14,473 research outputs found
Interpolating Between Hilbert-Samuel and Hilbert-Kunz Multiplicity
We define a function, called s-multiplicity, that interpolates between
Hilbert-Samuel multiplicity and Hilbert-Kunz multiplicity by comparing powers
of ideals to the Frobenius powers of ideals. The function is continuous in s,
and its value is equal to Hilbert-Samuel multiplicity for small values of s and
is equal to Hilbert-Kunz multiplicity for large values of s. We prove that it
has an Associativity Formula generalizing the Associativity Formulas for
Hilbert-Samuel and Hilbert-Kunz multiplicity. We also define a family of
closures such that if two ideals have the same s-closure then they have the
same s-multiplicity, and the converse holds under mild conditions. We describe
the s-multiplicity of monomial ideals in toric rings as a certain volume in
real spaceComment: 19 page
The Supreme Court and Recent School Desegregation Cases: The Role of Social Science in a Period of Judicial Retrenchment
Through an analysis of the Supreme Court\u27s post-1973 rulings, argues that the Court has not repudiated any doctrine that it had adopted Before 1973 but has exhibited a reluctance to extend previously announced legal principles to claims for new remedies
Non-conformal entanglement entropy
We explore the behaviour of renormalized entanglement entropy in a variety of
holographic models: non-conformal branes; the Witten model for QCD; UV
conformal RG flows driven by explicit and spontaneous symmetry breaking and
Schr\"odinger geometries. Focussing on slab entangling regions, we find that
the renormalized entanglement entropy captures features of the previously
defined entropic c-function but also captures deep IR behaviour that is not
seen by the c-function. In particular, in theories with symmetry breaking, the
renormalized entanglement entropy saturates for large entangling regions to
values that are controlled by the symmetry breaking parameters.Comment: 33 pages, 4 figure
The holographic F theorem
The F theorem states that, for a unitary three dimensional quantum field
theory, the F quantity defined in terms of the partition function on a three
sphere is positive, stationary at fixed point and decreases monotonically along
a renormalization group flow. We construct holographic renormalization group
flows corresponding to relevant deformations of three-dimensional conformal
field theories on spheres, working to quadratic order in the source. For these
renormalization group flows, the F quantity at the IR fixed point is always
less than F at the UV fixed point, but F increases along the RG flow for
deformations by operators of dimension . Therefore the
strongest version of the F theorem is in general violated
Inhomogeneity simplified
We study models of translational symmetry breaking in which inhomogeneous
matter field profiles can be engineered in such a way that black brane metrics
remain isotropic and homogeneous. We explore novel Lagrangians involving square
root terms and show how these are related to massive gravity models and to
tensionless limits of branes. Analytic expressions for the DC conductivity and
for the low frequency scaling of the optical conductivity in phenomenological
models are derived, and the optical conductivity is studied in detail
numerically. The square root Lagrangians are associated with linear growth in
the DC resistivity with temperature and also lead to minima in the optical
conductivity at finite frequency, suggesting that our models may capture many
features of heavy fermion systems.Comment: 58 pages; v2 references adde
Real deal or no deal? A comparative analysis of raw milk cheese regulation in Australia and France
Australia’s regulatory framework has resulted in the standardisation of cheese production based on pasteurisation. Up until early 2015, regulations effectively prohibited raw milk cheese-making in Australia and thus stifled artisanal on-farm production. Although the introduction of Food Standards Australia New Zealand Standard 4.2.4 has allowed the production of certain hard, low-moisture raw milk cheeses, the new standard is rigid and does not encourage new entrants into the emerging raw milk cheese consumer market. This article compares the Australian system with the French raw milk cheese regulation and production system, and argues that its approach in encouraging and supporting small farmhouse artisanal traditional raw milk cheese is beneficial to both producer and consumer, and has not resulted in any significant health risks. The Australian approach amounts to a missed opportunity to encourage the emergence of a value-added industry with local and export potential, and is at odds with important movements in food policy, such as recognition of the value of localism and terroir
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