Sortable Elements for Quivers with Cycles

Each Coxeter element c of a Coxeter group W defines a subset of W called the c-sortable elements. The choice of a Coxeter element of W is equivalent to the choice of an acyclic orientation of the Coxeter diagram of W. In this paper, we define a more general notion of Omega-sortable elements, where Omega is an arbitrary orientation of the diagram, and show that the key properties of c-sortable elements carry over to the Omega-sortable elements. The proofs of these properties rely on reduction to the acyclic case, but the reductions are nontrivial; in particular, the proofs rely on a subtle combinatorial property of the weak order, as it relates to orientations of the Coxeter diagram. The c-sortable elements are closely tied to the combinatorics of cluster algebras with an acyclic seed; the ultimate motivation behind this paper is to extend this connection beyond the acyclic case.Comment: Final version as published. An error corrected in the previous counterexample, other minor improvement

Sortable elements in infinite Coxeter groups

In a series of previous papers, we studied sortable elements in finite Coxeter groups, and the related Cambrian fans. We applied sortable elements and Cambrian fans to the study of cluster algebras of finite type and the noncrossing partitions associated to Artin groups of finite type. In this paper, as the first step towards expanding these applications beyond finite type, we study sortable elements in a general Coxeter group W. We supply uniform arguments which transform all previous finite-type proofs into uniform proofs (rather than type by type proofs), generalize many of the finite-type results and prove new and more refined results. The key tools in our proofs include a skew-symmetric form related to (a generalization of) the Euler form of quiver theory and the projection \pidown^c mapping each element of W to the unique maximal c-sortable element below it in the weak order. The fibers of \pidown^c essentially define the c-Cambrian fan. The most fundamental results are, first, a precise statement of how sortable elements transform under (BGP) reflection functors and second, a precise description of the fibers of \pidown^c. These fundamental results and others lead to further results on the lattice theory and geometry of Cambrian (semi)lattices and Cambrian fans.Comment: This is essentially the final version, which will appear in Transactions of the AMS. Minor changes have been made in response to comments by referee

Scanning optical pyrometer for measuring temperatures in hollow cathodes

Life-limiting processes in hollow cathodes are determined largely by the temperature of the electron emitter. To support cathode life assessment, a noncontact temperature measurement technique which employs a stepper motor-driven fiber optic probe was developed. The probe is driven inside the hollow cathode and collects light radiated by the hot interior surface of the emitter. Ratio pyrometry is used to determine the axial temperature profile. Thermocouples on the orifice plate provide measurements of the external temperature during cathode operation and are used to calibrate the pyrometer system in situ with a small oven enclosing the externally heated cathode. The diagnostic method and initial measurements of the temperature distribution in a hollow cathode are discussed

Enacting Efficacy In Early Career: Narratives Of Agency, Growth, And Identity

Aim/Purpose: To explore how early career faculty in the field of higher education administration develop and enact their personal and professional identities. Background: Participants sought to understand themselves, to understand their environments and the “rules” of the academic “game,” and to reconcile conflicts between their own values and identities and the expectations and culture of their environments. Methodology: In-depth case studies of seventeen early career scholars in the field. Contribution: The participants’ experiences underscore important implications for mentoring and socialization that takes into consideration the unique motivation and identity development of aspiring and new faculty members. Findings: Identifies the early career period as one where new faculty are working to develop a strong internal foundation upon which they can manage the many challenges of their personal and professional lives. Recommendations: The findings point to implications for practice, both in graduate education and in departments hiring new faculty members

Structure of the crust and upper mantle beneath Bass Strait, southeast Australia, from teleseismic body wave tomography

© 2019 Elsevier B.V. We present new constraints on the lithospheric velocity structure of Bass Strait and the adjoining landmasses of mainland Australia and Tasmania in order to better constrain their geological and tectonic relationship. This is achieved by performing teleseismic tomography using data from fifteen deployments of WOMBAT and BASS transportable arrays, which span southeastern Australia. The starting model for the teleseismic tomography includes crustal velocity structure constrained by surface waves extracted from ambient seismic noise data and a Moho surface and broad-scale variations in 3-D upper mantle velocity structure from the Australian seismological reference Earth model (AuSREM). As a consequence, we produce a model with a high level of detail in both the crust and upper mantle. Our new results strengthen the argument for a low velocity upper mantle anomaly that extends down to ~150 km depth directly beneath the Newer Volcanics Province in Victoria, which is likely related to recent intra-plate volcanism. Beneath Bass Strait, which is thought to host the entrained VanDieland microcontinent, upper mantle velocities are low relative to those typically found beneath Precambrian continental crust; it is possible that failed rifting in Bass Strait during the Cretaceous, opening of the Tasman Sea, extension of VanDieland during Rodinian break-up and recent plume activity in the past 5 Ma may have altered the seismic character of this region. The data nevertheless suggest: (1) the velocity structure of the VanDieland microcontinent lacks continuity within its lithosphere; (2) the Moyston Fault defines an area of strong velocity transition at the boundary between the Cambrian Delamerian Orogen and the Cambrian-Carboniferous Lachlan Orogen; and (3) there is a rapid decrease in mantle velocity inboard of the east coast of Australia, which is consistent with substantial thinning of the lithosphere towards the passive margin

High-Energy Calculation of K-Shell Ejection Cross-Sections as a Function of Projectile Charge

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