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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 Jun 1999

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 Jun 1999

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 Jan 1999

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 …


International R&D Spillovers: An Application Of Estimation And Inference In Panel Cointegration, Chihwa Kao, Min-Hsien Chiang, Bangtian Chen Jan 1999

International R&D Spillovers: An Application Of Estimation And Inference In Panel Cointegration, Chihwa Kao, Min-Hsien Chiang, Bangtian Chen

Center for Policy Research

In this paper, we apply the asymptotic theory of panel cointegration developed by Kao and Chiang (1997) to Coe and Helpman's (1995) international R&D spillovers regression. The OLS with bias-correction, the fully-modified (FM) and the dynamic OLS (DOLS) estimations produce different predictions about the impact of foreign R&D on total factor productivity (TFP), although all the estimations support the result that domestic R&D is related to TFP.


A Monte Carlo Comparison Of Tests For Cointegration In Panel Data, Chihwa Kao Jan 1999

A Monte Carlo Comparison Of Tests For Cointegration In Panel Data, Chihwa Kao

Center for Policy Research

This paper surveys recent developments and provides Monte Carlo comparison on various tests proposed for cointegration in panel data. In particular, tests for two panel models, varying intercepts and varying slopes, and varying intercepts and common slopes are presented from the literature with a total of seven tests being simulated. In all cases, results on empirical size and size-adjusted power are given.


On The Estimation And Inference Of A Cointegrated Regression In Panel Data, Chihwa Kao Jan 1999

On The Estimation And Inference Of A Cointegrated Regression In Panel Data, Chihwa Kao

Center for Policy Research

The main contribution of this paper is to add to the literature by suggesting a dynamic OLS (DOLS) estimator and providing a serious comparison of the finite sample properties of the OLS, fully modified OLS (FMOLS), and DOLS estimators in panel cointegrated regression models. Monte Carlo results illustrate the sampling behavior of the proposed estimators and show that (1) the OLS estimator has a non-negligible bias in finite samples, (2) the FMOLS estimator does not improve over the OLS estimator in general, and (3) the DOLS outperforms both the OLS and FMOLS estimators.


On The Estimation Of A Linear Time Trend Regression With A One-Way Error Component Model In The Presence Of Serially Correlated Errors, Chihwa Kao, Jamie Emerson Jan 1999

On The Estimation Of A Linear Time Trend Regression With A One-Way Error Component Model In The Presence Of Serially Correlated Errors, Chihwa Kao, Jamie Emerson

Center for Policy Research

In this paper we study the limiting distributions for ordinary least squares (OLS), fixed effects (FE), first difference (FD), and generalized least squares (GLS) estimators in a linear time trend regression with a one-way error component model in the presence of serially correlated errors. We show that when the error term is I(0), the FE is asymptotically equivalent to the GLS. However, when the error term is I(1) the GLS could be less efficient than the FD or FE estimators, and the FD is the most efficient estimator. However, when the intercept is included in the model and the error …