1,547 research outputs found
A finite-temperature liquid-quasicrystal transition in a lattice model
We consider a tiling model of the two-dimensional square-lattice, where each
site is tiled with one of the sixteen Wang tiles. The ground states of this
model are all quasi-periodic. The systems undergoes a disorder to
quasi-periodicity phase transition at finite temperature. Introducing a proper
order-parameter, we study the system at criticality, and extract the critical
exponents characterizing the transition. The exponents obtained are consistent
with hyper-scaling
Bound on the multiplicity of almost complete intersections
Let be a polynomial ring over a field of characteristic zero and let be a graded ideal of height which is minimally generated by
homogeneous polynomials. If where has degree
and has height , then the multiplicity of is
bounded above by .Comment: 7 pages; to appear in Communications in Algebr
A note on the Schur multiplier of a nilpotent Lie algebra
For a nilpotent Lie algebra of dimension and dim, we find
the upper bound dim, where denotes the
Schur multiplier of . In case the equality holds if and only if
, where is an abelian Lie algebra of dimension
and H(1) is the Heisenberg algebra of dimension 3.Comment: Paper in press in Comm. Algebra with small revision
Homalg: A meta-package for homological algebra
The central notion of this work is that of a functor between categories of
finitely presented modules over so-called computable rings, i.e. rings R where
one can algorithmically solve inhomogeneous linear equations with coefficients
in R. The paper describes a way allowing one to realize such functors, e.g.
Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra
system. Once this is achieved, one can compose and derive functors and even
iterate this process without the need of any specific knowledge of these
functors. These ideas are realized in the ring independent package homalg. It
is designed to extend any computer algebra software implementing the
arithmetics of a computable ring R, as soon as the latter contains algorithms
to solve inhomogeneous linear equations with coefficients in R. Beside
explaining how this suffices, the paper describes the nature of the extensions
provided by homalg.Comment: clarified some points, added references and more interesting example
Burning Questions: Changing Legal Narratives on Cannabis in Indian Country
In the not-so-distant past, thoughts of Cannabis legalization in the United States were radical. In the present day, the narratives around Cannabis are changing. The term “present day” affixes this Article to early 2023, a snapshot in time. To understand the current legal narratives surrounding Cannabis, and what they might become in the future, it is important to examine the history of Cannabis law and policy in United States. This Article begins by discussing Cannabis regulation in the United States, from the rise of federal regulation to the gradual deregulation by states with tacit federal consent. The Article then examines the jurisdictional conflicts between tribes and states for tribes that attempt to decriminalize Cannabis on the reservation with specific attention paid to enforcement of criminal laws on reservation, regulation of commercial activity, and regulations regarding cannabis research in Indian Country. This Article then examines the recent marijuana policy statement issued by the Biden administration and current Congressional activity, including their possible implications for Cannabis in Indian Country and issues to watch. Finally, this Article concludes with a call to recognize the self-determination of tribes in establishing and enforcing their own Cannabis policies on reservation land
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