Morse theory of harmonic forms

We consider the problem of whether it is possible to improve the Novikov inequalities for closed 1-forms, or any other inequalities of a similar nature, if we assume, additionally, that the given 1-form is harmonic with respect to some Riemannian metric. We show that, under suitable assumptions, it is impossible. We use, in an essential way, a theorem of E.Calabi characterizing 1-forms which are harmonic with respect to some metric. We also study some interesting examples illustrating our results.Comment: 16 pages, AMSTex, 12 figure

A Study of the Effects on Sigma D and Resolved Lines as a Function of Spatial Multi-Superposition of Images

In photography the fidelity of the image is often degraded due to the random graininess associated with photographic emulsions. A study was performed to obtain objective and subjective data on the effects of granularity and graininess as a function of the number of spatially superpositioned images. A target was designed and built.* Individual negatives were made utilizing copy equipment with a vacuum back to ensure precise registration during exposure. These individual negatives were then imaged onto 16mm film utilizing standard motion picture equipment and a vacuum platen which was designed and built to ensure precise registration of individual negatives during the motion picture exposure. This study showed a significant enhancement of Images brought about by a technique which might be made practical on a routine basis

Swearing down the Law – A Debate

The following debate between Jérôme Bourgon and Paul R. Katz treats one of the most important issues in the study of Chinese social history in general and Chinese legal culture in particular, namely the striking similarities, or correspondences, between litigation and judicial rituals performed to resolve disputes or even deal with plaints filed by the dead

Swearing down the Law – A Debate (continued)

PK: The key difference in our views lies in the way we define the term “continuum”. This can be seen in the following two statements: a) “The term continuum causes us to believe that there is something like a continuity between earthly and underworld justice, or at least that both were included in a coherent framework”; b) “Continuum leads one to expect not mere coexistence but a real coherence or a continuous sequence in which adjacent elements are not perceptibly different from each other, although the extremes are quite distinct”. If I understand you correctly, you seem to be arguing in favour of identity transcending differentiation, while I am stressing continuity amidst difference. I think my definition better reflects the term’s etymology, including the Latincontinuus. The Latin term can mean both “continuous and uninterrupted” and “following one after another, successive, continuous”, including days, consulships, battles, itineraries, labours. In my book, I use the term to describe a continuous spectrum of judicial beliefs and practices, linked by the overarching “ideology of justice” but differing in time, agent, and intent. To me, the fact that the adjective describes very different consulships, battles, itineraries, and even days as successively linked (continuous) would seem to support my usage

Service utilisation and family support of people with dementia: a cohort study in England.

Objectives This study aimed to compare costs of caring for people with dementia in domiciliary and residential settings, central England. Methods A cohort of people with dementia was recruited during a hospital stay 2008–2010. Data were collected by interview at baseline, and 6- and 12-month follow-up, covering living situation (own home with or without co-resident carer, care home); cognition, health status and functioning of person with dementia; carer stress; utilisation of health and social services; and informal (unpaid) caring input. Costs of formal services and informal caring (replacement cost method) were calculated. Costs of residential and domiciliary care packages were compared. Results Data for 109 people with dementia were collected at baseline; 95 (87.2%) entered hospital from their own homes. By 12 months, 40 (36.7%) had died and 85% of the survivors were living in care homes. Over one-half of people with dementia reported social care packages at baseline; those living alone had larger packages than those living with others. Median caring time for co-resident carers was 400 min/day and 10 h/week for non co-resident carers. Residential care was more costly than domiciliary social care for most people. When the value of informal caring was included, the total cost of domiciliary care was higher than residential care, but not significantly so. Carer stress reduced significantly after the person with dementia entered a care home. Conclusions Caring for people with dementia at home may be more expensive, and more stressful for carers, than care in residential settings

Effects of Aerobic Exercise Training in Community-Based Subjects Aged 80 and Older: A Pilot Study

To assess the ability of sedentary, frail subjects aged 80 and older to train in a community-based exercise program and to evaluate clinical factors that predict improvements in peak oxygen consumption (VO 2 peak). DESIGN: Pretest, posttest. SETTING: Charlestown Retirement Community, Catonsville, Maryland PARTICIPANTS: Twenty-two (11 male, 11 female; mean age ± standard deviation = 84 ± 4.0, range 80–92) self-referred. INTERVENTION: Six months of moderate-intensity aerobic exercise training, two to three sessions/week, 20 to 30 minutes per session. Training modes included treadmill walking and/or stationary cycling. MEASUREMENTS: Baseline and follow-up maximal exercise treadmill tests (ETTs) with electrocardiogram monitoring and respiratory gas analysis. RESULTS: Six months of aerobic exercise training resulted in significant increases (mean ± standard deviation) in ETT duration (11.9 ± 3.3 vs 15.9 ± 4.3 minutes; P = .01), VO 2 peak (1.23 ± 0.37 vs 1.31 ± 0.36 L/min; P = .04), and oxygen pulse (9.3 ± 2.8 vs 10.1 ± 3.2; P = .03). Mean heart rate was significantly lower during submaximal ETT stages 1 through 4 ( P < .05), and resting systolic blood pressure decreased (146 ± 18 vs 133 ± 14 mmHg; P = .01) after training. Multiple regression analysis indicated that baseline VO 2 peak ( r = 0.75, P = .002) and the total amount of time spent in exercise training ( r = 0.55, P = .008) were independent predictors of the training-related improvements in VO 2 peak. CONCLUSION: Subjects aged 80 and older can increase aerobic capacity and reduce systolic blood pressure in a community-based exercise program of moderate intensity. The most important predictors of change in VO 2 peak were baseline VO 2 peak and the time spent in exercise training. Subjects with a lower baseline VO 2 peak had the greatest improvements in VO 2 peak after training.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65501/1/j.1532-5415.2002.50613.x.pd

A Transdisciplinary Collaboration and Innovation Education Model and Experience

As the interconnectedness of the world grows, the need to prepare college students capable of addressing complexity likewise grows. In this context, the University of Dayton has developed and tested a transdisciplinary model for education. This model links multiple classes from different disciplines via a common theme and within a common space. It also employs an educational model premised on the following trajectory: disciplinary content development / transdisciplinary observation (empathy); transdisciplinary disruption leading to “A-Ha” observations which transform the disciplinary directions; and lastly transdisciplinary informed design and research. Central to this model is a 3,500 square foot common space used only by the classes participating in the experience. In this space classes share their reflections and content with other classes via both personal linkages and analog communications. The other classes respond to these from their disciplinary and personal perspectives. Thirteen classes, fourteen faculty, and over three-hundred students participated in a themed experience centered on the addiction crisis in Dayton, Ohio. Participants included faculty in applied creativity, engineering, health and sport science, education, theater, and religious studies. Also serving as co-teacher were community stakeholders. Assessment of the experience revealed variable student takeaways. Most prominent among these was student recognition that the experience had expanded their perspectives of the other disciplines. Most suggested that it had improved their ability to collaborate in a transdisciplinary environment and that it had significantly impacted their career aspirations. Fewer acknowledged the experience had improved their ability to create