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Full-Text Articles in Mathematics
Resolutions Of Subsets Of Finite Sets Of Points In Projective Space, Steven P. Diaz, Anthony V. Geramita, Juan C. Migliore
Resolutions Of Subsets Of Finite Sets Of Points In Projective Space, Steven P. Diaz, Anthony V. Geramita, Juan C. Migliore
Mathematics - All Scholarship
Given a finite set, X, of points in projective space for which the Hilbert function is known, a standard result says that there exists a subset of this finite set whose Hilbert function is "as big as possible'' inside X. Given a finite set of points in projective space for which the minimal free resolution of its homogeneous ideal is known, what can be said about possible resolutions of ideals of subsets of this finite set? We first give a maximal rank type description of the most generic possible resolution of a subset. Then we show that this generic resolution …
On-Off Intermittency In Stochastically Driven Electrohydrodynamic Convection In Nematics, Thomas John, Ralf Stannarius, Ulrich Behn
On-Off Intermittency In Stochastically Driven Electrohydrodynamic Convection In Nematics, Thomas John, Ralf Stannarius, Ulrich Behn
Mathematics - All Scholarship
We report on-off intermittency in electroconvection of nematic liquid crystals driven by a dichotomous stochastic electric voltage. With increasing voltage amplitude we observe laminar phases of undistorted director state interrupted by shorter bursts of spatially regular stripes. Near a critical value of the amplitude the distribution of the duration of laminar phases is governed over several decades by a power law with exponent -3/2. The experimental findings agree with simulations of the linearized electrohydrodynamic equations near the sample stability threshold.
Recurrence And Ergodicity Of Interacting Particle Systems, J. Theodore Cox, Achim Klenke
Recurrence And Ergodicity Of Interacting Particle Systems, J. Theodore Cox, Achim Klenke
Mathematics - All Scholarship
Many interacting particle systems with short range interactions are not ergodic, but converge weakly towards a mixture of their ergodic invariant measures. The question arises whether a.s. the process eventually stays close to one of these ergodic states, or if it changes between the attainable ergodic states infinitely often ("recurrence"). Under the assumption that there exists a convergence--determining class of distributions that is (strongly) preserved under the dynamics, we show that the system is in fact recurrent in the above sense. We apply our method to several interacting particle systems, obtaining new or improved recurrence results. In addition, we answer …