Morse-Bott functions on orthogonal groups

We make a detailed study of various (quadratic and linear) Morse-Bott trace functions on the orthogonal groups $O(n)$. We describe the critical loci of the quadratic trace function Tr$(AXBX^T)$ and determine their indices via perfect fillings of tables associated with the multiplicities of the eigenvalues of $A$ and $B$. We give a simplified treatment of T. Frankel's analysis of the linear trace function on $SO(n)$, as well as a combinatorial explanation of the relationship between the mod $2$ Betti numbers of $SO(n)$ and those of the Grassmannians $\mathbb{G}(2k,n)$ obtained from this analysis. We review the basic notions of Morse-Bott cohomology in a simple case where the set of critical points has two connected components. We then use these results to give a new Morse-theoretic computation of the mod $2$ Betti numbers of $SO(n)$.Comment: 28 page

Book Review: Democracy, Schooling and Political Education

This paper reviews the book Democracy, Schooling and Political Education, written by Colin Wringe (published in 2012 by Routledge, first ed. in 1984, 126 p.). Although, the book was written in the last quarter of the 20th century towards the end of the cold war period, it is highly up-to-date in terms of the topic it covers. Wringe’s work addresses the teachers and other professionals in education, and also all who are interested in relationship between education and democracy, without a strong background in the field

Two pioneers of modem economic thought in Japan and the Ottoman Empire : Fukuzawa Yukichi and Ahmet Mithat

Istambul, 1996年10月7日-11

Communications of the median nerve in foetuses

Background: Communications between the median, ulnar and musculocutaneous nerves in the arm, forearm and hand were reported in adult cadaveric and electrophysiological studies. These communicant branches may lead conflicting clinical and electrodiagnostic outcomes. While there are many studies on adult patients or cadavers, there is poor regarding foetuses. The present study was conducted to examine the frequencies of these communications and their coexistences in human foetuses.Materials and methods: Anterior aspect of the forearms of 50 foetuses (29 females, 20 males, and 1 unknown) were dissected bilaterally (totally 100 sides) for this purpose.Results: Communications between the median and the musculocutaneous nerves in the arm were found unilaterally in 4%. Communications from the median to the ulnar nerve in the forearm were encountered unilaterally in 22%, and bilaterally in 12%; from the ulnar to the median nerve in the hand unilaterally in 28%, and bilaterally in 12%. Coexistence of all these variations was not encountered in any foetus. But coexistence of two different types of communicant branch was encountered in 4%.Conclusions: Precise knowledge of nerve communications, variations and rate of coexistences in foetuses may have significance for clinicians and researchers dealing with subjects in foetal period

The Case for Improving the Robinson Formulas

Auroral particle precipitation is the main source of ionization on the nightside, making it a critical factor in geospace physics. This magnetosphere‐ionosphere linkage directly contributes to, even controls, the nonlinear feedback within this coupled system. One study has dominated our understanding of this connection, presenting a pair of equations relating auroral particle precipitation to ionospheric Pedersen and Hall conductance, the famous Robinson formulas. This Commentary examines the history of the development and usage of the Robinson formulas and the recent studies exploring corrections and expansions to it. The conclusion is that more work needs to be done; the space physics research community should take up the task to develop improvements and enhancements to better quantify the connection of auroral precipitation to ionospheric conductance.Key PointsThe development and usage of the famous Robinson formulas, relating auroral precipitation to ionospheric conductance, is recountedRecent approaches to address shortcomings of these formulas are reviewed and discussed, noting shortcomings in some of these studiesThe space physics research community is urged to take on the action of improving the connection between precipitation and conductancePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163473/2/jgra56025.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163473/1/jgra56025_am.pd

Traumatic abdominal wall hernias: disruptions of the abdominal wall muscles associated to pelvic bone fractures illustrated by two case reports.

Blunt abdominal traumas are often associated with intra-abdominal injuries and pelvic fractures. Traumatic abdominal wall hernias due to disruption of the abdominal wall muscles may be overlooked. Delayed diagnosis can lead to hernia related complications. We present two cases of high kinetic trauma with pelvic fractures and acute traumatic abdominal wall herniation. Both of these cases suffered from a delayed diagnosis and needed surgery to treat the symptomatic herniation. Clinical reassessment and appropriate medical imaging are mandatory in patients with high kinetic abdominal blunt traumas and associated pelvic fracture, in order to prevent delayed diagnosis and possible complications

Brieskorn manifolds as contact branched covers of spheres

We show that Brieskorn manifolds with their standard contact structures are contact branched coverings of spheres. This covering maps a contact open book decomposition of the Brieskorn manifold onto a Milnor open book of the sphere.Comment: 8 pages, 1 figur

Trajectories of charged particles trapped in Earth's magnetic field

I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and present particle trajectories in a dipolar field. I provide twelve computational exercises that can be used as classroom assignments or for self-study. Two of the exercises, drift-shell bifurcation and Speiser orbits, are adapted from active magnetospheric research. The Python code provided in the supplement can be used to replicate the trajectories and can be easily extended for different field geometries.Comment: 10 pages, 7 figures. Submitted to American Journal of Physic