Unitarization of Total Cross Section and Coherent Effect in pQCD

A formula to unitarize the leading-log BFKL-Pomeron amplitude is derived using a coherent property of two-body collision in the peripheral region. This procedure also allows an algebraic characterization of the Reggeon in QCD based on color, instead of the total angular momentum of the gluons being exchanged.Comment: Talk given at the DIS99 Meeting in Zeuthen, Germany. April, 1999. 3 page

The Murnaghan-Nakayama rule for k-Schur functions

We prove the Murgnaghan--Nakayama rule for $k$-Schur functions of Lapointe and Morse, that is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a $k$-Schur function in terms of $k$-Schur functions. This is proved using the noncommutative $k$-Schur functions in terms of the nilCoxeter algebra introduced by Lam and the affine analogue of noncommutative symmetric functions of Fomin and Greene.Comment: 23 pages, updated to reflect referee comments, to appear in Journal of Combinatorial Theory, Series

Is imagination too liberal for modal epistemology?

Appealing to imagination for modal justification is very common. But not everyone thinks that all imaginings provide modal justification. Recently, Gregory and Kung :620–663, 2010) have independently argued that, whereas imaginings with sensory imageries can justify modal beliefs, those without sensory imageries don’t because of such imaginings’ extreme liberty. In this essay, I defend the general modal epistemological relevance of imagining. I argue, first, that when the objections that target the liberal nature of non-sensory imaginings are adequately developed, those objections also threaten the sensory imaginings. So, if we think that non-sensory imaginings are too liberal for modal justification, we should say the same about sensory imaginings. I’ll finish my defense by showing that, when it comes to deciding between saying that all imaginings are prima facie justificatory and saying that no imaginings are justificatory, there is an independent reason for accepting the former

An analytical model for turbulence scattered rays in the shadow zone for outdoor sound propagation calculation

In outdoor sound propagation, an inherent problem of the ray tracing method is its inability to determine the sound pressure level in the shadow zone, where geometrical rays do not penetrate. This is a serious problem in a turbulent atmosphere where significant sound energy will be scattered into the shadow. Empirical corrections that are determined from measurements or numerical simulations are limited to situations within the bounds of the empirical corrections. This paper describes a different approach where the ray tracing model is modified analytically into a scattered ray model. Rays are first diffracted from the shadow boundary, which is determined by the geometrical ray paths. The diffracted rays are then scattered by turbulence in their way to the receiver. The amount of scatter is determined from turbulence statistics that are determined from a Gaussian turbulence model. Most of the statistics are determined analytically except one element, which is determined empirically from numerical simulations. This turbulence scattered ray model is shown to have good accuracy against calculations based on the parabolic equation, and against previously published measurement data. It was found that the agreement is good both with and without turbulence, at distance up to 2 km from the shadow boundary. © 2009 Acoustical Society of Americ

Recent research and development in semi-rigid composite joints with precast hollowcore slabs

Composite structure incorporating steel beams and precast hollowcore slabs is a recently developed composite floor system for building structures. This form of composite construction is so far limited to simple beam-column connections. Although the concept of semi-rigid composite joints has been widely research in the past, most of the researches have been carried out on composite joints with metal deck flooring and solid concrete slabs. Research on composite joints with precast hollowcore slabs is rather limited. As the construction industry demands for rapid construction with reduction in cost and environmental impacts, this form of composite floor system, which does not require major onsite concreting, has become very popular among the designers and engineers in the UK. In this paper, full-scale tests of beam-to-column semi-rigid composite joints with steel beam and precast hollowcore slabs are reported. Based on the tests data; the structural behaviour of these semi-rigid composite joints is discussed together with numerical and finite element modelling. Through parametric studies, an analytical model for the semirigid composite joints is proposed and is verified by both the experimental data and finite element model; and good agreement is obtained

Dimers, webs, and positroids

We study the dimer model for a planar bipartite graph N embedded in a disk, with boundary vertices on the boundary of the disk. Counting dimer configurations with specified boundary conditions gives a point in the totally nonnegative Grassmannian. Considering pairing probabilities for the double-dimer model gives rise to Grassmann analogues of Rhoades and Skandera's Temperley-Lieb immanants. The same problem for the (probably novel) triple-dimer model gives rise to the combinatorics of Kuperberg's webs and Grassmann analogues of Pylyavskyy's web immanants. This draws a connection between the square move of plabic graphs (or urban renewal of planar bipartite graphs), and Kuperberg's square reduction of webs. Our results also suggest that canonical-like bases might be applied to the dimer model. We furthermore show that these functions on the Grassmannian are compatible with restriction to positroid varieties. Namely, our construction gives bases for the degree two and degree three components of the homogeneous coordinate ring of a positroid variety that are compatible with the cyclic group action.Comment: 25 page