20,940 research outputs found
Introduction to Categories and Categorical Logic
The aim of these notes is to provide a succinct, accessible introduction to
some of the basic ideas of category theory and categorical logic. The notes are
based on a lecture course given at Oxford over the past few years. They contain
numerous exercises, and hopefully will prove useful for self-study by those
seeking a first introduction to the subject, with fairly minimal prerequisites.
The coverage is by no means comprehensive, but should provide a good basis for
further study; a guide to further reading is included. The main prerequisite is
a basic familiarity with the elements of discrete mathematics: sets, relations
and functions. An Appendix contains a summary of what we will need, and it may
be useful to review this first. In addition, some prior exposure to abstract
algebra - vector spaces and linear maps, or groups and group homomorphisms -
would be helpful.Comment: 96 page
A study of the writing strategies of renowned conservationists: Implications for place-based education in Turkey
Cataloged from PDF version of article.In today’s world, many young people are disconnected from the natural world. One way to
promote constructive engagements with nature has been for learning to take place in local environments, including
school grounds, neighborhoods, and community parks. This process, often called place-based education, utilizes many
field study techniques including nature journaling. Keeping a journal helps students observe their local environments
more in-depth by identifying relationships among living and non-living things and building an appreciation about and
for one’s “place.” Providing students with models and guidelines can help them keep a meaningful and useful journal.
To identify some best practices for keeping a journal, this study compared writing strategies employed by famous
conservationists from the recent history of two different countries. While the writings of Aldo Leopold—the
conservationist from the United States—have been used for many years to promote a “Land Ethic,” Hikmet Birand’s
work—the conservationist from Turkey—has yet to be used to its full potential for environmental education. Through a
content analysis, a framework of five writing themes was created to showcase the attributes and writing intentions of
these scientists. The article concludes with recommendations for using the framework to help promote place-based
nature journaling into the Turkish national curriculum
Ultracold, radiative charge transfer in hybrid Yb ion - Rb atom traps
Ultracold hybrid ion-atom traps offer the possibility of microscopic
manipulation of quantum coherences in the gas using the ion as a probe.
However, inelastic processes, particularly charge transfer can be a significant
process of ion loss and has been measured experimentally for the Yb ion
immersed in a Rb vapour. We use first-principles quantum chemistry codes to
obtain the potential energy curves and dipole moments for the lowest-lying
energy states of this complex. Calculations for the radiative decay processes
cross sections and rate coefficients are presented for the total decay
processes. Comparing the semi-classical Langevin approximation with the quantum
approach, we find it provides a very good estimate of the background at higher
energies. The results demonstrate that radiative decay mechanisms are important
over the energy and temperature region considered. In fact, the Langevin
process of ion-atom collisions dominates cold ion-atom collisions. For spin
dependent processes \cite{kohl13} the anisotropic magnetic dipole-dipole
interaction and the second-order spin-orbit coupling can play important roles,
inducing couplingbetween the spin and the orbital motion. They measured the
spin-relaxing collision rate to be approximately 5 orders of magnitude higher
than the charge-exchange collision rate \cite{kohl13}. Regarding the measured
radiative charge transfer collision rate, we find that our calculation is in
very good agreement with experiment and with previous calculations.
Nonetheless, we find no broad resonances features that might underly a strong
isotope effect. In conclusion, we find, in agreement with previous theory that
the isotope anomaly observed in experiment remains an open question.Comment: 7 figures, 1 table accepted for publication in J. Phys. B: At. Mol.
Opt. Phys. arXiv admin note: text overlap with arXiv:1107.114
Direct radiative capture of p-wave neutrons
The neutron direct radiative capture (DRC) process is investigated,
highlighting the role of incident p-wave neutrons. A set of calculations is
shown for the 12-C(n,gamma) process at incoming neutron energies up to 500 keV,
a crucial region for astrophysics. The cross section for neutron capture
leading to loosely bound s, p and d orbits of 13-C is well reproduced by the
DRC model demonstrating the feasibility of using this reaction channel to study
the properties of nuclear wave functions on and outside the nuclear surface. A
sensitivity analysis of the results on the neutron-nucleus interaction is
performed for incident s- as well as p-waves. It turned out that the DRC cross
section for p-wave neutrons is insensitive to this interaction, contrary to the
case of incident s-wave neutrons.
PACS number(s): 25.40Lw,21.10Gv,23.40.HcComment: 16 pages, REVTeX file, PostScript file, .dvi fil
The application of total positivity to computer aided curve and surface design
technical reportOf particular importance in an interactive curve and surface design system is the interface to the user. The mathematical model employed in the system must be sufficiently flexible for interaction between designer and machine to converge to a satisfactory result. The mathematical theory of Total Positivity is combined with the interactive techniques of Bezier and Riesenfeld in developing new methods of shape representation which retain the valuable variation-diminishing and convex hull properties of Bernstein and B-spline approximation, while providing improvements in the interactive interface to the user. Specifically, extending the Bezier notion of using a polygon to describe a smooth curve, methods of assigning a weight to each vertex which will control the amount of local fit to the polygon or polygonal net are provided. Thus, the designer can cause "cusps" and "flats" easily by manipulating the "tension" at each vertex. Further, the generalization from curves to surfaces can be done with rectilinear data or triangular data. Illustrations are provided from an experimental implementation of the newly constructed models as a demonstration of their feasibility and utility in computer aided curve and surface design
Buckling of built-up columns of pultruded fiber-reinforced polymer C-sections
This paper presents the test results of an experimental investigation to evaluate the buckling behavior of built-up columns of pultruded profiles, subjected to axial compression. Specimens are assembled by using four (off the shelf) channel shaped profiles of E-glass fiber-reinforced polymer (FRP), having similar detailing to strut members in a large FRP structure that was executed in 2009 to start the restoration of the Santa Maria Paganica church in L’Aquila, Italy. This church had partially collapsed walls and no roof after the April 6, 2009, earthquake of 6.3 magnitude. A total of six columns are characterized with two different configurations for the bolted connections joining the channel sections into a built-up strut. Test results are discussed and a comparison is made with closed-form equation predictions for flexural buckling resistance, with buckling resistance values established from both eigenvalue and geometric nonlinear finite element analyses. Results show that there is a significant role played by the end loading condition, the composite action, and imperfections. Simple closed-form equations overestimate the flexural buckling strength, whereas the resistance provided by the nonlinear analysis provides a reasonably reliable numerical approach to establishing the actual buckling behavior
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