Fast Arithmetics Using Chinese Remaindering

In this paper, some issues concerning the Chinese remaindering representation are discussed. Some new converting methods, including an efficient probabilistic algorithm based on a recent result of von zur Gathen and Shparlinski \cite{Gathen-Shparlinski}, are described. An efficient refinement of the NC$^1$ division algorithm of Chiu, Davida and Litow \cite{Chiu-Davida-Litow} is given, where the number of moduli is reduced by a factor of $\log n$

Form and index of Ginsparg-Wilson fermions

We clarify the questions rised by a recent example of a lattice Dirac operator found by Chiu. We show that this operator belongs to a class based on the Cayley transformation and that this class on the finite lattice generally does not admit a nonvanishing index, while in the continuum limit, due to operator properties in Hilbert space, this defect is no longer there. Analogous observations are made for the chiral anomaly. We also elaborate on various aspects of the underlying sum rule for the index.Comment: 10 pages; v2: equation corrected, conclusions unchange

Ginsparg-Wilson relation with R=(a \gamma_5 D)^{2k}

The Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$ with $R = (a \gamma_5 D)^{2k}$ is discussed. An explicit realization of D is constructed. It is shown that this sequence of topologically-proper lattice Dirac operators tend to a nonlocal operator in the limit $k \to \infty$. This suggests that the locality of a lattice Dirac operator is irrelevant to its index.Comment: 4 pages, 1 EPS figure, talk presented at Lattice'00 (Chiral Fermion

Some remarks on the Ginsparg-Wilson fermion

We note that Fujikawa's proposal of generalization of the Ginsparg-Wilson relation is equivalent to setting $R = (a \gamma_5 D)^{2k}$ in the original Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$. An explicit realization of D follows from the Overlap construction. The general properties of D are derived. The chiral properties of these higher-order (k > 0) realizations of Overlap Dirac operator are compared to those of the Neuberger-Dirac operator (k = 0), in terms of the fermion propagator, the axial anomaly and the fermion determinant in a background gauge field. Our present results (up to lattice size 16 x 16) indicate that the chiral properties of the Neuberger-Dirac operator are better than those of higher-order ones.Comment: 20 pages, minor changes in v3, to appear in Nucl. Phys.

Democracy without Autonomy: Moral and Personal Autonomy in Democratic Confucianism

Given contemporary international ethical and political norms, a viable democratic Confucianism must contend with the importance of autonomy. Joseph Chan’s modern reconstruction of Confucianism, in Confucian Perfectionism: A Political Philosophy for Modern Times, is one of the leading conceptions of neo-Confucianism, and claims to accept some forms of moral autonomy, while finding that personal autonomy not necessary for the Confucian democratic project. I argue that his modern Confucian perfectionism in fact does the opposite: it lacks genuine moral autonomy while relying on the exercise of personal autonomy. The respective absence and presence of moral and personal autonomy raises doubts about how Confucianism and democracy can be reconciled, if at all.published_or_final_versio

THE IMPACT ACCELERATION ON THE BILATERAL TIBIA DURING TREADMILL RUNNING

The purpose of this study was to investigate the changes of the impact acceleration on the left and right tibia during treadmill running for experienced treadmill runners. The bilateral tibial accelerations of 14 subjects were measured during thirty-minutes of running at their preferred speed. Acceleration data was collected every 5 minutes for 30 seconds. There were no significant statistical differences in the peak tibial accelerations during thirty-minutes of treadmill running. The results showed that five subjects had greater right peak tibial accelerations and two subjects had greater left peak tibial accelerations. Experienced treadmill runners seemed to choose their preferred speed at that which they can run for thirty minutes and eventually there was no significant increase in the peak tibial accelerations