On the Margulis constant for Kleinian groups, I curvature

The Margulis constant for Kleinian groups is the smallest constant $c$ such that for each discrete group $G$ and each point $x$ in the upper half space ${\bold H}^3$, the group generated by the elements in $G$ which move $x$ less than distance c is elementary. We take a first step towards determining this constant by proving that if $\langle f,g \rangle$ is nonelementary and discrete with $f$ parabolic or elliptic of order $n \geq 3$, then every point $x$ in ${\bold H}^3$ is moved at least distance $c$ by $f$ or $g$ where $c=.1829\ldots$. This bound is sharp

Apparatus for purging systems handling toxic, corrosive, noxious and other fluids Patent

Fluid transferring system design for purging toxic, corrosive, or noxious fluids and fumes from materials handling equipment for cleansing and accident preventio

The Fatou Theorem for Functions Harmonic in a Half‐Space

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135177/1/plms0149.pd

Coping as a Mediator between Symptom Burden and Distress in Lung Cancer Patients

Lung cancer is considered the leading cause of cancer death worldwide. An estimated 224,390 new cases of lung cancer are expected to be diagnosed and 158,080 Americans are expected to die from lung cancer in 2016 (National Institutes of Health, 2016; Siegel, Miller, & Jemal, 2016). Lung cancer patients also report the highest levels of psychological distress and symptom burden than any other forms of cancer (Linden, Vodermaier, MacKenzie, & Greig, 2012). Given the prevalence and impact of lung cancer, it is imperative to address the emotional toll this diagnosis can have on those suffering with the disease to develop helpful strategies for those coping with lung cancer. The goal of this study is to determine how much lung cancer patients’ symptom burden affects their level of distress, and how much of this effect is mediated by approach and/or avoidance coping styles. Adults (N = 109, 57% female,) with an average age of 67 (SD = 10.1) diagnosed with lung cancer completed a questionnaire assessing for physical and psychological functioning at two medical centers in Southern California. Results: There was a significant positive relationship between total symptom burden and distress. Avoidance coping was a significant mediator of the relationship between total symptom burden and distress. Approach coping was not a significant mediator of this relationship. Conclusions: Results suggest that a patient experiences more distress as his/her symptom burden increases, and this effect is partially explained by engaging in avoidant coping. Therefore, it is important to find ways to help patients cope more effectively to reduce their levels of stress. The findings of this study show the importance of continued research to find effective coping strategies and as well to inhibit patients from engaging in an avoidant coping style