Pion form factor in large NcN_c QCD

The electromagnetic form factor of the pion is obtained using a particular realization of QCD in the large $N_c$ limit, which sums up the infinite number of zero-width resonances to yield an Euler's Beta function of the Veneziano type. This form factor agrees with space-like data much better than single rho-meson dominance. A simple unitarization ansatz is illustrated, and the resulting vector spectral function in the time-like region is shown to be in reasonable agreement with the ALEPH data from threshold up to about 1.3 ${GeV}^2$.Comment: Plain Latex, 9 pages, 2 figure

Corrections to the SU(3)×SU(3){\bf SU(3)\times SU(3)} Gell-Mann-Oakes-Renner relation and chiral couplings L8rL^r_8 and H2rH^r_2

Next to leading order corrections to the $SU(3) \times SU(3)$ Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is $\psi_5(0) = (2.8 \pm 0.3) \times 10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $\delta_K = (55 \pm 5)$. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability regions, and to a much lesser extent due to the uncertainties in the strong coupling and the strange quark mass. Higher order quark mass corrections, vacuum condensates, and the hadronic resonance sector play a negligible role in this determination. These results confirm an independent determination from chiral perturbation theory giving also very large corrections, i.e. roughly an order of magnitude larger than the corresponding corrections in chiral $SU(2) \times SU(2)$. Combining these results with our previous determination of the corrections to GMOR in chiral $SU(2) \times SU(2)$, $\delta_\pi$, we are able to determine two low energy constants of chiral perturbation theory, i.e. $L^r_8 = (1.0 \pm 0.3) \times 10^{-3}$, and $H^r_2 = - (4.7 \pm 0.6) \times 10^{-3}$, both at the scale of the $\rho$-meson mass.Comment: Revised version with minor correction

An optimal Q-state neural network using mutual information

Starting from the mutual information we present a method in order to find a hamiltonian for a fully connected neural network model with an arbitrary, finite number of neuron states, Q. For small initial correlations between the neurons and the patterns it leads to optimal retrieval performance. For binary neurons, Q=2, and biased patterns we recover the Hopfield model. For three-state neurons, Q=3, we find back the recently introduced Blume-Emery-Griffiths network hamiltonian. We derive its phase diagram and compare it with those of related three-state models. We find that the retrieval region is the largest.Comment: 8 pages, 1 figur

The more they’re beaten the better they be : Gendered Violence and Abuse in Victorian Laws and Literature

During the Victorian age, the law and society were in conversation with each other, and the law reflected Victorian gender norms. Nineteenth-century gender attitudes intersected with the law, medical discourse, and social customs in a multitude of ways. Abuse and gender violence occurred beneath the veneer of Victorian respectability. The models of nineteenth-century social conduct were highly gendered and placed men and women in separate social spheres. As this research indicates, the lived practices of Victorians, across social and economic strata, deviated from these accepted models of behavior. This thesis explores the ways that accepted and unaccepted standards of female behavior manifest in Victorian legal discourse and literary sources. The three tropes of female behavior analyzed in this thesis are: “the angel in the house,” “the mad woman,” and “the fallen woman.” Victorian men repeatedly failed to protect their wives, daughters, and companions and were often the sources of abuse and violence. Women, in turn, were unable to shape themselves to fit the accepted model of Victorian womanhood. This thesis suggests that widespread Victorian gender attitudes and social causes that are taken up by politicians are reflected in the legal system. This thesis unearths the voices of Victorian women, both literary and historical ones, in order to tell their stories and analyze the ways that their experiences are a result of social conventions and legal standards of the nineteenth-century

UH-60A Airloads Flight Test Program: Data Counter 9017

Aeromechanics Branch interns at Ames Research Center have been directly contributing to the data quality analysis and reporting of the UH-60A Airloads Flight Test Program for many years. In chronological order (together with the semester and year): Caroline Edwards (Summer 2011); Joni DeGuzman and Carson Turner (Fall 2011); Eric Fritz (Spring 2012); Connor Beierle (Fall 2012); Christopher Olinger (Spring and Summer 2013); Needa Lin, Anatole Levkoff, Maxwell Loebig, Jose Orejel, Megan Prout, and Albert Sue (Summer 2014); Jared Archey (Fall 2014); Alexander Crone (Summer 2015); Jeffrey Diament, Austin Djang, and Jessica Swan (Summer 2016); Makenzie Allen (Summer 2017); Colin Lauzon (Fall 2017); Eric Gilkey (Spring 2018); and Nicholas Masso (Summer 2019). These interns have spent their internships reviewing flight logs, extracting the data out of TRENDS, formatting the data into spreadsheets, writing code to automate the process, and plotting results. Without their efforts, much of the work would be unfinished. The authors appreciate the achievements of the UH-60A Airloads Working Group during its 20-year lifetime, as well the contributions of Randy Peterson, Tom Norman, and William Warmbrodt to the data processing and assistance with the report preparation. Lastly, this report is dedicated to William Bousman for his efforts preceding, during, and subsequent to the UH-60A Airloads Flight Test Program

Chiral corrections to the SU(2)×SU(2)SU(2)\times SU(2) Gell-Mann-Oakes-Renner relation

The next to leading order chiral corrections to the $SU(2)\times SU(2)$ Gell-Mann-Oakes-Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, $\delta_\pi$, the value $\delta_\pi = (6.2, \pm 1.6)$. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate $\simeq \equiv |_{2\,\mathrm{GeV}} = (- 267 \pm 5 MeV)^3$. As a byproduct, the chiral perturbation theory (unphysical) low energy constant $H^r_2$ is predicted to be $H^r_2 (\nu_\chi = M_\rho) = - (5.1 \pm 1.8)\times 10^{-3}$, or $H^r_2 (\nu_\chi = M_\eta) = - (5.7 \pm 2.0)\times 10^{-3}$.Comment: A comment about the value of the strong coupling has been added at the end of Section 4. No change in results or conslusion

Dynamical Critical Phenomena and Large Scale Structure of the Universe: the Power Spectrum for Density Fluctuations

As is well known, structure formation in the Universe at times after decoupling can be described by hydrodynamic equations. These are shown here to be equivalent to a generalization of the stochastic Kardar--Parisi--Zhang equation with time-- dependent viscosity in epochs of dissipation. As a consequence of the Dynamical Critical Scaling induced by noise and fluctuations, these equations describe the fractal behavior (with a scale dependent fractal dimension) observed at the smaller scales for the galaxy--to--galaxy correlation function and $also$ the Harrison--Zel'dovich spectrum at decoupling. By a Renormalization Group calculation of the two--point correlation function between galaxies in the presence of (i) the expansion of the Universe and (ii) non--equilibrium, we can account, from first principles, for the main features of the observed shape of the power spectrum.Comment: 13 pages with 2 encapsulated PostScript figures included, gzipped tar forma