A Caputo Boundary Value Problem in Nabla Fractional Calculus

Boundary value problems have long been of interest in the continuous differential equations context. However, with the advent of new areas like Nabla Fractional Calculus, we may consider such problems in new contexts. In this work, we will consider several right focal boundary value problems, involving a Caputo fractional difference operator, in the Nabla Fractional Calculus context. Properties of the Green\u27s functions for each of these boundary value problems will be investigated and, in the case of a particular boundary value problem, used to establish the existence of positive solutions to a nonlinear version of the boundary value problem. Adviser: Allan C. Peterso

734-4 Can Intracoronary Ultrasound Improve PTCA Results?: Preliminary Core Lab Ultrasound Analysis from the CLOUT Pilot Study

The CLOUT Pilot Study hypothesis is that intracoronary ultrasound (ICUS) guidance can maximize the potential of balloon angioplasty through the safe application of carefully chosen oversized balloons. PTCA was performed until success was obtained using standard angiographic criteria. ICUS was then performed and, based on the degree of reference segment disease, balloons were upsized from 0.25 to 0.75mm (mean 0.4mm) regardless of the angiographic results. There have been no complications using this strategy in the initial 14 of a planned 100 patients. ICUS measures were performed using semiautomated programs at a core laboratory.ResultsIn the reference segment, ICUS revealed a mean lumen diameter of 2.60±0.35mm and plaque thickness of 0.78±0.11mm; on average 54.75±11.05% of the reference vessel was occupied by atheroma. At initial ICUS evaluation after angiographically successful PTCA, the lesion had a minimal lumen diameter (MLD) of 1.78±0.22mm and lumen area of 3.14±0.88mm2. Following balloon upsizing, the lesion MLD increased to 1.95±0.15mm (8.7% gain, p<0.02) and lumen area to 3.76±0.63mm2(16.7% gain, p<0.01). When compared to the reference segment lumen area, the lesional %lumen area reduction improved from 38.14±16.74% to 25.91±12.17% (p<0.01). Lumen improvement occurred primarily by expansion of the total vessel area (12.08±3.01mm2to 12.51±3.11 mm2, p=ns). As expected, there was a large degree of residual atheroma (68.62±7.47% cross sectional narrowing). After routine PTCA, only 5 of 12 patients reached a target MLD of 75% of the reference lumen diameter. Following balloon upsizing, 8 of 12 had reached this criteria.ConclusionsICUS guided balloon upsizing based on the degree of reference segment disease may be safely performed and results in significant improvement in luminal cross sectional area above that achieved by angiographic guidance alone. This may potentially lower restenosis rates if these initial gains are sustained long term

Characterizing Mathematics Graduate Student Teaching Assistants’ Opportunities to Learn from Teaching

Exemplary models to inform novice instruction and the development of graduate teaching assistants (TAs) exist. What is missing from the literature is the process of how graduate students in model professional development programs make sense of and enact the experiences offered. A first step to understanding TAs’ learning to teach is to characterize how and whether they link observations of student work to hypotheses about student thinking and then connect those hypotheses to future teaching actions. A reason to be interested in these connections is that their strength and coherence determine how well TAs can learn from experiences. We found TAs can connect observations and future teaching, but that the connections vary in quality. Our analysis suggests future revisions to TA development programs, which we discuss in the conclusion

Port-access coronary artery bypass grafting: A proposed surgical method

AbstractMinimally invasive surgical methods have been developed to provide patients the benefits of open operations with decreased pain and suffering. We have developed a system that allows the performance of cardiopulmonary bypass and myocardial protection with cardioplegic arrest without sternotomy or thoracotomy. In a canine model, we successfully used this system to anastomose the internal thoracic artery to the left anterior descending coronary artery in nine of 10 animals. The left internal thoracic artery was dissected from the chest wall, and the pericardium was opened with the use of thoracoscopic techniques and single lung ventilation. The heart was arrested with a cold blood cardioplegic solution delivered through the central lumen of a balloon occlusion catheter (Endoaortic Clamp; Heartport, Inc., Redwood City, Calif.) in the ascending aorta, and cardiopulmonary bypass was maintained with femorofemoral bypass. An operating microscope modified to allow introduction of the 3.5× magnification objective into the chest was positioned through a 10 mm port over the site of the anastomosis. The anastomosis was performed with modified surgical instruments introduced through additional 5 mm ports. In the cadaver model (n = 7) the internal thoracic artery was harvested and the pericardium opened by means of similar techniques. A precise arteriotomy was made with microvascular thoracoscopic instruments under the modified microscope on four cadavers. In three other cadavers we assessed the exposure provided by a small anterior incision (4 to 6 cm) over the fourth intercostal space. This anterior port can assist in dissection of the distal internal thoracic artery and provides direct access to the left anterior descending, circumflex, and posterior descending arteries. We have demonstrated the potential feasibility of grafting the internal thoracic artery to coronary arteries with the heart arrested and protected, without a major thoracotomy or sternotomy. (J THORAC CARDIOVASC SURG 1996;111:567-73

Personal Papers (MS 80-0002)

Card with letter from Charles E. St. Goar to Isaac Herbert Kempner regarding the hurricanes in Galveston that he read in the paper. So, he's writing to check if they're okay since news has exaggerated about it