilicity N index of the TAC with the feasibility of these non-polar reaction. These results allow the introduction of the pr index, which comprises the two aforementioned DFT reactivity indices. The increase of the pr index for an allylic-type TAC goes accompanied by a linear decrease of the activation enthalpy of the reaction. The present study makes it possible to establish a useful classification of 32CA reactions into zw-type reactions involving TACs with a high zwitterionic character, and pr-type reactions involving TACs with a high pseudodiradical character.     

Efficient numerical analysis of optical imaging data: A comparative study

The computational efficiency of 14 optical detectors over six types of transformations, namely: blur, illumination, rotation, viewpoint, zoom, and zoom-rotation changes, was analyzed. Images with the same resolution (750 × 500 pixels) were studied, in terms of correspondences, repeatability and computing time, and the correspondence was measured by using homographies i.e. projective transformations, to obtain the best efficiency for imaging applications. Results show that the multi-scale Harris Hessian detector is the most efficient for blur, illumination, and zoom-rotation changes. Meanwhile, multi-scale Hessian and Hessian Laplace are the best methods for rotation, viewpoint, and zoom changes.