Degenerate two-boundary centralizer algebras

Diagram algebras (e.g. graded braid groups, Hecke algebras, Brauer algebras) arise as tensor power centralizer algebras, algebras of commuting operators for a Lie algebra action on a tensor space. This work explores centralizers of the action of a complex reductive Lie algebra $\mathfrak{g}$ on tensor space of the form $M \otimes N \otimes V^{\otimes k}$. We define the degenerate two-boundary braid algebra $\mathcal{G}_k$ and show that centralizer algebras contain quotients of this algebra in a general setting. As an example, we study in detail the combinatorics of special cases corresponding to Lie algebras $\mathfrak{gl}_n$ and $\mathfrak{sl}_n$ and modules $M$ and $N$ indexed by rectangular partitions. For this setting, we define the degenerate extended two-boundary Hecke algebra $\mathcal{H}_k^{\mathrm{ext}}$ as a quotient of $\mathcal{G}_k$, and show that a quotient of $\mathcal{H}_k^{\mathrm{ext}}$ is isomorphic to a large subalgebra of the centralizer. We further study the representation theory of $\mathcal{H}_k^{\mathrm{ext}}$ to find that the seminormal representations are indexed by a known family of partitions. The bases for the resulting modules are given by paths in a lattice of partitions, and the action of $\mathcal{H}_k^{\mathrm{ext}}$ is given by combinatorial formulas.Comment: 45 pages, to appear in Pacific Journal of Mathematic

Secrecy vs. Disclosure of the Intelligence Community Budget: An Enduring Debate

Little known U.S. congressional documents, dating from the 1970s, debate public disclosure of Intelligence Community (IC) budget. The documents offer a rich repository of the arguments on both sides of the debate and shine a light on the thoughtful, measured congressional oversight practiced in formative years of the House and Senate intelligence committees

Centralizers of the infinite symmetric group

We review and introduce several approaches to the study of centralizer algebras of the infinite symmetric group $S_\infty$. Our study is led by the double commutant relationships between finite symmetric groups and partition algebras; each approach produces a centralizer algebra that is contained in a partition algebra. Our goal is to incorporate invariants of $S_\infty$, which ties our work to the study of symmetric functions in non-commuting variables. We resultantly explore sequence spaces as permutation modules, which yields families of non-unitary representations of $S_\infty$

Braking and cornering studies on an air cushion landing system

An experimental investigation was conducted to evaluate several concepts for braking and steering a vehicle equipped with an air cushion landing system (ACLS). The investigation made use of a modified airboat equipped with an ACLS. Braking concepts were characterized by the average deceleration of the vehicle. Reduced lobe flow and cavity venting braking concepts were evaluated in this program. The cavity venting braking concept demonstrated the best performance, producing decelerations on the test vehicle on the same order as moderate braking with conventional wheel brakes. Steering concepts were evaluated by recording the path taken while attempting to follow a prescribed maneuver. The steering concepts evaluated included using rudders only, using differential lobe flow, and using rudders combined with a lightly loaded, nonsteering center wheel. The latter concept proved to be the most accurate means of steering the vehicle on the ACLS, producing translational deviations two to three times higher than those from conventional nose-gear steering. However, this concept was still felt to provide reasonably precise steering control for the ACLS-equipped vehicle

Evaluation of the Relationship between Bulk Organic Precursors and Disinfection Byproduct Formation for Advanced Oxidation Processes

Advanced oxidation processes (AOPs) are gaining traction as they offer mineralization potential rather than transferring contaminants between media. However, AOPs operated with limited energy and/or chemical inputs can exacerbate disinfection byproduct (DBP) formation, even as precursors such as dissolved organic carbon, UV254, and specific UV absorbance (SUVA) decrease. This study examined the relationship between DBP precursors and formation using TiO2 photocatalysis experiments, external AOP and non-AOP data, and predictive DBP models. The top-performing indicator, SUVA, generally correlated positively with trihalomethanes and haloacetic acids, but limited-energy photocatalysis yielded contrasting negative correlations. The accuracy of predicted DBP values from models based on bulk parameters was generally poor, regardless of use and extent of AOP treatment and type of source water. Though performance improved for scenarios bounded by conditions used in model development, only 0.5% of the model/dataset pairings satisfied all measured parameter boundary conditions, thereby introducing skepticism toward model usefulness. Study findings suggest that caution should be employed when using bulk indicators and/or models as a metric for AOP mitigation of DBP formation potential, particularly for limited-energy/chemical inputs

Advances in Polarization Engineering

Polarization plays an important role in many optical systems and device. This includes devices designed to advantageously use polarization, like liquid crystal displays, and optical systems that measure polarization to obtain information not otherwise available, like instruments found in many modern telescopes. Polarization also needs to be considered in some systems where it is not a primary aspect of the design, like image formation in very high numerical aperture objective lenses. This manuscript discusses three optical engineering projects where accurate polarization analysis or testing was required. Chapter one discusses a case where the need for polarization engineering arises from extreme optical requirements. Exoplanet direct imaging requires extremely high contrast, so any possible phase errors need to be considered. This includes the effects of form birefringence, which had previously not been measured over a large diameter mirror. Chapter one presents the first measurements of form birefringence over a large diameter telescope mirror. Measurements of the 3.75-meter, spherical mirror, coated by vacuum deposition of aluminum, indicate low levels of retardance and diattenuation that vary over the face of the mirror. The retardance and diattenuation had maximum values of about 2x10-3 radians and 0.025% respectively. Initial modeling by Davis J., et al. shows that this level of form birefringence could be impactful in direct imaging systems. The chapter discusses the design of the metrology system used to perform the measurements. The polarization engineering in chapter 2 relates to a remote sensing instrument that detects polarization to provide information in addition to its spectral reflectance measuring capabilities. Chapter two covers the design and testing of the second-generation polarization state generator used for the calibration and testing of Jet Propulsion Laboratory’s (JPL) air-based, multispectral polarimetric imager (AirMSPI). The chapter focuses on the requirements of a polarization standard. The first-generation instrument is analyzed carefully and the lessons learned are applied to improving the second. The updated version has been successfully used for AirMSPI calibration prior to multiple airborne science campaigns. The third chapter discusses the analysis and modification of a nominally non-polarizing optical sub-system that has polarization design requirements. This highlights important polarization issues that occur is systems containing a large number of surfaces. The issues with the systems polarization performance are identified. A method to improve the polarization performance that can be implemented without any additional calculations is demonstrated. The system is then modified to improve the polarization performance while maintaining other important optical properties. Finally, the manufacturability of the modified design is considered

Measurements of Flow Rate and Trajectory of Aircraft Tire-Generated Water Spray

An experimental investigation was conducted at the NASA Langley Research Center to measure the flow rate and trajectory of water spray generated by an aircraft tire operating on a flooded runway. Tests were conducted in the Hydrodynamics Research Facility and made use of a partial airframe and a nose tire from a general aviation aircraft. Nose tires from a commercial transport aircraft were also used. The effects of forward speed, tire load, and water depth on water spray patterns were evaluated by measuring the amount and location of water captured by an array of tubes mounted behind the test tire. Water ejected from the side of the tire footprint had the most significant potential for ingestion into engine inlets. A lateral wake created on the water surface by the rolling tire can dominate the shape of the spray pattern as the distance aft of the tire is increased. Forward speed increased flow rates and moved the spray pattern inboard. Increased tire load caused the spray to become less dense. Near the tire, increased water depths caused flow rates to increase. Tests using a fuselage and partial wing along with the nose gear showed that for certain configurations, wing aerodynamics can cause a concentration of spray above the wing