The Lambda-structure Of The Representation Rings Of The Classical Weyl Groups

First, we introduce a class of operations, called {dollar}\phi{dollar}-operations, on the representation rings of the classical Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar}. These operations are shown to generate the exterior power operations in the representation rings {dollar}R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} and {dollar}R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})).{dollar} Given integers l, h satisfying {dollar}l + h=k{dollar}, let {dollar}\beta{dollar} be a partition of l and {dollar}\alpha{dollar} be a partition of h. The main theorem shows that induced representations of the form {dollar}{dollar}Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,\alpha{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1,{dollar}{dollar}where {dollar}{lcub}\cal W{rcub}\sb{lcub}B,a{rcub}=\prod{lcub}\cal W{rcub}(B\sb{lcub}B{rcub})\times\prod{lcub}\cal W{rcub}(A\sb{lcub}a{rcub}),{dollar} can be expressed as an algebraic combination of {dollar}\phi{dollar}-operations acting on the two canonical induced representations {dollar}{dollar}\eqalign{lcub}X\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub})\times{lcub}\cal W{rcub}(B\sb1){rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1\cr\cr Y\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub}){rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1.\cr{rcub}{dollar}{dollar};Next, we show that the set {dollar}{dollar}\left\{lcub}1 \otimes Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,a{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1\right\{rcub}{dollar}{dollar}is a basis of {dollar}\doubq \otimes R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar}. Since the {dollar}\phi{dollar}-operations generate the {dollar}\lambda{dollar}-operations, one can deduce that {dollar}\doubq\otimes R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} is generated as a {dollar}\lambda{dollar}-ring over {dollar}\doubq{dollar} by the elements {dollar}1 \otimes X\sb{lcub}k{rcub}{dollar} and {dollar}1 \otimes Y\sb{lcub}k{rcub}{dollar}. By applying a result of Lusztig which characterizes the irreducible representations of the Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar} it follows, as a corollary, that {dollar}\doubq\otimes R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})){dollar} is generated by two elements as a {dollar}\lambda{dollar}-ring over {dollar}\doubq{dollar}

Star - Planet - Debris Disk Alignment in the HD 82943 system: Is planetary system coplanarity actually the norm?

Recent results suggest that the two planets in the HD 82943 system are inclined to the sky plane by 20 +/- 4deg. Here, we show that the debris disk in this system is inclined by 27 +/- 4deg, thus adding strength to the derived planet inclinations and suggesting that the planets and debris disk are consistent with being aligned at a level similar to the Solar System. Further, the stellar equator is inferred to be inclined by 28 +/- 4deg, suggesting that the entire star - planet - disk system is aligned, the first time such alignment has been tested for radial velocity discovered planets on ~AU wide orbits. We show that the planet-disk alignment is primordial, and not the result of planetary secular perturbations to the disk inclination. In addition, we note three other systems with planets at >10AU discovered by direct imaging that already have good evidence of alignment, and suggest that empirical evidence of system-wide star - planet - disk alignment is therefore emerging, with the exception of systems that host hot Jupiters. While this alignment needs to be tested in a larger number of systems, and is perhaps unsurprising, it is a reminder that the system should be considered as a whole when considering the orientation of planetary orbits.Comment: Accepted to MNRA

Huisgen-based conjugation of water-soluble porphyrins to deprotected sugars: Towards mild strategies for the labelling of glycans

Fully deprotected alkynyl-functionalised mono- and oligosaccharides undergo CuAAC-based conjugation with water-soluble porphyrin azides in aqueous environments. The mild reaction conditions are fully compatible with the presence of labile glycosidic bonds. This approach provides an ideal strategy to conjugate tetrapyrroles to complex carbohydrates

Origin of the Mediterranean outflow

Toe origin of the Mediterranean outflow is one of oceanography\u27s oldest problems. In this work, the flow of western Mediterranean deep water up and over the sill at Gibraltar is investigated from hydrographic observations and current measurements. The deep water is found to flow westward along the Moroccan continental slope in the western Mediterranean or Alboran Sea and to rise as it approaches the Strait of Gibraltar...

A Proposed Implementation of Tarjan\u27s Algorithm for Scheduling the Solution Sequence of Systems of Federated Models

Tarjan\u27s algorithm schedules the solution of systems of equations by noting the coupling and grouping between the equations. Simulating complex systems, e.g., advanced power plants, aerodynamic systems, or the multi-scale design of components, requires the linkage of large groups of coupled models. Currently, this is handled manually in systems modeling packages. That is, the analyst explicitly defines both the method and solution sequence necessary to couple the models. In small systems of models and equations this works well. However, as additional detail is needed across systems and across scales, the number of models grows rapidly. This precludes the manual assembly of large systems of federated models, particularly in systems composed of high fidelity models. This paper examines extending Tarjan\u27s algorithm from sets of equations to sets of models. The proposed implementation of the algorithm is demonstrated using a small one-dimensional system of federated models representing the heat transfer and thermal stress in a gas turbine blade with thermal barrier coating. Enabling the rapid assembly and substitution of different models permits the rapid turnaround needed to support the “what-if” kinds of questions that arise in engineering design

The circumbinary disk of HD 98800B: Evidence for disk warping

The quadruple young stellar system HD 98800 consists of two spectroscopic binary pairs with a circumbinary disk around the B component. Recent work by Boden and collaborators using infrared interferometry and radial velocity data resulted in a determination of the physical orbit for HD 98800B. We use the resulting inclination of the binary and the measured extinction toward the B component stars to constrain the distribution of circumbinary material. Although a standard optically and geometrically thick disk model can reproduce the spectral energy distribution, it cannot account for the observed extinction if the binary and the disk are coplanar. We next constructed a dynamical model to investigate the influence of the A component, which is not in the Ba‐Bb orbital plane, on the B disk. We find that these interactions have a substantial impact on the inclination of the B circumbinary disk with respect to the Ba‐Bb orbital plane. The resulting warp would be sufficient to place material into the line of sight and the noncoplanar disk orientation may also cause the upper layers of the disk to intersect the line of sight if the disk is geometrically thick. These simulations also support that the dynamics of the Ba‐Bb orbit clear the inner region to a radius of~3 AU. We then discuss whether the somewhat unusual properties of the HD 98800B disk are consistent with material remnant from the star formation process or with more recent creation by collisions from larger bodies