Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol

We study the problem of pointwise convergence for equations of the type $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ with $s>(n-\alpha+1)/2$ the solution $u$ converges to $f$ $\mathcal{H}^\alpha$-a.e, where $\mathcal{H}^\alpha$ is the $\alpha$-dimensional Hausdorff measure. We improve upon this result depending on the dispersive strength of the symbol. On the other hand, we prove negative results for a wide family of polynomial symbols $P$. Given $\alpha$, we exploit a Talbot-like effect to construct regular initial data whose solutions $u$ diverge in sets of Hausdorff dimension $\alpha$. However, for quadratic symbols like the saddle, other kind of examples show that our positive results are sometimes best possible. To compute the dimension of the sets of divergence we use a Mass Transference Principle from Diophantine approximation theory

Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick

We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same regularity as Du's counterexamples for weighted $L^2$ restriction estimates is achieved for the convergence problem. To do so, we need to construct the set of divergence explicitly and compute its Hausdorff dimension, for which we use the Mass Transference Principle, a technique originated from Diophantine approximation.FJC2019-039804-

Salmonella enterica biofilm-mediated dispersal by nitric oxide donors in association with cellulose nanocrystal hydrogels

Protected by extracellular polymers, microbes within biofilms are significantly more resistant to disinfectants. Current research has been instrumental in identifying nitric oxide donors and hydrogels as potential disinfectant additives. Nitric oxide (NO) donors are considered a very promising molecule as biofilm dispersal agents and hydrogels have recently attracted a lot of interest due to their biocompatible properties and ability to form stable thin films. When the NO donor MAHMA NONOate was dissolved in phosphate saline buffer, it was able to reduce the biomass of well-established biofilms up to 15% for at least 24 h of contact time. Encapsulation of MAHMA NONOate and molsidomine within a hydrogel composed of cellulose nanocrystals (CNC) has shown a synergistic effect in dispersing well-established biofilms: after 2 h of exposure, moderate but significant dispersion was measured. After 6 h of exposure, the number of cells transitioning from the biofilm to the planktonic state was up to 0.6 log higher when compared with non-treated biofilms. To further explore the transport processes of NO donors within hydrogels, we measured the nitric oxide flux from gels, at 25°C for a composite of 0.1 µM MAHMA NONOate–CNC. Nitric oxide diffuses up to 500 µm from the hydrogel surface, with flux decreasing according to Fick’s law. 60% of NO was released from the hydrogel composite during the first 23 min. These data suggest that the combined treatments with nitric oxide donor and hydrogels may allow for new sustainable cleaning strategies

Nutrition is Perceived as an Ecosystem Service of the Mangrove by Rural People in Ecuador

The mangrove ecosystem is considered as the source of livelihood, particularly for coastal areas. This study explores the perception of the inhabitants of Puerto El Morro and the island of Costa Rica (Ecuador) against the ecosystem services of the mangrove. Seven quantitative variables were used on the Likert scale by performing exploratory factor analysis. The results were based on a sample of 94 participants finding 2 factors, tourism (29.07% of variance) and nutritious food production (25.45% of variance remaining). The reliability of the questionnaire was acceptable according to Cronbach’s Alpha 0.654. A confirmatory factor analysis is necessary to revalidate the items of the factors. Keywords: coastal communities, eating, mangroves, livelihoods, nutrition. Resumen El ecosistema de manglar se considera fuente de medios de vida, en particular para zonas costeras. Este estudio explora la percepción de los habitantes de Puerto El Morro y la isla Costa Rica (Ecuador) frente a los servicios ecosistémicos del manglar. Se utilizaron 7 variables cuantitativas en escala de Likert realizando análisis factorial exploratorio. Los resultados parten de una muestra de 94 participantes, hallando 2 factores: turismo (29,07% de varianza) y producción alimentos nutritivos (25,45% de varianza restante). La confiabilidad del cuestionario fue aceptable según el Alfa de Cronbach 0.654. Es necesario un análisis factorial confirmatorio para revalidar los ítems de los factores. Palabras Clave: comunidades costeras; alimentación; manglares; medios de vida; nutrición

Mathematical and physical techniques of modeling and simulation of pattern recognition in the stock market

The following article presents the analysis through mathematical and physical techniques of large databases, which are very common today, due to the large number of variables (especially in the information and physics industry) and the amount of information that results from a process, therefore an analysis is necessary that allows the Decision in a responsible manner, looking for scientific criteria that support said decisions, in our case a database of the forex system will be taken. Initially, a study and calculation of different measurements between the samples and their characteristics will be carried out to make a good prediction of the data and their behavior using different classification methods inspired by basic sciences. Below is an explanation of the techniques based on the analysis of data components and the correlations that exist between the variables, which is a technique widely used in physical processes to determine the correlations between variables

New insights into the fossil record of the turtle genus Chelus Duméril, 1806 including new specimens with information on cervicals and limb bones

Matamata turtles (Chelus Duméril, 1806) are composed of two extant species, Chelus fimbriata ­Schneider, 1783 and Chelus orinocensis Vargas-Ramírez, Caballero, Morales-Betancourt, Lasso, Amaya, Martínez, Silva-Viana, Vogt, Farias, Hrbek, Campbell & Fritz, 2020, inhabitants of the main freshwater drainages of northern South America. The systematics and palaeobiogeography of Chelus is still unresolved. Here, we describe several new fossil specimens from the Late Miocene of Urumaco (Venezuela) and Tatacoa (Colombia). The fossils are mostly complete, articulated shells that allow reestablishing validity of two extinct taxa, Chelus colombiana Wood, 1976 and Chelus lewisi Wood, 1976. One of the specimens of C. lewisi from Urumaco represents the first record within the genus for which autopodial bones (a left manus) and additional limb bones are preserved together with ashell, demonstrating evolutionary conservatism in limb anatomy for the genus. The specimen comes from the Socorro Formation, representing the earliest so far known record of Chelus for the Urumaco sequence. Additionally, one specimen from Tatacoa is the first fossil for which cervical and pectoral girdle elements are preserved. Phylogenetic analysis supports the existence of two separate clades inside of Chelus, one formed by the extinct species and the other by the extant ones

Fish oil rich diet in comparison to saturated fat rich diet offered protection against lipopolysaccharide-induced inflammation and insulin resistance in mice

<p>Abstract</p> <p>Background and Objective</p> <p>Systemic chronic inflammation is linked to metabolic syndrome, type-2 diabetes, and heart disease. Lipopolysaccharide (LPS), a Gram negative microbial product, triggers inflammation through toll-like-receptor-4 (TLR-4) signaling. It has been reported that dietary fatty acids also modulate inflammation through TLR-4. We investigated whether fish oil (FO) rich diet in comparison to saturated fat (SF) rich diet would confer protection from pathologies induced by LPS.</p> <p>Methods</p> <p>Twenty C57BL/6 mice were divided into two groups. One group received FO-diet and other received SF-diet <it>ad libitum </it>for 60 days. Diets were isocaloric containing 45% energy from fat. After 60-days of feeding, blood was collected after overnight fast. Mice were allowed to recover for 4-days, fasted for 5-hours, challenged with 100 ng/mL of LPS intraperitonially, and bled after 2-hours. After 7-days of recuperation, mice were challenged with 500 ng/mL of LPS intraperitonially and observed for physical health.</p> <p>Results</p> <p>Food intake was similar in FO- and SF-fed mice. FO-fed mice compared to SF-fed mice had significantly less body weight gain (P = 0.005), epididymal fat weight (P = 0.005), fasting blood glucose (70.8 vs 83.3 ng/dL; P < 0.05), HOMA-IR (5.0 vs 13.6; P < 0.019), and serum cholesterol (167 vs 94 mg/dL; P < 0.05). When challenged with LPS, FO-fed mice had significantly lower serum IL-1β compared to SF-fed mice (2.0 vs 30.0 pg/mL; P < 0.001). After LPS-challenge, SF-fed mice had higher mortality, lost more body weight, and had greater decrease in blood glucose compared to FO-fed mice.</p> <p>Conclusion</p> <p>Overall, FO-diet compared to SF-diet offered protection against deleterious effects of LPS in mice.</p