10,870 research outputs found

    Classification of multiplicity free quasi-Hamiltonian manifolds

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    A quasi-Hamiltonian manifold is called multiplicity free if all of its symplectic reductions are 0-dimensional. In this paper, we classify compact, multiplicity free, twisted quasi-Hamiltonian manifolds for simply connected, compact Lie groups. Thereby, we recover old and find new examples of these structures.Comment: v1: 35 pages, this is a complete revision of arxiv:1612.03843. Since some omitted parts have already been cited, I opted for a new submission under a new title. v2: 39 pages, revised according to the advice of a very helpful refere

    Towards A Practical High-Assurance Systems Programming Language

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    Writing correct and performant low-level systems code is a notoriously demanding job, even for experienced developers. To make the matter worse, formally reasoning about their correctness properties introduces yet another level of complexity to the task. It requires considerable expertise in both systems programming and formal verification. The development can be extremely costly due to the sheer complexity of the systems and the nuances in them, if not assisted with appropriate tools that provide abstraction and automation. Cogent is designed to alleviate the burden on developers when writing and verifying systems code. It is a high-level functional language with a certifying compiler, which automatically proves the correctness of the compiled code and also provides a purely functional abstraction of the low-level program to the developer. Equational reasoning techniques can then be used to prove functional correctness properties of the program on top of this abstract semantics, which is notably less laborious than directly verifying the C code. To make Cogent a more approachable and effective tool for developing real-world systems, we further strengthen the framework by extending the core language and its ecosystem. Specifically, we enrich the language to allow users to control the memory representation of algebraic data types, while retaining the automatic proof with a data layout refinement calculus. We repurpose existing tools in a novel way and develop an intuitive foreign function interface, which provides users a seamless experience when using Cogent in conjunction with native C. We augment the Cogent ecosystem with a property-based testing framework, which helps developers better understand the impact formal verification has on their programs and enables a progressive approach to producing high-assurance systems. Finally we explore refinement type systems, which we plan to incorporate into Cogent for more expressiveness and better integration of systems programmers with the verification process

    Beam scanning by liquid-crystal biasing in a modified SIW structure

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    A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium

    Harder's conjecture II

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    Let ff be a primitive form of weight 2k+j−22k+j-2 for SL2(Z)SL_2(Z), and let p\mathfrak p be a prime ideal of the Hecke field of ff. We denote by SPm(Z)SP_m(Z) the Siegel modular group of degree mm. Suppose that k≡0mod  2, j≡0mod  4k \equiv 0 \mod 2, \ j \equiv 0 \mod 4 and that p\mathfrak p divides the algebraic part of L(k+j,f)L(k+j,f). Put k=(k+j/2,k+j/2,j/2+4,j/2+4){\bf k}=(k+j/2,k+j/2,j/2+4,j/2+4). Then under certain mild conditions, we prove that there exists a Hecke eigenform FF in the space of modular forms of weight (k+j,k)(k+j,k) for SP2(Z)SP_2(Z) such that [I2(f)]k[I_2(f)]^{\bf k} is congruent to A4(I)(F)A^{(I)}_4(F) modulo p\mathfrak p. Here, [I2(f)]k[I_2(f)]^{\bf k} is the Klingen-Eisenstein lift of the Saito-Kurokawa lift I2(f)I_2(f) of ff to the space of modular forms of weight k{\bf k} for SP4(Z)SP_4(Z), and A4(I)(F)A^{(I)}_4(F) is a certain lift of FF to the space of cusp forms of weight k{\bf k} for SP4(Z)SP_4(Z). As an application, we prove Harder's conjecture on the congruence between the Hecke eigenvalues of FF and some quantities related to the Hecke eigenvalues of ff

    On the representation theory of Schur algebras in type BB

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    We study the representation theory of the type B Schur algebra Ln(m)\mathcal{L}^n(m) with unequal parameters introduced in work of Lai, Nakano and Xiang. For generic values of q,Qq,Q, this algebra is semi-simple and Morita equivalent to the Hecke algebra, but for special values, its category of modules is more complicated. We study this representation theory by comparison with the cyclotomic qq-Schur algebra of Dipper, James and Mathas, and use this to construct a cellular algebra structure on Ln(m)\mathcal{L}^n(m). This allows us to index the simple Ln(m)\mathcal{L}^n(m)-modules as a subset of the set of bipartitions of nn. For mm large, this will be all bipartitions of nn if and only if Ln(m)\mathcal{L}^n(m) is quasi-hereditary, in which case, Ln(m)\mathcal{L}^n(m) is Morita equivalent to the cyclotomic qq-Schur algebra. We prove a modified version of a conjecture of Lai, Nakano and Xiang giving the values of (q,Q)(q,Q) where this holds: if mm is large and odd, Q≠−qkQ\neq -q^k for all kk satisfying 4−n2≤k<n\frac{4-n}{2}\leq k<n; if mm is large and even, Q≠−qkQ\neq -q^k for all kk satisfying −n<k<n.-n<k<n. We also prove two strengthenings of this result: an indexing of the simple modules when qq is not a root of unity, and a characterization of the quasi-hereditary blocks of Ln(m)\mathcal{L}^n(m).Comment: preliminary version, comments welcom

    Geometric G-functions and Atypicality

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    We describe a general method for giving pp-adic interpretations of GG-functions arising from degenerating periods of smooth projective algebraic varieties. Using this, we are able to implement a strategy due to Andr\'e for bounding heights of moduli points where period functions acquire unusual algebraic relations. This leads to new results on Galois lower bounds for special moduli, and new cases of the Zilber-Pink conjecture. In particular, we establish the first Galois-orbit lower bounds on CM moduli in non-Shimura settings. As a more technical contribution, we introduce a refinement of the Pila-Zannier strategy capable of handling Zilber-Pink-type atypical intersection problems in arbitrary dimension and for arbitrary smooth projective families.Comment: v2: Updated and streamlined introduction, giving a clearer explanation of proof strategy and ideas. Significant updates to section 7.2, including a discussion on Hodge-theoretic Siegel sets, orbits of Siegel sets on Hodge-theoretic idempotents, and a height theorem for such orbits. The last of these replaces a mistaken Siegel-set argument in the previous version. Other smaller changes/fixe

    Some Properties of Internal Locale Morphisms Externalised

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    We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise those morphisms of internal locales that induce surjective geometric morphisms and geometric embeddings, demonstrating that both can be computed `pointwise'. We also show that the co-frame operations on the co-frame of internal sublocales can also be computed `pointwise' too.Comment: 46 pages. Updated version for submission. New sections on examples and applications, in addition to general improvement

    2023-2024 Boise State University Undergraduate Catalog

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    This catalog is primarily for and directed at students. However, it serves many audiences, such as high school counselors, academic advisors, and the public. In this catalog you will find an overview of Boise State University and information on admission, registration, grades, tuition and fees, financial aid, housing, student services, and other important policies and procedures. However, most of this catalog is devoted to describing the various programs and courses offered at Boise State
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