The Cauchy Operator for Basic Hypergeometric Series

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator $T(bD_q)$. Using this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy integral, Sears' two-term summation formula, as well as the $q$-analogues of Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big $q$-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic

Finite Form of the Quintuple Product Identity

The celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula.Comment: 1 pag

An environmental assessment of the John Pennekamp Coral Reef State Park and the Key Largo Coral Reef Marine Sanctuary (Unpublished 1983 Report)

The Pennekamp Coral Reef State Park was established in 1960 and the Key Largo National Marine Sanctuary in 1975. Field studies, funded by NOAA, were conducted in 1980 - 1981 to determine the state of the coral reefs and surrounding areas in relation to changing environmental conditions and resource management that had occurred over the intervening years. Ten reef sites within the Sanctuary and seven shallow grass and hardbottom sites within the Park were chosen for qualitative and quantitative studies. At each site, three parallel transects not less than 400 m long were run perpendicular to the reef or shore, each 300 m apart. Observations, data collecting and sampling were done by two teams of divers. Approximately 75 percent of the bottom within the 18-m isobath was covered by marine grasses, predominantly turtle grass. The general health of the seagrasses appeared good but a few areas showed signs of stress. The inner hardbottom of the Park was studied at the two entrances to Largo Sound. Though at the time of the study the North Channel hardbottom was subjected to only moderate boat traffic, marked changes had taken place over the past years, the most obvious of which was the loss of the extensive beds of Sargassum weed, one of the most extensive beds of this alga in the Keys. Only at this site was the green alga Enteromorpha encountered. This alga, often considered a pollution indicator, may denote the effects of shore run off. The hardbottom at South Channel and the surrounding grass beds showed signs of stress. This area bears the heaviest boat traffic within the Park waters causing continuous turbidity from boat wakes with resulting siltation. The offshore hardbottom and rubble areas in the Sanctuary appeared to be in good health and showed no visible indications of deterioration. Damage by boat groundings and anchors was negligible in the areas surveyed. The outer reefs in general appear to be healthy. Corals have a surprising resiliency to detrimental factors and, when conditions again become favorable, recover quickly from even severe damage. It is, therefore, a cause for concern that Grecian Rocks, which sits somewhat inshore of the outer reef line, has yet to recover from die-off in 1978. The slow recovery, if occurring, may be due to the lower quality of the inshore waters. The patch reefs, more adapted to inshore waters, do not show obvious stress signs, at least those surveyed in this study. It is apparent that water quality was changing in the keys. Water clarity over much of the reef tract was observed to be much reduced from former years and undoubtedly plays an important part in the stresses seen today over the Sanctuary and Park. (PDF contains 119 pages

THE CONNECTION BETWEEN DOMESTIC VIOLENCE AND ANIMAL CRUELTY IN PUERTO RICO: AN ANTHROPOLOGICAL STUDY

Violence against women is one of Puerto Rico’s most critical social problems and for this reason, anthropological thought is critically necessary. Some women in Puerto Rico are vulnerable to situations of violence and control through domestic violence while their animals become involved in the same tangle of abuse. Women’s voices about their animals have not been heard simply because nobody has inquired. I asked women survivors of domestic abuse whether or not their male partners had engaged in any type of animal cruelty against household and domesticated animals. My intention in conducting this research was to examine, both from an anthropological and from a gender perspective, the correlation in Puerto Rico between domestic violence and animal cruelty through ethnographic work. Interviews with professional shelter staff were conducted as well to establish whether or not women seeking shelter talk about their pets being hurt by their male partners—and if so, what consequences that abuse has for the women. My main objective was to determine whether the results of research that had been conducted in other cultures that demonstrated a link between animal abuse and domestic violence findings would be translatable to Puerto Rican culture. There is a remarkable void in this area of study in the Caribbean and Latin America that needs to be addressed and this study is a contribution toward analysis, dialogue, and change

IL-33 ameliorates Alzheimer’s disease-like pathology and cognitive decline

Alzheimer’s disease (AD) is a devastating condition with no known effective treatment. AD is characterized by memory loss as well as impaired locomotor ability, reasoning, and judgment. Emerging evidence suggests that the innate immune response plays a major role in the pathogenesis of AD. In AD, the accumulation of β-amyloid (Aβ) in the brain perturbs physiological functions of the brain, including synaptic and neuronal dysfunction, microglial activation, and neuronal loss. Serum levels of soluble ST2 (sST2), a decoy receptor for interleukin (IL)-33, increase in patients with mild cognitive impairment, suggesting that impaired IL-33/ST2 signaling may contribute to the pathogenesis of AD. Therefore, we investigated the potential therapeutic role of IL-33 in AD, using transgenic mouse models. Here we report that IL-33 administration reverses synaptic plasticity impairment and memory deficits in APP/PS1 mice. IL-33 administration reduces soluble Aβ levels and amyloid plaque deposition by promoting the recruitment and Aβ phagocytic activity of microglia; this is mediated by ST2/p38 signaling activation. Furthermore, IL-33 injection modulates the innate immune response by polarizing microglia/macrophages toward an antiinflammatory phenotype and reducing the expression of proinflammatory genes, including IL-1β, IL-6, and NLRP3, in the cortices of APP/PS1 mice. Collectively, our results demonstrate a potential therapeutic role for IL-33 in AD

The emerging role of autophagy in Parkinson's disease

Parkinson's disease (PD) is the most common neurodegenerative movement disorder that affects about 1% of the population worldwide. Despite significant advances in the identification of genetic mutations and signaling pathways that are associated with the disease, the precise mechanisms implicated in the pathophysiology of the disease are not well understood. More importantly, treatments that are effective in reversing the progression of the disease is essentially lacking. Further investigation into the pathogenic mechanisms of PD thus presents a pressing concern for neuroscientists. Recently, deregulation of the autophagic pathway is observed in the brains of PD patients and in models of PD. In this review we summarize current literature on the emerging involvement of autophagy in PD, and the implication for future development of treatment against the disorder

Personality and Values Based Materialism: Their Relationship and Origins

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141942/1/jcpy389.pd

Colorectal Cancer: How Does an Existing Tool Perform in Predicting Risk in Young, High-Risk Patients?

https://openworks.mdanderson.org/sumexp22/1101/thumbnail.jp