1,536 research outputs found
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
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
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
Bilateral Ureteral Stenosis with Hydronephrosis as First Manifestation of Granulomatosis with Polyangiitis (Wegener's Granulomatosis): A Case Report and Review of the Literature.
Ureteral stenosis is a rare manifestation of granulomatosis with polyangiitis (formerly known as Wegener's granulomatosis). We report the case of a 76-year-old woman with progressive renal failure in which bilateral hydronephrosis due to ureteral stenosis was the first manifestation of the disease. Our patient also had renal involvement with pauci-immune crescentic glomerulonephritis associated with high titers of anti-proteinase 3 c-ANCAs, but no involvement of the upper or lower respiratory tract. The hydronephrosis and renal function rapidly improved under immunosuppressive therapy with high-dose corticosteroids and intravenous pulse cyclophosphamide. We reviewed the literature and found only ten other reported cases of granulomatosis with polyangiitis/Wegener's granulomatosis and intrinsic ureteral stenosis: in two cases, the presenting clinical manifestation was unilateral hydronephrosis and in only two others was the hydronephrosis bilateral, but this complication developed during a relapse of the disease. This case emphasizes the importance of including ANCA-related vasculitis in the differential diagnosis of unusual cases of unilateral or bilateral ureteral stenosis
Intimal lesions detected by optical coherence tomography herald intraluminal progression of cardiac allograft vasculopathy associated with humoral rejection.
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
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
Symmetric Groups and Quotient Complexity of Boolean Operations
The quotient complexity of a regular language L is the number of left
quotients of L, which is the same as the state complexity of L. Suppose that L
and L' are binary regular languages with quotient complexities m and n, and
that the transition semigroups of the minimal deterministic automata accepting
L and L' are the symmetric groups S_m and S_n of degrees m and n, respectively.
Denote by o any binary boolean operation that is not a constant and not a
function of one argument only. For m,n >= 2 with (m,n) not in
{(2,2),(3,4),(4,3),(4,4)} we prove that the quotient complexity of LoL' is mn
if and only either (a) m is not equal to n or (b) m=n and the bases (ordered
pairs of generators) of S_m and S_n are not conjugate. For (m,n)\in
{(2,2),(3,4),(4,3),(4,4)} we give examples to show that this need not hold. In
proving these results we generalize the notion of uniform minimality to direct
products of automata. We also establish a non-trivial connection between
complexity of boolean operations and group theory
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