A Note on Systems of Linear Equations

This note is a comment on reference [1] and a generalization of the method there presented. We consider a system of m linear equations in n unknowns x_1, x_2,...x_n (1) Σ^(n)_(j=1) a_(ij)x_j = c_i i=1, 2,...m, a_(ij), c_i real or A∙x=c in matrix notation. We distinguish three cases: (I) There is no finite vector x satisfying (1) (inconsistent case); (II) There is a unique vector x satisfying (1); (III) There are an infinity of vectors x satisfying (1), such that their endpoints lie on some line, plane, or higher-dimensional linear manifold

Empowering International Students by Embedding Formative Experience in Course Design

No abstract available

Portable high-speed photometry systems for observing occultations

Because of their high spatial resolution, stellar occultations have proven extremely effective for learning about planetary upper atmospheres, asteroids, and planetary rings. The ring orbit studies for Uranus have been particularly fruitful because researchers have been able, through occultations, to obtain data of high spatial resolution (approximately 2 km) at the rate of 1 to 2 times per year. THe occultation program at M.I.T. involves: (1) identifying the scientific questions that can be answered by occultation events, (2) predicting the zone of visibilty for the useful events, (3) maintaining and improving a set of portable high-speed photometric systems, (4) obtaining the observations, and (5) reducing the data and interpreting the results. Accomplishments during the past year include: (1) a comprehensive analysis of stellar occultation data to obtain an oblateness for Uranus at the 10 ubar level of 0.0193 plus or minus 0.0010, a value consistent with the planet being in hydrostatic equilibrium and undergoing rotation at the period found by Voyger; (2) establishing an upper limit of 0.004 km on the equivalent depth of 1986U1R from 2.2 micrometer occultation data; (3) the discovery of low-amplitude waves on the edges of the epsilon ring of Uranus; and (4) the acquisition of several hundred charge coupled device strip scans of 6 weeks at Mauna Kea for the purpose of generating a prediction for the stellar occultation of Pluto

Development of lubricating oils suitable for use with liquid oxidizers Final summary report, 4 Dec. 1969 - 4 Oct. 1970

Development of lubricating oils suitable for use with liquid oxidizer

The intersection of race, sexual orientation, socioeconomic status, trans identity, and mental health outcomes

The present study examined patterns in trans individuals’ multiple identities and mental health outcomes. Cluster 1 (socioeconomic and racial privilege; n = 239) was characterized by individuals who identified as trans women or cross-dressers, lesbian, bisexual, or questioning; had associates degrees; reported household incomes of $60,000 or more a year; and were non-Latino White. Cluster 2 (educational privilege; n = 191) was characterized by individuals who identified as trans men or genderqueer, gay, or queer; had a bachelor’s degree; reported household incomes of$10,000 or less a year; and were people of color. There was a pattern of individuals in Cluster 1 who identified with two privileged identities (identifying as White and having higher household incomes), whereas individuals in Cluster 2 identified only formal education as a privilege. Individuals in Cluster 2 reported statistically significant levels of anxiety. Implications of these results for future research and clinical practice are examined.Accepted manuscrip

Escape from the List: Courage, Sacrifice, Survival

Anne Frank has been described as Hitler’s most famous victim. By virtue of her diary, which was in fact a heavily revised memoir that today might be considered to belong to the genre of creative non-fiction, Anne Frank has attained a kind of immortality that the art form of writing frequently provides. This should not, of course, trivialize her fate, nor the suffering of the multitudes of other victims of the Nazi regime, a group comprised of Jews, as well as non-Jews. Some of these stories have been told in great detail, while many others have not. What follows is the story of Elisabeth Rodrigues Lopes de la Peña, a Jewish girl whose family had fled the Spanish Inquisition to settle in the Netherlands. During the German occupation of Amsterdam during the Second World War, this family faced yet another existential threat, one that some of them did not survive. Elisabeth may well have ended up as yet one more entry in the long list of the Nazi’s victims, if not for the intervention and courageous efforts of her non-Jewish neighbors—efforts that were based in large part on their own deeply held religious beliefs and sense of morals. Elisabeth’s rescuers are known to Holocaust historians, and their names are enshrined in the Yad Vashem World Holocaust Remembrance Museum in Israel, as well as in the United States Holocaust Memorial Museum in Washington, DC. Along with my Research Assistant Angelica Roman, I have conducted personal meetings and interviews with Elisabeth’s daughter, Carolyn Stewart. Ms. Stewart has graciously shared many heretofore unknown details of her mother’s story of rescue, as well as photographs and documents, including some that have been unseen by anyone in over sixty years. What follows is new insight into Elisabeth Rodrigues’ escape from the list: a true story of courage, sacrifice, and survival. I would like to acknowledge with gratitude the assistance and support of the following people: Jennifer Crespo, Student Success Coordinator at Pace University in New York City, who generously provided funding for this project as part of the Pace Undergraduate Student – Faculty Research Program; Bonnie and Howard J. Price, without whose help this project would never have seen the light of day; my colleague at Pace University Dr. Maria Plochocki, for reviewing the manuscript and providing valuable suggestions; Gertjan Broek and Karolien Stocking Korzen at the Anne Frank House in Amsterdam; Beth Slepian at The Anne Frank Center NYC, and my superbly talented Research Assistant, Angelica E. Roman ‘19, who tirelessly conducted research, helped revise early drafts, and patiently fielded a multitude of my requests while putting up with my numerous anxieties. Special thanks go to Carolyn Stewart, who traveled from Maryland to New York City for interviews, and who spent many hours communicating with Angelica and me over the course of several months. Carolyn shared many details and primary historical artifacts with us, and she relates her mother’s fascinating tale in a captivating and compelling manner. Our hope is that we can do this wonderful, inspiring story justice in the pages that follow

Occultation studies of planets and satellites: The occultation of epsilon Geminorum by Mars

The occultation of epsilon Geminorum by Mars on 1976 April 8 was observed at three wavelengths and 4 ms time resolution with the 91 cm telescope. Temperature, pressure, and number density profiles of the Martian atmosphere were obtained for both the immersion and emersion events. Within the altitude range of 50 to 80 km above the mean surface, the mean temperature is 145 K, and the profiles exhibit wavelike structures with a peak to peak amplitude of 35 K and a vertical scale of about 20 km. The ratio of the refractivity of the atmosphere at 4500 A and 7500 A, determined from the time shift of the light curves for these wavelengths, is consistent with the atmospheric composition measured by Viking 1, 15 weeks later. From the central flash - a bright feature in the light curve midway between immersion and emersion - an optical depth is found at 4500 A of 3.3 plus or minus 1.7 per km atm (about 0.23 per equivalent Martian air mass) for the atmosphere about 25 km above the mean surface, near the south polar region. This large value and its weak wavelength dependence rule out Rayleigh scattering as the principal cause of the observed extinction

A Survey of the Arithmetical Concepts of Children in the Elementary Grades Pertaining to the Use of Money

It was the purpose of this study: (1) to survey the present concepts of money and its use, in a specific elementary grade level, in a cross section of a city that included all socio-economic levels; (2) to determine the extent to which knowledge of economic concepts is related to socio-economic level; and (3) make suggestions as to areas where greater emphasis towards understanding of money concepts should be placed

Abnormal flowers and pattern formation in floral

“From our acquaintance with this abnormal enabled to unveil the secrets that normal us, and to see distinctly what, from the regular we can only infer.” - J. W. von Goethe (1790

Bikesharing and Bicycle Safety

The growth of bikesharing in the United States has had a transformative impact on urban transportation. Major cities have established large bikesharing systems, including Boston, Chicago, Denver, Minneapolis-Saint Paul, New York City, Salt Lake City, the San Francisco Bay Area, Seattle, Washington DC, and others. These systems began operating as early as 2010, and no fatalities have occurred within the US as of this writing. However, three have happened in North America—two in Canada and one in Mexico. Bikesharing has some qualities that appear inherently unsafe for bicyclists. Most prominently, helmet usage is documented to be quite low in most regions. Bikesharing is also used by irregular bicyclists who are less familiar with the local terrain. In this study, researchers take a closer look at bikesharing safety from qualitative and quantitative perspectives. Through a series of four focus groups, they discussed bikesharing usage and safety with bikesharing members and nonmembers in the Bay Area. They further engaged experts nationwide from a variety of fields to evaluate their opinions and perspectives on bikesharing and safety. Finally, researchers conducted an analysis of bicycle and bikesharing activity data, as well as bicycle and bikesharing collisions to evaluate injury rates associated with bikesharing when compared with benchmarks of personal bicycling. The data analysis found that collision and injury rates for bikesharing are lower than previously computed rates for personal bicycling. Experts and focus group participants independently pointed to bikesharing rider behavior and bikesharing bicycle design as possible factors. In particular, bikesharing bicycles are generally designed in ways that promote stability and limited speeds, which mitigate the conditions that contribute to collisions. Data analysis also explored whether there was evidence of a “safety in numbers benefit” that resulted from bikesharing activity. However, no significant impact from bikesharing activity on broader bicycle collisions could be found within the regions in which they operate. Discussion and recommendations are presented in the conclusion