We capture the off-shell as well as the on-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian densities of the four (3 + 1)-dimensional (4D) (non-)Abelian 1-form gauge theories within the framework of
the superfield formalism. In particular, we provide the geometrical interpretations for (i) the above nilpotent symmetry invariance, and (ii) the above Lagrangian densities, in the language of the specific quantities defined in the domain of the above superfield formalism. Some of the subtle points, connected with the 4D (non-)Abelian 1-form gauge theories, are clarified within the framework of the above superfield formalism where the 4D ordinary gauge theories are considered on the (4, 2)-dimensional supermanifold parametrized by the four spacetime coordinates x^mu (with mu = 0, 1, 2, 3) and a pair of Grassmannian variables theta and bartheta. One of the key results of our present investigation is a great deal of simplification in the geometrical understanding of the nilpotent (anti-)BRST symmetry invariance.
Lattice contribution to the electronic self-energy in complex correlated oxides is a fascinating subject that has lately stimulated lively discussions. Expectations of electron-phonon self-energy effects for simpler materials, such as Pd and Al, have
resulted in several misconceptions in strongly correlated oxides. Here we analyze a number of arguments claiming that phonons cannot be the origin of certain self-energy effects seen in high-$T_c$ cuprate superconductors via angle resolved photoemission experiments (ARPES), including the temperature dependence, doping dependence of the renormalization effects, the inter-band scattering in the bilayer systems, and impurity substitution. We show that in light of experimental evidences and detailed simulations, these arguments are not well founded.
We show that a determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata. The proof involves a bijection from these automata to certain marked lattice paths and a sign-reversing involution to evaluate the determinant.
We discuss the results from the combined IRAC and MIPS c2d Spitzer Legacy observations of the Serpens star-forming region. In particular we present a set of criteria for isolating bona fide young stellar objects, YSOs, from the extensive background c
ontamination by extra-galactic objects. We then discuss the properties of the resulting high confidence set of YSOs. We find 235 such objects in the 0.85 deg^2 field that was covered with both IRAC and MIPS. An additional set of 51 lower confidence YSOs outside this area is identified from the MIPS data combined with 2MASS photometry. We describe two sets of results, color-color diagrams to compare our observed source properties with those of theoretical models for star/disk/envelope systems and our own modeling of the subset of our objects that appear to be star+disks. These objects exhibit a very wide range of disk properties, from many that can be fit with actively accreting disks to some with both passive disks and even possibly debris disks. We find that the luminosity function of YSOs in Serpens extends down to at least a few x .001 Lsun or lower for an assumed distance of 260 pc. The lower limit may be set by our inability to distinguish YSOs from extra-galactic sources more than by the lack of YSOs at very low luminosities. A spatial clustering analysis shows that the nominally less-evolved YSOs are more highly clustered than the later stages and that the background extra-galactic population can be fit by the same two-point correlation function as seen in other extra-galactic studies. We also present a table of matches between several previous infrared and X-ray studies of the Serpens YSO population and our Spitzer data set.
Results from spectroscopic observations of the Intermediate Polar (IP) EX Hya in quiescence during 1991 and 2001 are presented. Spin-modulated radial velocities consistent with an outer disc origin were detected for the first time in an IP. The spin
pulsation was modulated with velocities near ~500-600 km/s. These velocities are consistent with those of material circulating at the outer edge of the accretion disc, suggesting corotation of the accretion curtain with material near the Roche lobe radius. Furthermore, spin Doppler tomograms have revealed evidence of the accretion curtain emission extending from velocities of ~500 km/s to ~1000 km/s. These findings have confirmed the theoretical model predictions of King & Wynn (1999), Belle et al. (2002) and Norton et al. (2004) for EX Hya, which predict large accretion curtains that extend to a distance close to the Roche lobe radius in this system. Evidence for overflow stream of material falling onto the magnetosphere was observed, confirming the result of Belle et al. (2005) that disc overflow in EX Hya is present during quiescence as well as outburst. It appears that the hbeta and hgamma spin radial velocities originated from the rotation of the funnel at the outer disc edge, while those of halpha were produced due to the flow of material along the field lines far from the white dwarf (narrow component) and close to the white dwarf (broad-base component), in agreement with the accretion curtain model.
In the article [Petojevic 2006], A. Petojevi c verified useful properties of the $K_{i}(z)$ functions which generalize Kurepas [Kurepa 1971] left factorial function. In this note, we present simplified proofs of two of these results and we answer the
open question stated in [Petojevic 2006]. Finally, we discuss the differential transcendency of the $K_{i}(z)$ functions.
We get asymptotics for the volume of large balls in an arbitrary locally compact group G with polynomial growth. This is done via a study of the geometry of G and a generalization of P. Pansus thesis. In particular, we show that any such G is weakly
commensurable to some simply connected solvable Lie group S, the Lie shadow of G. We also show that large balls in G have an asymptotic shape, i.e. after a suitable renormalization, they converge to a limiting compact set which can be interpreted geometrically. We then discuss the speed of convergence, treat some examples and give an application to ergodic theory. We also answer a question of Burago about left invariant metrics and recover some results of Stoll on the irrationality of growth series of nilpotent groups.
We study a recently proposed formulation of overlap fermions at finite density. In particular we compute the energy density as a function of the chemical potential and the temperature. It is shown that overlap fermions with chemical potential reproduce the correct continuum behavior.
This is a supplement to the paper arXiv:q-bio/0701050, containing the text of correspondence sent to Nature in 1990.
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold,
we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic exponential Lie series. They become stochastic Lie group integrator schemes if we use Munthe-Kaas methods as the underlying ordinary differential integrator. Further, we show that some Castell--Gaines methods are uniformly more accurate than the corresponding stochastic Taylor schemes. Lastly we demonstrate our methods by simulating the dynamics of a free rigid body such as a satellite and an autonomous underwater vehicle both perturbed by two independent multiplicative stochastic noise processes.
