Julia Lawrence to Susan Ursin Niemcewicz, December 24, 1819

Julia Lawrence wrote from Jamaica to Susan Ursin Niemcewicz, her aunt, addressed to Elizabethtown, NJ. She talks about Jamaica and the enslaved people there are allowed three days off to celebrate around Christmas, that is all the time the have off during the year. She remarks that they should do everything in their power to contribute to their happiness. She also talks about family and how she and her husband were both recently sick. People Included: John Kean (JK1814), Julia Ursin Niemcewicz Kean, Peter Philip James Kean, Sarah Sabina Morris Kean, Philip Livingston, John Tharp Lawrence, John Thraphttps://digitalcommons.kean.edu/lhc_1810s/1021/thumbnail.jp

On a coordinate independent description of string worldsheet theory

We study worldsheet conformal invariance for bosonic string propagating in a curved background using the hamiltonian formalism. In order to formulate the problem in a background independent manner we first rewrite the worldsheet theory in a language where it describes a single particle moving in an infinite-dimensional curved spacetime. This language is developed at a formal level without regularizing the infinite-dimensional traces. Then we adopt DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of quantum mechanics in the present context. Given the expressions for the classical Virasoro generators, this procedure enables us to define the coordinate invariant quantum analogues which we call DeWitt-Virasoro generators. This framework also enables us to calculate the invariant matrix elements of an arbitrary operator constructed out of the DeWitt-Virasoro generators between two arbitrary scalar states. Using these tools we further calculate the DeWitt-Virasoro algebra in spin-zero representation. The result is given by the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. Further analysis need to be performed in order to precisely relate this with the beta function computation of Friedan and others. Finally, we explain how this analysis improves the understanding of showing conformal invariance for certain pp-wave that has been recently discussed using hamiltonian framework.Comment: 32 pages, some reorganization for more elaborate explanation, no change in conclusio

Mutually unbiased binary observable sets on N qubits

The Pauli operators (tensor products of Pauli matrices) provide a complete basis of operators on the Hilbert space of N qubits. We prove that the set of 4^N-1 Pauli operators may be partitioned into 2^N+1 distinct subsets, each consisting of 2^N-1 internally commuting observables. Furthermore, each such partitioning defines a unique choice of 2^N+1 mutually unbiased basis sets in the N-qubit Hilbert space. Examples for 2 and 3 qubit systems are discussed with emphasis on the nature and amount of entanglement that occurs within these basis sets.Comment: 5 pages, 5 figures. Replacement - expanded introduction and conclusions; added reference

The inverse moment problem for convex polytopes

The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.Comment: LaTeX2e, 24 pages including 1 appendi

Natural Theories of Ultra-Low Mass PNGB's: Axions and Quintessence

We consider the Wilson Line PNGB which arises in a U(1)^N gauge theory, abstracted from a latticized, periodically compactified extra dimension U(1). Planck scale breaking of the PNGB's global symmetry is suppressed, providing natural candidates for the axion and quintessence. We construct an explicit model in which the axion may be viewed as the 5th component of the U(1)_Y gauge field in a 1+4 latticized periodically compactified extra dimension. We also construct a quintessence PNGB model where the ultra-low mass arises from Planck-scale suppressed physics itself.Comment: 20 pages, fixed typo and reference

Group Process and Organizational Environment: Student Organizations in the University

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68768/2/10.1177_089976407400300305.pd

Mental Health Changes Over Time: a Longitudinal Perspective: Summary Report: Mental Health and Wellbeing Transition Study

Bryant, R., Lawrence-Wood, E., Baur, J., McFarlane, A., Hodson, S., Sadler, N., Benassi, H., Howell, S., Abraham, M., Iannos, M., Hansen, C., Searle, A., Van Hooff, M

Mental Health Changes Over Time: a Longitudinal Perspective: Mental Health and Wellbeing Transition Study

Bryant, R., Lawrence-Wood, E., Baur, J., McFarlane, A., Hodson, S., Sadler, N., Benassi, H., Howell, S., Abraham, M., Iannos, M., Hansen, C., Searle, A., Van Hooff, M

Black Hole, Jet, and Disk: The Universal Engine

In this paper I review the results of our ongoing project to investigate the coupling between accretion disk and radio jet in galactic nuclei and stellar mass black holes. We find a good correlation between the UV bump luminosity and the radio luminosities of AGN, which improves upon the usual [OIII]/radio correlations. Taking mass and energy conservation in the jet/disk system into account we can successfully model the correlation for radio-loud and radio-weak quasars. We find that jets are comparable in power to the accretion disk luminosity, and the difference between radio-loud and radio-weak may correspond to two natural stages of the relativistic electron distribution -- assuming that radio weak quasars have jets as well. The distribution of flat- and steep-spectrum sources is explained by bulk Lorentz factors gamma_j ~ 5-10. The absence of radio-loud quasars below a critical optical luminosity coincides with the FR I/FR II break and could be explained by a powerdependent, ``closing'' torus. This points towards a different type of obscuring torus in radio-loud host galaxies which might be a consequence of past mergers (e.g. by the temporary formation of a binary black-hole). Interaction of the jet with the closing torus might in principle also help to make a jet radio-loud. Turning to stellar-mass black holes we find that galactic jet sources can be described with the same coupled jet/disk model as AGN which is suggestive of some kind of universal coupling between jet and accretion disk around compact objects.Comment: to appear in ``Jets from Stars and Galactic Nuclei'', Springer Lecture Notes, plain TeX, 16 pages, also at http://www.astro.umd.edu/~hfalcke/publications.htm

A Kinematically Complete Measurement of the Proton Structure Function F2 in the Resonance Region and Evaluation of Its Moments

We measured the inclusive electron-proton cross section in the nucleon resonance region (W < 2.5 GeV) at momentum transfers Q**2 below 4.5 (GeV/c)**2 with the CLAS detector. The large acceptance of CLAS allowed for the first time the measurement of the cross section in a large, contiguous two-dimensional range of Q**2 and x, making it possible to perform an integration of the data at fixed Q**2 over the whole significant x-interval. From these data we extracted the structure function F2 and, by including other world data, we studied the Q**2 evolution of its moments, Mn(Q**2), in order to estimate higher twist contributions. The small statistical and systematic uncertainties of the CLAS data allow a precise extraction of the higher twists and demand significant improvements in theoretical predictions for a meaningful comparison with new experimental results.Comment: revtex4 18 pp., 12 figure