Hardy type spaces on certain noncompact manifolds and applications

In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below, positive injectivity radius and spectral gap b. We introduce a sequence X^1(M), X^2(M), ... of new Hardy spaces on M, the sequence Y^1(M/, Y^2(M), ... of their dual spaces, and show that these spaces may be used to obtain endpoint estimates for purely imaginary powers of the Laplace-Beltrami operator and for more general spectral multipliers associated to the Laplace--Beltrami operator L on M. Under the additional condition that the volume of the geodesic balls of radius r is controlled by C r^a e^{2\sqrt{b} r} for some real number a and for all large r, we prove also an endpoint result for first order Riesz transforms D L^{-1/2}. In particular, these results apply to Riemannian symmetric spaces of the noncompact type.Comment: 27 pages, v2: the first version has been revised and rearranged, with additions, in two papers, of which this new version is the first. The second paper is posted as arXiv:1002.1161v

Mathematical modeling with digital technological tools for interpretation of contextual situations

This article has the goal of proposing physical contextual situations modeling as a way to interpret mathematical representations that are produced by digital technological tools. Thus, there is an experimental situation-problem about a physical phenomenon that is modeled through video analysis and dynamic geometry software; the methodological model Cuvima conducts the experimental activity. Pre-testing and post-testing measuring instruments were designed to obtain the information and previous conceptions of ten graduate students in Mathematical Education, which showed a conceptual change. Similarly, results prove that digital technology, from a didactical sequence, supports and strengthens experimental work simplifying modeling processes of a physical phenomenon, promoting the use of mathematical representations to solve a situation-problem

Means of Transportation to Work in the United States, 1990-2018

Introduction: This report examines how people commuted to work in the United States between 1990 and 2018, focusing on disparities with respect to race and ethnicity, sex, marital status, income, and poverty status Methods: This report uses the American Community Survey PUMS (Public Use Microdata Series) data for all years released by the Census Bureau and reorganized for public use by the Minnesota Population Center, University of Minnesota, IPUMSusa, (https://usa.ipums.org/usa/index.shtml). See Public Use Microdata Series Steven Ruggles, J. Trent Alexander, Katie Genadek, Ronald Goeken, Matthew B. Schroeder, and Matthew Sobek. Integrated Public Use Microdata Series: Version 5.0 [Machine-readable database]. Minneapolis: University of Minnesota, 2019. Discussion: Car use had a slight decline among non-Hispanic whites but is increasing steadily among other race and ethnic groups. While in 1990, 88.6% of non-Hispanic white workers commuted by car, a slightly smaller proportion of 86.6% did so in 2018. Among non-Hispanic blacks, however, car use went up from 77.5% to 82.5% over the same period and from 79.8% to 85.3% among Latinos. Car use among Asians remained relatively stable at 79%. Conversely, other means of transportation to work that once were more common are declining. For example, public transportation use dropped five percentage points from 15.2% to 10.1% among non-Hispanic blacks and from 11.1% to 6.6% among Latinos between 1990 and 2018. Working from home rates increased steadily among all racial and ethnic groups. For example, Asians working at home went from 2.1% of those employed in 1990 to 4.7% in 2018. These data are pre-COVID-19. Other trends by sex, income, marital status, and poverty status are further analyzed in the report

Commuting Times to Work in the United States, 1990-2018

Introduction: This report documents the evolution of commuting times in the United States between 1990 and 2018, focusing on disparities with respect to race and ethnicity, sex, marital status, income, and poverty status Methods: This report uses the American Community Survey PUMS (Public Use Microdata Series) data for all years released by the Census Bureau and reorganized for public use by the Minnesota Population Center, University of Minnesota, IPUMSusa, (https://usa.ipums.org/usa/index.shtml). See Public Use Microdata Series Steven Ruggles, J. Trent Alexander, Katie Genadek, Ronald Goeken, Matthew B. Schroeder, and Matthew Sobek. Integrated Public Use Microdata Series: Version 5.0 [Machine-readable database]. Minneapolis: University of Minnesota, 2019. Discussion: There are two main findings. First, about half of the population in the country took between 10 and 30 minutes to commute to work—a figure consistent over time. That said, the second finding is that the proportion of people taking more than half an hour to get to work has been increasing steadily. In terms of race, non-Hispanic whites have the highest proportion of people in the shorter commuting times (less than 30 minutes) compared to other racial and ethnic groups. For example, by 2018, 25.4% of non-Hispanic white workers took less than 10 minutes to get to work, compared to 18.2% of Asians in the same category. Latinos (21.3%) and non-Hispanic blacks (19.5%) were in between of the other two racial and ethnic groups.These data are pre-COVID-19. Other trends by sex, income, marital status, and poverty status are further analyzed in the report

Racial and Ethnic Composition among Latinos in the United States (1990-2017)

Introduction: This report examines the socioeconomic trends and differences among not only the four major racial and ethnic groups in the country (non-Hispanic whites, non-Hispanic blacks, Latinos, and Asians) but also within the Latino population from 1990 to 2017. Methods: This report uses the American Community Survey PUMS (Public Use Microdata Series) data for all years released by the Census Bureau and reorganized for public use by the Minnesota Population Center, University of Minnesota, IPUMSusa, (https://usa.ipums.org/usa/index.shtml). See Public Use Microdata Series Steven Ruggles, J. Trent Alexander, Katie Genadek, Ronald Goeken, Matthew B. Schroeder, and Matthew Sobek. Integrated Public Use Microdata Series: Version 5.0 [Machine-readable database]. Minneapolis: University of Minnesota, 2017. Discussion: The four major racial and ethnic groups within the Latino population present a high variety. The majority of Latinos in the U.S. identify as white (65% in 2017), followed by mixed-race (31.8%); Afro-Latinos (2.2%) and Indigenous Latinos (1.0%) are very few in comparison. Latinos are the youngest racial and ethnic group in the country, but it is Afro-Latinos who are the youngest of them—in 2017, 20.6% of Afro-Latinos were aged 0-9 years old. In terms of education, high-school non-completion decreased significantly between 1990 and 2017 among Latinos in general. A similar decreasing trend was found in terms of the lowest income strata. Finally, while the foreign-born white and mixed-race Latino population decreased slightly in this period (about one percentage point difference), it was the foreign-born Afro-Latinos who experienced the largest drop, from 38.2% to 26.4%. In contrast, the proportion of Indigenous Latinos grew substantially over this period, from 15.4% in 1990 to 27.6% in 2017