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Business Training, Volume 1, Number 5, August 1914
Newsletter of the Rhode Island Commercial School (RICS) owned by Henry Jacobs. In 1916 RICS merged with Bryant & Stratton when Jacobs bought Bryant. Photos of teachers Gertrude Johnson and Mary Wales appear on page 5. Johnson and Wales left RICS to form Johnson & Wales (now Johnson & Wales University) in 1914
Two mod-p Johnson filtrations
We consider two mod-p central series of the free group given by Stallings and
Zassenhaus. Applying these series to definitions of Dennis Johnson's filtration
of the mapping class group we obtain two mod-p Johnson filtrations. Further, we
adapt the definition of the Johnson homomorphisms to obtain mod-p Johnson
homomorphisms.
We calculate the image of the first of these homomorphisms. We give
generators for the kernels of these homomorphisms as well. We restrict the
range of our mod-p Johnson homomorphisms using work of Morita. We finally prove
the announced result of Perron that a rational homology 3-sphere may be given
as a Heegaard splitting with gluing map coming from certain members of our
mod-p Johnson filtrations.Comment: 35 pages, 1 figure; added referenc
Alternative versions of the Johnson homomorphisms and the LMO functor
Let be a compact connected oriented surface with one boundary
component and let denote the mapping class group of . By
considering the action of on the fundamental group of it
is possible to define different filtrations of together with some
homomorphisms on each term of the filtration. The aim of this paper is twofold.
Firstly we study a filtration of introduced recently by Habiro
and Massuyeau, whose definition involves a handlebody bounded by . We
shall call it the "alternative Johnson filtration", and the corresponding
homomorphisms are referred to as "alternative Johnson homomorphisms". We
provide a comparison between the alternative Johnson filtration and two
previously known filtrations: the original Johnson filtration and the
Johnson-Levine filtration. Secondly, we study the relationship between the
alternative Johnson homomorphisms and the functorial extension of the
Le-Murakami-Ohtsuki invariant of -manifolds. We prove that these
homomorphisms can be read in the tree reduction of the LMO functor. In
particular, this provides a new reading grid for the tree reduction of the LMO
functor.Comment: 62 pages, several figures. v_2 minor change
Progress in Time-Dependent Density-Functional Theory
The classic density-functional theory (DFT) formalism introduced by
Hohenberg, Kohn, and Sham in the mid-1960s, is based upon the idea that the
complicated N-electron wavefunction can be replaced with the mathematically
simpler 1-electron charge density in electronic struc- ture calculations of the
ground stationary state. As such, ordinary DFT is neither able to treat
time-dependent (TD) problems nor describe excited electronic states. In 1984,
Runge and Gross proved a theorem making TD-DFT formally exact. Information
about electronic excited states may be obtained from this theory through the
linear response (LR) theory formalism. Begin- ning in the mid-1990s, LR-TD-DFT
became increasingly popular for calculating absorption and other spectra of
medium- and large-sized molecules. Its ease of use and relatively good accuracy
has now brought LR-TD-DFT to the forefront for this type of application. As the
number and the diversity of applications of TD-DFT has grown, so too has grown
our understanding of the strengths and weaknesses of the approximate
functionals commonly used for TD-DFT. The objective of this article is to
continue where a previous review of TD-DFT in this series [Annu. Rev. Phys.
Chem. 55: 427 (2004)] left off and highlight some of the problems and solutions
from the point of view of applied physical chemistry. Since doubly-excited
states have a particularly important role to play in bond dissociation and
formation in both thermal and photochemistry, particular emphasis will be
placed upon the problem of going beyond or around the TD-DFT adiabatic
approximation which limits TD-DFT calculations to nominally singly-excited
states. Posted with permission from the Annual Review of Physical Chemistry,
Volume 63 \c{opyright} 2012 by Annual Reviews, http://www.annualreviews.org
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Hypernetworks for reconstructing the dynamics of multilevel systems
Networks are fundamental for reconstructing the dynamics of many systems, but have the drawback that they are restricted to binary relations. Hypergraphs extend relational structure to multi-vertex edges, but are essentially set-theoretic and unable to represent essential structural properties. Hypernetworks are a natural multidimensional generalisation of networks, representing n-ary relations by simplices with n vertices. The assembly of vertices to make simplices is key for moving between levels in multilevel systems, and integrating dynamics between levels. It is argued that hypernetworks are necessary, if not sufficient, for reconstructing the dynamics of multilevel complex systems
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