Quiver Varieties, Category O for Rational Cherednik Algebras, and Hecke Algebras

We relate the representations of the rational Cherednik algebras associated with the complex reflection group µℓ ≀ Sn to sheaves on Nakajima quiver varieties associated with extended Dynkin graphs via a Z-algebra construction. This is done so that as the parameters defining the Cherednik algebra vary, the stability conditions defining the quiver variety change. This construction motivates us to use the geometry of the quiver varieties to interpret the ordering function (the c-function) used to define a highest weight structure on category O of the Cherednik algebra. This interpretation provides a natural partial ordering on O which we expect will respect the highest weight structure. This partial ordering has appeared in a conjecture of Yvonne on the composition factors in O and so our results provide a small step towards a geometric picture for that. We also interpret geometrically another ordering function (the a-function) used in the study of Hecke algebras. (The connection between Cherednik algebras and Hecke algebras is provided by the KZ-functor.) This is related to a conjecture of Bonnafé and Geck on equivalence classes of weight functions for Hecke algebras with unequal parameters since the classes should (and do for type B) correspond to the G.I.T. chambers defining the quiver varieties. As a result anything that can be defined via the quiver varieties

Federal Corporate Law, Federalism, and the Federal Courts

To parallelize a sequential source code, a parallelization strategy must be defined that transforms the sequential source code into an equivalent parallel version. Since parallelizing compilers can sometimes transform sequential loops and other well-structured codes into parallel ones automatically, we are interested in finding a solution to parallelize semi-automatically codes that compilers are not able to parallelize automatically, mostly because of weakness of classical data and control dependence analysis, in order to simplify the process of transforming the codes for programmers.Invasive Interactive Parallelization (IIP) hypothesizes that by using anintelligent system that guides the user through an interactive process one can boost parallelization in the above direction. The intelligent system's guidance relies on a classical code analysis and pre-defined parallelizing transformation sequences. To support its main hypothesis, IIP suggests to encode parallelizing transformation sequences in terms of IIP parallelization strategies that dictate default ways to parallelize various code patterns by using facts which have been obtained both from classical source code analysis and directly from the user.In this project, we investigate how automated reasoning can supportthe IIP method in order to parallelize a sequential code with an acceptable performance but faster than manual parallelization. We have looked at two special problem areas: Divide and conquer algorithms and loops in the source codes. Our focus is on parallelizing four sequential legacy C programs such as: Quick sort, Merge sort, Jacobi method and Matrix multipliation and summation for both OpenMP and MPI environment by developing an interactive parallelizing assistance tool that provides users with the assistanceneeded for parallelizing a sequential source code

\u3cem\u3eYoungstown\u3c/em\u3e, \u3cem\u3eHamdan\u3c/em\u3e, and Inherent Emergency Presidential Policymaking Powers

This brief article explores the contribution that Hamdan v Rumsfeld may have made to clarifying what should happen in the large interstices of the rules created by the Youngstown case for determining the validity of claims of Presidential power. It offers its own view of the scope of Presidential powers in extreme emergencies involving the incapacitation of the legislative branch

Wikis in Tuple Spaces

We consider storing the pages of a wiki in a tuple space and the effects this might have on the wiki experience. In particular, wiki pages are stored in tuples with a few identifying values such as title, author, revision date, content, etc. and pages are retrieved by sending the tuple space templates, such as one that gives the title but nothing else, leaving the tuple space to resolve to a single tuple. We use a tuple space wiki to avoid deadlocks, infinite loops, and wasted efforts when page edit contention arises and examine how a tuple space wiki changes the wiki experience.Comment: To appear at WMSCI 200

Mount Pleasant Cottage Union Free School District and Mount Pleasant Cottage School Association of Teachers

In the matter of the fact-finding between the Mount Pleasant Cottage Union Free School District, employer, and the Mount Pleasant Cottage School Association of Teachers, union. PERB case no. M2013-227. Before: Melinda G. Gordon, Esq., fact finder.M2013_227.pdf: 33 downloads, before Oct. 1, 2020

Applications of quantum message sealing

In 2003, Bechmann-Pasquinucci introduced the concept of quantum seals, a quantum analogue to wax seals used to close letters and envelopes. Since then, some improvements on the method have been found. We first review the current quantum sealing techniques, then introduce and discuss potential applications of quantum message sealing, and conclude with some discussion of the limitations of quantum seals.Comment: Presented as SPIE paper 5815-25 at Quantum Information and Computation III, part of the SPIE Defense & Security Symposium 200

Dynamical control of quantum state transfer within hybrid open systems

We analyze quantum state-transfer optimization within hybrid open systems, from a "noisy" (write-in) qubit to its "quiet" counterpart (storage qubit). Intriguing interplay is revealed between our ability to avoid bath-induced errors that profoundly depend on the bath-memory time and the limitations imposed by leakage out of the operational subspace. Counterintuitively, under no circumstances is the fastest transfer optimal (for a given transfer energy)

A study of exhaust noise as it relates to the turbofan engine

Prediction formula for sound generating mechanism of turbofan engine exhaus