Matrix Realization of Gauge Theory on Discrete Group Z2Z_2

We construct a $2\times 2$ matrix algebra as representation of functions on discrete group $Z_2$ and develop the gauge theory on discrete group proposed by Starz in the matrix algebra. Accordingly, we show that the non-commutative geometry model built by R.Conquereax, G.Esposito-Farese and G.Vaillant results from this approach directly. For the purpose of Physical model building, we introduce a free fermion Lagrangian on $M_4\times Z_2$ and study Yang-Mills like gauge theory.Comment: Latex file, 10 pages, ASITP-94-

Reconstruction of SU(5) Grand Unified Model In Noncommutative Geometry Approach

Based on the generalized gauge theory on $M^4\times Z_2\times Z_3$, we reconstructed the realistic SU(5) Grand Unified model by a suitable assignment of fermion fields. The action of group elements $Z_2$ on fermion fields is the charge conjugation while the action of $Z_3$ elements represent generation translation. We find that to fit the spontaneous symmetry breaking and gauge hierarchy of SU(5) model a linear term of curvature has to be introduced. A new mass relation is obtained in our reconstructed model.Comment: 16 pages, Late

Response to Comments on PCA Based Hurst Exponent Estimator for fBm Signals Under Disturbances

In this response, we try to give a repair to our previous proof for PCA Based Hurst Exponent Estimator for fBm Signals by using orthogonal projection. Moreover, we answer the question raised recently: If a centered Gaussian process $G_t$ admits two series expansions on different Riesz bases, we may possibly study the asymptotic behavior of one eigenvalue sequence from the knowledge on the asymptotic behaviors of another.Comment: This is a response for a mistake in Li Li, Jianming Hu, Yudong Chen, Yi Zhang, PCA based Hurst exponent estimator for fBm signals under disturbances, IEEE Transactions on Signal Processing, vol. 57, no. 7, pp. 2840-2846, 200

Standard Model With Higgs As Gauge Field On Fourth Homotopy Group

Based upon a first principle, the generalized gauge principle, we construct a general model with $G_L\times G'_R \times Z_2$ gauge symmetry, where $Z_2=\pi_4(G_L)$ is the fourth homotopy group of the gauge group $G_L$, by means of the non-commutative differential geometry and reformulate the Weinberg-Salam model and the standard model with the Higgs field being a gauge field on the fourth homotopy group of their gauge groups. We show that in this approach not only the Higgs field is automatically introduced on the equal footing with ordinary Yang-Mills gauge potentials and there are no extra constraints among the parameters at the tree level but also it most importantly is stable against quantum correlation.Comment: 19 pages, Latex, ASITP-94-2