This report presents a condensed summary on foundations of gauge theory and its application to mecanics. In particular, we will see how the involved mathematical concepts allow to describe the reorientation of a free falling cat in a coordinate free (and nearly calculation free) manner.

What a study of the historical development of mathematical concepts can offer teaching is still being debated. This study examines use of a combination of the historical development of number systems and modelling, with concrete materials as a way of deepening students’ understanding of positional notation. It looks at place value in different number bases as a way of enhancing students’ unders...

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran's index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran's...

This first chapter is mostly informal. The rest of this book has no dependency on this chapter, save the definitions in §7 concerning asymptotic notations. Hence a light reading may be sufficient. We recommend re-reading this chapter after finishing the rest of the book, when many of the remarks here may take on more concrete meaning. An appendix collects useful mathematical concepts that are u...

In this paper, I show that, by gathering evidence from the past literature and by presenting new evidence, subjects can undergo scrambling in Japanese, contrary to Saito’s (1985) Ban on Scrambling of Subject (BOSS), which has been a classic and wide-spread claim. In so doing, I argue that Japanese scrambling in general is subject to a version of minimality/superiority effect, a Feature-based Mi...

In this report, nine patients with insulinoma who were operated on between 19H5 and I <J<J3 at the Shohada Medical Center affiliated to the Shahid Beheshti University of Medical Sciences in Tehran are presented. There were three males and six females (male to female ratio I :2) and the patients' age ranged from 23 to 60 years old (mean age 37.6 years old). Duration of symptoms was from thr...

Meniscal root tears are defined as radial tears located within 1 cm from the meniscal attachment or a bony rootavulsion. This injury is biomechanically comparable to a total meniscectomy, leading to compromised hoop stressesresulting in decreased tibiofemoral contact area and increased contact pressures in the involved compartment.These changes are detrimental to the articular cartilage and ult...