5,251 research outputs found
Toric rings, inseparability and rigidity
This article provides the basic algebraic background on infinitesimal
deformations and presents the proof of the well-known fact that the non-trivial
infinitesimal deformations of a -algebra are parameterized by the
elements of cotangent module of . In this article we focus on
deformations of toric rings, and give an explicit description of in
the case that is a toric ring.
In particular, we are interested in unobstructed deformations which preserve
the toric structure. Such deformations we call separations. Toric rings which
do not admit any separation are called inseparable. We apply the theory to the
edge ring of a finite graph. The coordinate ring of a convex polyomino may be
viewed as the edge ring of a special class of bipartite graphs. It is shown
that the coordinate ring of any convex polyomino is inseparable. We introduce
the concept of semi-rigidity, and give a combinatorial description of the
graphs whose edge ring is semi-rigid. The results are applied to show that for
, is not rigid while for , is
rigid. Here is the complete bipartite graph with one
edge removed.Comment: 33 pages, chapter 2 of the Book << Multigraded Algebra and
Applications>> 2018, Springer International Publishing AG, part of Springer
Natur
Torus invariant divisors
Using the language of polyhedral divisors and divisorial fans we describe
invariant divisors on normal varieties X which admit an effective codimension
one torus action. In this picture X is given by a divisorial fan on a smooth
projective curve Y. Cartier divisors on X can be described by piecewise affine
functions h on the divisorial fan S whereas Weil divisors correspond to certain
zero and one dimensional faces of it. Furthermore we provide descriptions of
the divisor class group and the canonical divisor. Global sections of line
bundles O(D_h) will be determined by a subset of a weight polytope associated
to h, and global sections of specific line bundles on the underlying curve Y.Comment: 16 pages; 5 pictures; small changes in the layout, further typos
remove
Nontwist non-Hamiltonian systems
We show that the nontwist phenomena previously observed in Hamiltonian
systems exist also in time-reversible non-Hamiltonian systems. In particular,
we study the two standard collision/reconnection scenarios and we compute the
parameter space breakup diagram of the shearless torus. Besides the Hamiltonian
routes, the breakup may occur due to the onset of attractors. We study these
phenomena in coupled phase oscillators and in non-area-preserving maps.Comment: 7 pages, 5 figure
Non-Hamiltonian dynamics in optical microcavities resulting from wave-inspired corrections to geometric optics
We introduce and investigate billiard systems with an adjusted ray dynamics
that accounts for modifications of the conventional reflection of rays due to
universal wave effects. We show that even small modifications of the specular
reflection law have dramatic consequences on the phase space of classical
billiards. These include the creation of regions of non-Hamiltonian dynamics,
the breakdown of symmetries, and changes in the stability and morphology of
periodic orbits. Focusing on optical microcavities, we show that our adjusted
dynamics provides the missing ray counterpart to previously observed wave
phenomena and we describe how to observe its signatures in experiments. Our
findings also apply to acoustic and ultrasound waves and are important in all
situations where wavelengths are comparable to system sizes, an increasingly
likely situation considering the systematic reduction of the size of electronic
and photonic devices.Comment: 6 pages, 4 figures, final published versio
Affine T-varieties of complexity one and locally nilpotent derivations
Let X=spec A be a normal affine variety over an algebraically closed field k
of characteristic 0 endowed with an effective action of a torus T of dimension
n. Let also D be a homogeneous locally nilpotent derivation on the normal
affine Z^n-graded domain A, so that D generates a k_+-action on X that is
normalized by the T-action. We provide a complete classification of pairs (X,D)
in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1.
This generalizes previously known results for surfaces due to Flenner and
Zaidenberg. As an application we compute the homogeneous Makar-Limanov
invariant of such varieties. In particular we exhibit a family of non-rational
varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo
Metrical structure and the perception of time-compressed speech
In the absence of explicitly marked cues to word boundaries, listeners tend to segment spoken English at the onset of strong syllables. This may suggest that under difficult listening conditions, speech should be easier to recognize where strong syllables are word-initial. We report two experiments in which listeners were presented with sentences which had been time-compressed to make listening difficult. The first study contrasted sentences in which all content words began with strong syllables with sentences in which all content words began with weak syllables. The intelligibility of the two groups of sentences did not differ significantly. Apparent rhythmic effects in the results prompted a second experiment; however, no significant effects of systematic rhythmic manipulation were observed. In both experiments, the strongest predictor of intelligibility was the rated plausibility of the sentences. We conclude that listeners' recognition responses to time-compressed speech may be strongly subject to experiential bias; effects of rhythmic structure are most likely to show up also as bias effects
The -Region of Shadowing Corrections in Nucleon Structure Functions
We discuss the experimental indications on the behaviour of F_2(x,Q^2) at
small x both in proton and nuclear targets. By comparing the parametrizations
of the data we conclude that shadowing correction effects in a proton target
can appear at a noticeable level for x=(2 - 4)\times10^{-4} and Q^2\sim 10^1
GeV^2, namely inside the HERA regime.Comment: 5 pages, Latex, no figure
- …