On the Kashiwara-Vergne conjecture

Let $G$ be a connected Lie group, with Lie algebra $g$. In 1977, Duflo constructed a homomorphism of $g$-modules $Duf: S(g) -> U(g)$, which restricts to an algebra isomorphism on invariants. Kashiwara and Vergne (1978) proposed a conjecture on the Campbell-Hausdorff series, which (among other things) extends the Duflo theorem to germs of bi-invariant distributions on the Lie group $G$. The main results of the present paper are as follows. (1) Using a recent result of Torossian (2002), we establish the Kashiwara-Vergne conjecture for any Lie group $G$. (2) We give a reformulation of the Kashiwara-Vergne property in terms of Lie algebra cohomology. As a direct corollary, one obtains the algebra isomorphism $H(g,S(g)) -> H(g,U(g))$, as well as a more general statement for distributions.Comment: 18 pages, final version, to be published in Inventiones Mat

G. Campbell Morgan, the preacher

https://place.asburyseminary.edu/ecommonsatsdissertations/2126/thumbnail.jp

Fifth annual conference on Alaskan placer mining

An abridged format of papers, presentations and addresses given during the 1983 conference held on March 30-31, 1983 compiled and edited by Bruce W. Campbell, Jim Madonna, and M. Susan Husted.Partial funding was provided by the Carl G. Parker Memorial Publishing Fund, University of Alaska, Fairbanks, and the Mining and Mineral Resources Research Institute, U.S. Department of the Interior, Bureau of Mines

Stress-induced modulation of endocannabinoid signaling leads to delayed strengthening of synaptic connectivity in the amygdala

none11siopenYasmin, F.; Colangeli, R.; Morena, M.; Filipski, S.; van der Stelt, M.; Pittman, Q.J.; Hillard, C.J.; Campbell Teskey, G.; McEwen, B.S.; Hill, M.N.; Chattarji, S.Yasmin, F.; Colangeli, R.; Morena, M.; Filipski, S.; van der Stelt, M.; Pittman, Q. J.; Hillard, C. J.; Campbell Teskey, G.; Mcewen, B. S.; Hill, M. N.; Chattarji, S

Some Heuristics and Results for Small Cycles of the Discrete Logarithm

Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditions on g and h. In this paper we extend these heuristics and prove results for some of them, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results.Comment: 32 pages; to appear in Mathematics of Computation; revisions as suggested by referees, including notation and minor improvement

Moser, John G. (SC 2728)

Finding aid only for Manuscripts Small Collection 2728. Paper titled “A History of Fort Campbell, Kentucky, 1941-1951” in which John G. Moser examines “events of major importance” that occurred at Fort Campbell during that ten years

Surveys of Scottish farmers and their vertebrate pests – case study from a long running dataset

Hartley, G., Campbell, S

Energy-momentum balance in quantum dielectrics

We calculate the energy-momentum balance in quantum dielectrics such as Bose-Einstein condensates. In agreement with the experiment [G. K. Campbell et al. Phys. Rev. Lett. 94, 170403 (2005)] variations of the Minkowski momentum are imprinted onto the phase, whereas the Abraham tensor drives the flow of the dielectric. Our analysis indicates that the Abraham-Minkowski controversy has its root in the Roentgen interaction of the electromagnetic field in dielectric media

A constructive algorithm for the Cartan decomposition of SU(2^N)

We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G of SU(2^N) in terms of its `Cartan' and `non-Cartan' components. This effectively factors G in terms of group elements that belong in SU(2^n) with n<N, a procedure that can be iterated down to n=2. We show that every step reduces to solving the zeros of a matrix polynomial, obtained by truncation of the Baker-Campbell-Hausdorff formula, numerically. All computational tasks involved are straightforward and the overall truncation errors are well under control.Comment: 15 pages, no figures, matlab file at http://cam.qubit.org/users/jiannis