Elliptic rook and file numbers

Utilizing elliptic weights, we construct an elliptic analogue of rook numbers for Ferrers boards. Our elliptic rook numbers generalize Garsia and Remmel's q-rook numbers by two additional independent parameters a and b, and a nome p. These are shown to satisfy an elliptic extension of a factorization theorem which in the classical case was established by Goldman, Joichi and White and later was extended to the q-case by Garsia and Remmel. We obtain similar results for our elliptic analogues of Garsia and Remmel's q-file numbers for skyline boards. We also provide an elliptic extension of the j-attacking model introduced by Remmel and Wachs. Various applications of our results include elliptic analogues of (generalized) Stirling numbers of the first and second kind, Lah numbers, Abel numbers, and r-restricted versions thereof.Comment: 45 pages; 3rd version shortened (elliptic rook theory for matchings has been taken out to keep the length of this paper reasonable

Hadronic Correlators from All-point Quark Propagators

A method for computing all-point quark propagators is applied to a variety of processes of physical interest in lattice QCD. The method allows, for example, efficient calculation of disconnected parts and full momentum-space 2 and 3 point functions. Examples discussed include: extraction of chiral Lagrangian parameters from current correlators, the pion form factor, and the unquenched eta-prime.Comment: LATTICE01(Algorithms and Machines

A novel potential/viscous flow coupling technique for computing helicopter flow fields

Because of the complexity of helicopter flow field, a zonal method of analysis of computational aerodynamics is required. Here, a new procedure for coupling potential and viscous flow is proposed. An overlapping, velocity coupling technique is to be developed with the unique feature that the potential flow surface singularity strengths are obtained directly from the Navier-Stokes at a smoother inner fluid boundary. The closed-loop iteration method proceeds until the velocity field is converged. This coupling should provide the means of more accurate viscous computations of the near-body and rotor flow fields with resultant improved analysis of such important performance parameters as helicopter fuselage drag and rotor airloads

Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation

We use elliptic Taylor series expansions and interpolation to deduce a number of summations for elliptic hypergeometric series. We extend to the well-poised elliptic case results that in the $q$-case have previously been obtained by Cooper and by Ismail and Stanton. We also provide identities involving S. Bhargava's cubic theta functions

Notes on Spinoptics in a Stationary Spacetime

In arXiv:1105.5629, equations of the modified geometrical optics for circularly polarized photon trajectories in a stationary spacetime are derived by using a (1+3)-decomposed form of Maxwell's equations. We derive the same results by using a four-dimensional covariant description. In our procedure, the null nature of the modified photon trajectory naturally appears and the energy flux is apparently null. We find that, in contrast to the standard geometrical optics, the inner product of the stationary Killing vector and the tangent null vector to the modified photon trajectory is no longer a conserved quantity along light paths. This quantity is furthermore different for left and right handed photon. A similar analysis is performed for gravitational waves and an additional factor of 2 appears in the modification due to the spin-2 nature of gravitational waves.Comment: 15 pages, to appear in PR

Explicit CP violation in a MSSM with an extra U(1)′U(1)'

We study that a minimal supersymmetric standard model with an extra $U(1)'$ gauge symmetry may accommodate the explicit CP violation at the one-loop level through radiative corrections. This model is CP conserving at the tree level and cannot realize the spontaneous CP violation for a wide parameter space at the one-loop level. In explicit CP violation scenario, we calculate the Higgs boson masses and the magnitude of the scalar-pseudoscalar mixings in this model at the one-loop level by taking into account the contributions of top quarks, bottom quarks, exotic quarks, and their superpartners. In particular, we investigate how the exotic quarks and squarks would affect the scalar-pseudoscalar mixings. It is observed that the size of the mixing between the heaviest scalar and pseudoscalar Higgs bosons is changed up to 20 % by a complex phase originated from the exotic quark sector of this model.Comment: 19 pages, 3 figure

Higgs bosons of a supersymmetric E6E_6 model at the Large Hadron Collider

It is found that CP symmetry may be explicitly broken in the Higgs sector of a supersymmetric $E_6$ model with two extra neutral gauge bosons at the one-loop level. The phenomenology of the model, the Higgs sector in particular, is studied for a reasonable parameter space of the model, in the presence of explicit CP violation at the one-loop level. At least one of the neutral Higgs bosons of the model might be produced via the $WW$ fusion process at the Large Hadron Collider.Comment: 23 pages, 5 figures, JHE