Discontinuous symplectic capacities

We show that the spherical capacity is discontinuous on a smooth family of ellipsoidal shells. Moreover, we prove that the shell capacity is discontinuous on a family of open sets with smooth connected boundaries.Comment: We include generalizations to higher dimensions due to the unknown referee and Janko Latschev. We add examples of open sets with connected boundary on which the shell capacity is not continuous. 3rd and 4th version: minor changes, to appear in J. Fixed Point Theory App

Remarks on Legendrian Self-Linking

The Thurston-Bennequin invariant provides one notion of self-linking for any homologically-trivial Legendrian curve in a contact three-manifold. Here we discuss related analytic notions of self-linking for Legendrian knots in Euclidean space. Our definition is based upon a reformulation of the elementary Gauss linking integral and is motivated by ideas from supersymmetric gauge theory. We recover the Thurston-Bennequin invariant as a special case.Comment: 42 pages, many figures; v2: minor revisions, published versio

Algebraic Torsion in Contact Manifolds

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.Comment: 53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a final update to agree with the published paper, and also corrects a minor error that appeared in the published version of the appendi

Tight Beltrami fields with symmetry

Let $M$ be a compact orientable Seifered fibered 3-manifold without a boundary, and $\alpha$ an $S^1$-invariant contact form on $M$. In a suitable adapted Riemannian metric to $\alpha$, we provide a bound for the volume $\text{Vol}(M)$ and the curvature, which implies the universal tightness of the contact structure $\xi=\ker\alpha$.Comment: 26 page

The f_LT Response Function of D(e,e'p)n at Q^2=0.33(GeV/c)^2

The interference response function f_LT (R_LT) of the D(e,e'p)n reaction has been determined at squared four-momentum transfer Q^2 = 0.33 (GeV/c)^2 and for missing momenta up to p_miss= 0.29 (GeV/c). The results have been compared to calculations that reproduce f_LT quite well but overestimate the cross sections by 10 - 20% for missing momenta between 0.1 (GeV/c) and 0.2 (GeV/c) .Comment: 12 Pages, 10 figure

A measurement of the axial form factor of the nucleon by the p(e,e'pi+)n reaction at W=1125 MeV

The reaction p(e,e'pi+)n was measured at the Mainz Microtron MAMI at an invariant mass of W=1125 MeV and four-momentum transfers of Q^2=0.117, 0.195 and 0.273 (GeV/c)^2. For each value of Q^2, a Rosenbluth separation of the transverse and longitudinal cross sections was performed. An effective Lagrangian model was used to extract the `axial mass' from experimental data. We find a value of M_A=(1.077+-0.039) GeV which is (0.051+-0.044) GeV larger than the axial mass known from neutrino scattering experiments. This is consistent with recent calculations in chiral perturbation theory.Comment: 14 pages, 5 figures, uses elsart.cl

State business: gender, sex and marriage in Tajikistan

This article examines the relation of the state to masculinity and sexuality by way of an exploration of the sexual problems of a young man and his wife in Tajikistan at the end of the Soviet era. It suggests that the regime’s inattention to this kind of issue was bound up with the importance to the state of projecting appropriate versions of masculinity. It further posits the idea that the continued refusal of the independent Tajik state to offer appropriate treatments for sexual dysfunction is consistent with the image of modernity President Rahmon wishes to present to the world. The article shows that as masculinity discursively occupies the superior gender position, with men expected to dominate, the state is itself impotent to respond when they are, in fact, unable to do so in sexual practice. However, the myth of male dominance persists to the point that it may prevent women from seeing beyond their subordination and finding mutually beneficial solutions in their familial and sexual relationships

Measurement of Rlt and Atl in the 4He(e,e'p)3H Reaction at pmiss of 130-300 MeV/c

We have measured the 4He(e,e'p)3H reaction at missing momenta of 130-300 MeV/c using the three-spectrometer facility at the Mainz microtron MAMI. Data were taken in perpendicular kinematics to allow us to determine the response function Rlt and the asymmetry term Atl. The data are compared to both relativistic and non-relativistic calculations.Comment: To be published in the European Physical Journal

Measurement of the recoil polarization in the p (\vec e, e' \vec p) pi^0 reaction at the \Delta(1232) resonance

The recoil proton polarization has been measured in the p (\vec e,e'\vec p) pi^0 reaction in parallel kinematics around W = 1232 MeV, Q^2 = 0.121 (GeV/c)^2 and epsilon = 0.718 using the polarized c.w. electron beam of the Mainz Microtron. Due to the spin precession in a magnetic spectrometer, all three proton polarization components P_x/P_e = (-11.4 \pm 1.3 \pm 1.4) %, P_y = (-43.1 \pm 1.3 \pm 2.2) %, and P_z/P_e = (56.2 \pm 1.5 \pm 2.6) % could be measured simultaneously. The Coulomb quadrupole to magnetic dipole ratio CMR = (-6.4\pm 0.7_{stat}\pm 0.8_{syst}) % was determined from P_x in the framework of the Mainz Unitary Isobar Model. The consistency among the reduced polarizations and the extraction of the ratio of longitudinal to transverse response is discussed.Comment: 5 pages LaTeX, 1 table, 2 eps figure

High-precision Studies of the 3^{\bf{3}}He(e,e′^{\bf{\prime}}p) Reaction at the Quasielastic Peak

Precision studies of the reaction $^{3}$He(e,e$^\prime$p) using the three-spectrometer facility at the Mainz microtron MAMI are presented. All data are for quasielastic kinematics at $|\vec{q} | =685$ MeV/c. Absolute cross sections were measured at three electron kinematics. For the measured missing momenta range from 10 to 165 MeV/c, no strength is observed for missing energies higher than 20 MeV. Distorted momentum distributions were extracted for the two-body breakup and the continuum. The longitudinal and transverse behavior was studied by measuring the cross section for three photon polarizations. The longitudinal and transverse nature of the cross sections is well described by a currently accepted and widely used prescription of the off-shell electron-nucleon cross-section. The results are compared to modern three-body calculations and to previous data.Comment: 4 pages, 3 figures. Submitted for publication in Phys. Rev. Let