Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces

We extend the theory of weighted norm inequalities on variable Lebesgue spaces to the case of bilinear operators. We introduce a bilinear version of the variable \A_\pp condition, and show that it is necessary and sufficient for the bilinear maximal operator to satisfy a weighted norm inequality. Our work generalizes the linear results of the first author, Fiorenza and Neugebauer \cite{dcu-f-nPreprint2010} in the variable Lebesgue spaces and the bilinear results of Lerner {\em et al.} \cite{MR2483720} in the classical Lebesgue spaces. As an application we prove weighted norm inequalities for bilinear singular integral operators in the variable Lebesgue spaces.Comment: Revised based on anonymous referee's reports. A number of typos and small errors corrected. One conjecture added to introductio

America's Hispanic Children: Gaining Ground, Looking Forward

The purpose of the study was to "widen the lens" by highlighting the positive trends among Hispanic youth. More young Latino children are enrolling in center-based care programs which are more likely to be of a higher educational quality than home-based care and other alternatives. Other highlights include Latino students posting solid gains on national assessments in key subject areas, more Latinos than ever before earning a high school diploma, and a record number of Hispanics enrolling in two- or four-year colleges. A greater sense of responsibility among Latino youth was also revealed in the study, indicated by falling teen pregnancy rates -- declines have been greater in the last four years for Latinas than other ethnic groups -- and a decrease in smoking and binge drinking habits among high school seniors. Latino teens' use of technology is also promising. While less likely to own a cell phone than their peers, they are avid users of smartphones and tablets. The Pew Research Center Hispanic Trends Project reported Hispanics are the only group to see poverty rates decline and incomes increase, but despite these gains, Hispanics have the largest number of people living in poverty when compared with other minority groups. "Nearly one-third of Latino children live below the poverty line, and a roughly equal share, while not poor by official definition, has family incomes just adequate to meet basic needs," the Child Trends study states

Embeddings between grand, small and variable Lebesgue spaces

We give conditions on the exponent function $p(\cdot)$ that imply the existence of embeddings between grand, small and variable Lebesgue spaces. We construct examples to show that our results are close to optimal. Our work extends recent results by the second author, Rakotoson and Sbordone.Comment: Final version to appear in Math. Note

Role of Strain on Electronic and Mechanical Response of Semiconducting Transition-Metal Dichalcogenide Monolayers: an ab-initio study

We characterize the electronic structure and elasticity of monolayer transition-metal dichalcogenides MX2 (M=Mo, W, Sn, Hf and X=S, Se, Te) with 2H and 1T structures using fully relativistic first principles calculations based on density functional theory. We focus on the role of strain on the band structure and band alignment across the series 2D materials. We find that strain has a significant effect on the band gap; a biaxial strain of 1% decreases the band gap in the 2H structures, by as a much 0.2 eV in MoS2 and WS2, while increasing it for the 1T materials. These results indicate that strain is a powerful avenue to modulate their properties; for example, strain enables the formation of, otherwise impossible, broken gap heterostructures within the 2H class. These calculations provide insight and quantitative information for the rational development of heterostructures based on these class of materials accounting for the effect of strain.Comment: 16 pages, 4 figures, 1 table, supplementary materia

The dynamics of copper intercalated molybdenum ditelluride

Layered transition metal dichalcogenides are emerging as key materials in nanoelectronics and energy applications. Predictive models to understand their growth, thermomechanical properties and interactions with metals are needed in order to accelerate their incorporation into commercial products. Interatomic potentials enable large-scale atomistic simulations at the device level, beyond the range of applications of first principle methods. We present a ReaxFF reactive force field to describe molybdenum ditelluride and its interactions with copper. We optimized the force field parameters to describe the properties of layered MoTe2 in various phases, the intercalation of Cu atoms and clusters within its van der Waals gap, including a proper description of energetics, charges and mechanical properties. The training set consists of an extensive set of first principle calculations computed from density functional theory. We use the force field to study the adhesion of a single layer MoTe2 on a Cu(111) surface and the results are in good agreement with density functional theory, even though such structures were not part of the training set. We characterized the mobility of the Cu ions intercalated into MoTe2 under the presence of an external electric fields via molecular dynamics simulations. The results show a significant increase in drift velocity for electric fields of approximately 0.4 V/A and that mobility increases with Cu ion concentration.Comment: 21 pages, 9 Figure

Measurement of income inequality in Mexico: methodology, assessment and empirical relationship with poverty and human development.

The intended contribution of this work is to systematically discuss a selection of methodological topics and some of the empirical and technical issues that have been driving the measurement of inequality in Mexico so far. This discussion has two strands: firstly, the general case, and second, the particular case of Mexico. The general case include some philosophical concerns, along with a review of the traditional inequality measurement, the most common operational decisions in empirical calculations, and the recent methodological contribution of development literature that is mostly centered around the capability approach of Sen (1985b). The philosophical part contrasted with other approaches and rejected the Marxist view of economic inequality, which is mostly viewed as an outcome of exploitation. The distributional judgments are compared with more ancient schools of thought in regards to justice. Another methodological issue is such that social inequality, approximated by income inequality, might be considered as an additional functioning that measures the degree of social cohesion in the country, this finding is an implication that comes from the definition of functionings within the capability approach; then, social inequality is a functioning that is different in nature from other measures of destitution, and it is also different from the destitution that is captured by absolute poverty measurement. Our general case includes a review of the most popular ways to measure inequality, such as normative and pragmatic inequality measures that are mentioned with their properties, with their rankings of the distributions provided by the use of stochastic dominance and quantile comparisons, and the construction of statistical models and some graphic representations of income economic inequality; the approach of inequality concerns included in the measurement of relative poverty is rejected for the sake of clarity. Then this general view would guide us to a better understanding of the Mexican literature for the consideration of income distribution. The measurement of destitution provided by governmental offices is necessary to discuss, because there might be some lack of coherence between the design of the measurement and the complex legal system in Mexico. We also consider a set of regulatory concerns that might not be unique to the Mexican law, but may be generalized for developing countries as a whole. Some of the methodological discussions that show how the Mexican research has been influenced by the international literature about human destitution will be good to clarify, looking at the value judgments that have been automatically accepted by the researchers. A sensitivity analysis was performed to the empirical calculation of inequality in Mexico, so the measurement showed to be different in regards to a variety of operational concerns: the recipient unit, the different data from income and consumption-expenditure surveys, various non-responses and underreported biases, the inclusion of a regional price index, among other things. In this work was also covered the reasons why it might be the case that destitution and poverty assessment was studied more deeply than inequality itself, so the possible ambiguity of inequality with poverty measurement is challenged in this work with a variety of theoretical remarks and empirical arguments. The final topic for the particular case of Mexico is to shed light in regards to the context of the capability approach and the use of equivalence scales, because these methodological approaches consider respectively directly and indirectly the assessment of distributional judgments. This discussion is followed by an empirical assessment of inequality measures that is related with a set of functionings and services, where a direct relationship of measures of inequality with other measures of destitution is made clear

Structural, Thermodynamic, and Electronic Properties of Mixed Ionic/Electronic Conductor Materials

Due to the mainstream CMOS technology facing a rapid approach to the fundamental downscaling limit, beyond CMOS technologies are under active investigation and development with the intention of revolutionizing and sustaining a wide range of applications including sensors, cryptography, neuromorphic and quantum computing, memory, and logic, among others. Resistive switching electronics, for example, are devices that can change their electrical resistance with an applied external field. Despite their simple metal-insulator-metal structure, resistive switching devices exhibit an intricate set of IV characteristics based on the chemical composition of the solid electrolyte that ranges from non-volatile bipolar and non-polar switching to volatile threshold switching (abrupt but reversible change in resistance). This rich variety of electrical responses offer new alternatives to traditional CMOS applications in the areas of RF-signal switching, relaxation oscillators, over-voltage protection, and notably, memory cells and two-terminal non-linear selector devices. With the aim of unraveling the physics behind two of such conduction mechanisms, filamentary and threshold, in electrochemical cells consisting solid mixed ionic-electronic conductor electrolytes, this work focused on using first-principles calculations to characterize the structural, thermodynamic, and electronic properties of copper-doped amorphous silicon dioxide and copper-doped germanium-based glassy chalcogenides. The Cu/a-SiO2 system is a promising candidate for resistive switching memory applications. The conduction mechanism in the low-resistance state is known to be filamentary, that is, a physical metallic filament bridges between the metallic electrodes through the amorphous silica. However, many fundamental materials processes that would aid the design and optimization of this devices, such the shape and size of stable metallic filaments, remain unknown. In the first part of this work, the morphology and diffusion of small copper clusters embedded in amorphous silicon dioxide were characterized by density functional theory calculations. The average formation energy of a single copper ion in the amorphous matrix is found to be 2.4 eV, about 50% lower than in the case of silicon dioxide in its cristobalite or quartz phases. The theoretical predictions show that copper clusters with an equiaxed morphology are always energetically favorable relative to the dissolved copper ions in a-SiO2; hence, stable clusters do not exhibit a critical size. The stochasticity in the atomistic structure of the amorphous silicon dioxide leads to a broad distribution activation energies for diffusion of copper in the matrix, ranging from 0.4 to 1.1 eV. Since ab initio molecular dynamics are prohibitively expensive to simulate the switching process in Cu/a-SiO2 electrochemical metallization cells, a multi-scale simulation approach based on electrochemical dynamics with implicit degrees of freedom and density functional theory was developed to study the electronic evolution during metallic filament formation cells. These simulations suggest that the electronic transport in the low-resistance configuration is attributed to copper derived states belonging to the filament bridging between electrodes. Interestingly, the participation of states derived from intrinsic defects in the amorphous SiO2 around the Fermi energy are negligible and do not contribute to conduction. Unlike the Cu/a-SiO2 system which only exhibits filamentary switching, copper-doped germanium-based glassy chalcogenides show filamentary or threshold type of conduction depending on the chemical composition of the glass and copper concentration. Ab initio molecular dynamics based on density functional theory is used to understand the atomistic origin of the electronic transport in these materials. The theoretical predictions show that glasses containing tellurium tend to favor the formation of copper clusters; hence, these materials exhibit filamentary conduction. Threshold conduction is predicted to be the transport mechanism for glassy sulfides and selenides due to the ability of copper to remain dissolved in the amorphous matrix even at high metal concentration. Furthermore, the charge carrier transport in sulfur and selenium glasses was found to be assisted by defective states derived from chalcogen atoms whose bonds exhibit a polar character. Finally, taking advantage of the van der Waals gap as intercalation sites and crystal order in molybdenum disulfide, a novel mixed ionic-electronic conductor material based on copper and silver intercalation of MoS2 is proposed. The theoretical predictions show that on average, the intercalation energy of copper into MoS2 is 1 eV, while intercalation of silver shows a strong dependence on concentration ranging from 2.2 to 0.75 eV for low and high concentrations, respectively. The activation energy for diffusion of copper and silver intercalated within the van der Waals gap of MoS2 is predicted to be 0.32 and 0.38 eV, respectively, comparable to other superionic conductors. Upon Cu and Ag intercalation, MoS2 undergoes a semiconductor-to-metal transition, where the in-plane and out-of-plane conductances are comparable and exhibit a linear dependence with metal concentration

Disseminated cutaneous gout: a rare manifestation of a common disease

Disseminated cutaneous gout is a rare atypical cutaneous manifestation of gout in which widespread dermal and subcutaneous tophi develop at extra-articular body sites. Given the lack of joint involvement that is typically a feature in tophaceous gout, the diagnosis may not be initially suspected. We present the case of a 50-year-old Hispanic man with poorly controlled gout who was evaluated for several years of firm papulonodules over the trunk and upper and lower extremities, sparing the joints; histopathology confirmed, the diagnosis of disseminated cutaneous gout. Per our literature review, disseminated cutaneous gout presents with polymorphous papules and nodules that can mimic other, more common cutaneous diseases. There is a preponderance of cases in males, Asians, and patients with longstanding gout. The lower extremities are involved in nearly all reports. Uric acid-lowering therapy with allopurinol has been reported to decrease the size and number of lesions in a minority of treated patients