Continuity properties of vectors realizing points in the classical field of values

For an $n$-by-$n$ matrix $A$, let $f_A$ be its "field of values generating function" defined as $f_A\colon x\mapsto x^*Ax$. We consider two natural versions of the continuity, which we call strong and weak, of $f_A^{-1}$ (which is of course multi-valued) on the field of values $F(A)$. The strong continuity holds, in particular, on the interior of $F(A)$, and at such points $z \in \partial F(A)$ which are either corner points, belong to the relative interior of flat portions of $\partial F(A)$, or whose preimage under $f_A$ is contained in a one-dimensional set. Consequently, $f_A^{-1}$ is continuous in this sense on the whole $F(A)$ for all normal, 2-by-2, and unitarily irreducible 3-by-3 matrices. Nevertheless, we show by example that the strong continuity of $f_A^{-1}$ fails at certain points of $\partial F(A)$ for some (unitarily reducible) 3-by-3 and (unitarily irreducible) 4-by-4 matrices. The weak continuity, in its turn, fails for some unitarily reducible 4-by-4 and untiarily irreducible 6-by-6 matrices.Comment: 9 pages, 2 figures. Linear and Multilinear Algebra 201

Intro to Primary Sources

The Identifying Primary Sources tutorial teaches students how they find, evaluate, and use primary sources in their own research. Along the way, they\u27ll learn about some great places to start researching when looking for primary sources.https://digitalcommons.usu.edu/elearning_all/1052/thumbnail.jp

The physiological stress response to anaerobic exercise is altered following sodium bicarbonate supplementation

Sodium bicarbonate (NaHCO3) is a nutritional aid that is proposed to enhance performance by reducing the state of exercise induced acidosis, however research is currently equivocal. Despite this, most research still focuses on its effects upon performance, and not whether the reduced acidosis impacts upon any other factors related to exercise. There is some research to suggest that such a reduction in [H+] can attenuate a number of physiological stress pathways such as stress hormones (1, 4), heat shock protein 72 (HSP72) and oxidative stress (3), suggesting a potential role in exercise recovery. However there are some limitations with this previous research as work intensities were not controlled for, hence making comparisons between treatments difficult. Also limited markers of stress were measured despite the physiological stress response being multi-faceted. The aim of this study was to examine whether the ingestion of NaHCO3 would influence the expression of several markers of stress measured simultaneously, following a work controlled anaerobic exercise

Flexible Ultrasound Transducer Fixture

Final report and team photo for Project 21 of ME450, Fall 2010 semester.This project involves developing an automated ultrasound transducer positioning system for blood flow monitoring that does not disrupt patient care, minimizes measurement variability and is operator independent.William Weitzel (Nephrology, U of M); Grant Kruger (Mechanical Engineering, U of M)http://deepblue.lib.umich.edu/bitstream/2027.42/86248/1/ME450 Fall2010 Final Report - Project 21 - Flexible Ultrasound Transducer Fixture.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/86248/2/ME450 Fall2010 Team Photo - Project 21 - Flexible Ultrasound Transducer Fixture.jp

Moyo Vol. VII N 2

Durica, Paul. Editor\u27s Letter . 4. Spears, Amy L. As If Lipstick Was A Sign of My Declining Mind (How ChickRock Happened) . 5. Frey, Randall. Portrait of the Cartoonist as a Young Man . 6. Clements, Nina. Grease Me Up: One Woman\u27s Descent into the Depths of Pittsburgh Dinner Culture . 7. Levine, Robert. Under the Needle\u27s Point (The Healing Power of Acupuncture) . 8. Durica, Paul. The Glory that was/is Greek: Denison Three Years After the Decision . 12. Lamont, Jean. Smokin\u27 Joe Lights Up . 13. Durica, Paul. Ode on a Second Grecian Turn: An Interview with President Michele T. Myers . 14. Fisher, Dan. Lenane on the Social Scene . 19. Combe, Kirk. Intellectual Bio-Diversity: A Faculty Perspective on the Greek Residential Issue . 20. Williams, Adam. Elephants on the Floor Above and Brats in the Basement: Life on the North Quad . 22. Pfleeger, Jon. New Kid on the Block (Sigma Phi Epsilon\u27s President Speaks) . 23. Werne, Kirsten. Coffee Talk at the Bandersnatch (An Interview with Kevin Clay and Adam) . 29