Abstract:
We report results for the virtual photon asymmetry $A_1$ on the nucleon from new Jefferson Lab measurements. The experiment, which used the CEBAF Large Acceptance Spectrometer and longitudinally polarized proton ($^{15}$NH$_3$) and deuteron ($^{15}$ND$_3$) targets, collected data with a longitudinally polarized electron beam at energies between 1.6 GeV and 5.7 GeV. In the present paper, we concentrate on our results for $A_1(x,Q^2)$ and the related ratio $g_1/F_1(x,Q^2)$ in the resonance and the deep inelastic regions for our lowest and highest beam energies, covering a range in momentum transfer $Q^2$ from 0.05 to 5.0 GeV$^2$ and in final-state invariant mass $W$ up to about 3 GeV. Our data show detailed structure in the resonance region, which leads to a strong $Q^2$--dependence of $A_1(x,Q^2)$ for $W$ below 2 GeV. At higher $W$, a smooth approach to the scaling limit, established by earlier experiments, can be seen, but $A_1(x,Q^2)$ is not strictly $Q^2$--independent. We add significantly to the world data set at high $x$, up to $x = 0.6$. Our data exceed the SU(6)-symmetric quark model expectation for both the proton and the deuteron while being consistent with a negative $d$-quark polarization up to our highest $x$. This data setshould improve next-to-leading order (NLO) pQCD fits of the parton polarization distributions.

Abstract:
New measurements of the spin structure functions of the proton and deuteron g1p(x,Q2) and g1d(x,Q2) in the nucleon resonance region are compared with extrapolations of target-mass-corrected next-to-leading-order (NLO) QCD fits to higher energy data. Averaged over the entire resonance region (W<2 GeV), the data and QCD fits are in good agreement in both magnitude and Q2 dependence for Q2>1.7 GeV2. This global duality appears to result from cancellations among the prominent local resonance regions: in particular strong sigma{3/2} contributions in the Delta(1232) region appear to be compensated by strong sigma{1/2} contributions in the resonance region centered on 1.5 GeV. These results are encouraging for the extension of NLO QCD fits to lower W and Q2 than have been used previously.

Abstract:
The spin structure functions g_1 for the proton and the deuteron have been measured over a wide kinematic range in x and Q2 using 1.6 and 5.7 GeV longitudinally polarized electrons incident upon polarized NH_3 and ND_3 targets at Jefferson Lab. Scattered electrons were detected in the CEBAF Large Acceptance Spectrometer, for 0.05 < Q^2 < 5 GeV^2 and W < 3 GeV. The first moments of g_1 for the proton and deuteron are presented -- both have a negative slope at low Q^2, as predicted by the extended Gerasimov-Drell-Hearn sum rule. The first result for the generalized forward spin polarizability of the proton gamma_0^p is also reported. This quantity shows strong Q^2 dependence at low Q^2, while Q^6\gamma_0^p seems to flatten out at the highest Q^2 accessed by our experiment. Although the first moments of g_1 are consistent with Chiral Perturbation Theory (ChPT) calculations up to approximately Q^2 = 0.06 GeV^2, a significant discrepancy is observed between the \gamma_0^p data and ChPT for gamma_0^p, even at the lowest Q2.

Abstract:
We present a significantly improved determination of the Bjorken Sum for 0.6$\leq Q^{2}\leq$4.8 GeV$^{2}$ using precise new $g_{1}^{p}$ and $g_{1}^{d}$ data taken with the CLAS detector at Jefferson Lab. A higher-twist analysis of the $Q^{2}$-dependence of the Bjorken Sum yields the twist-4 coefficient $f_{2}^{p-n}=-0.064 \pm0.009\pm_{0.036}^{0.032}$. This leads to the color polarizabilities $\chi_{E}^{p-n}=-0.032\pm0.024$ and $\chi_{B}^{p-n}=0.032\pm0.013$. The strong force coupling is determined to be $\alpha_{s}^{\overline{\mbox{ MS}}}(M_{Z}^{2})=0.1124\pm0.0061$, which has an uncertainty a factor of 1.5 smaller than earlier estimates using polarized DIS data. This improvement makes the comparison between $\alpha_{s}$ extracted from polarized DIS and other techniques a valuable test of QCD.

Abstract:
A new measurement of the parity violating asymmetry in elastic electron scattering on hydrogen at backward angles and at a four momentum transfer of Q^2=0.22 (GeV/c)^2 is reported here. The measured asymmetry is A_LR=(-17.23 +- 0.82_stat +-0.89_syst) ppm. The Standard Model prediction assuming no strangeness is A_0=(-15.87 +- 1.22) ppm. In combination with previous results from measurements at forward angles, it it possible to disentangle for the first time the strange electric and magnetic form factors at this momentum transfer, G_E^s(0.22)=0.050 +- 0.038 +- 0.019 and G_M^s(0.22)=-0.14 +- 0.11 +- 0.11.

Abstract:
For k>6, we determine the minimal area of a compact hyperbolic surface, and an oriented compact hyperbolic surface that can be tiled by embedded regular triangles of angle 2\pi/k. Based on this, all the cases of equality in Laszlo Fejes Toth's triangle bound for hyperbolic surfaces are described.

Abstract:
We have extracted QCD matrix elements from our data on double polarized inelastic scattering of electrons on nuclei. We find the higher twist matrix element \tilde{d_2}, which arises strictly from quark- gluon interactions, to be unambiguously non zero. The data also reveal an isospin dependence of higher twist effects if we assume that the Burkhardt-Cottingham Sum rule is valid. The fundamental Bjorken sum rule obtained from the a0 matrix element is satisfied at our low momentum transfer.

Abstract:
Wide-angle exclusive Compton scattering and single-pion photoproduction from the proton have been investigated via measurement of the polarization transfer from a circularly polarized photon beam to the recoil proton. The wide-angle Compton scattering polarization transfer was analyzed at an incident photon energy of 3.7~GeV at a proton scattering angle of \cma$= 70^\circ$. The longitudinal transfer \KLL, measured to be $0.645 \pm 0.059 \pm 0.048$, where the first error is statistical and the second is systematic, has the same sign as predicted for the reaction mechanism in which the photon interacts with a single quark carrying the spin of the proton. However, the observed value is $\sim$3~times larger than predicted by the generalized-parton-distribution-based calculations, which indicates a significant unknown contribution to the scattering amplitude.

Abstract:
We have examined the spin structure of the proton in the region of the nucleon resonances (1.085 GeV < W < 1.910 GeV) at an average four momentum transfer of Q^2 = 1.3 GeV^2. Using the Jefferson Lab polarized electron beam, a spectrometer, and a polarized solid target, we measured the asymmetries A_parallel and A_perp to high precision, and extracted the asymmetries A_1 and A_2, and the spin structure functions g_1 and g_2. We found a notably non-zero A_perp, significant contributions from higher-twist effects, and only weak support for polarized quark--hadron duality.