Mean Square Capacity of Power Constrained Fading Channels with Causal Encoders and Decoders

This paper is concerned with the mean square stabilization problem of discrete-time LTI systems over a power constrained fading channel. Different from existing research works, the channel considered in this paper suffers from both fading and additive noises. We allow any form of causal channel encoders/decoders, unlike linear encoders/decoders commonly studied in the literature. Sufficient conditions and necessary conditions for the mean square stabilizability are given in terms of channel parameters such as transmission power and fading and additive noise statistics in relation to the unstable eigenvalues of the open-loop system matrix. The corresponding mean square capacity of the power constrained fading channel under causal encoders/decoders is given. It is proved that this mean square capacity is smaller than the corresponding Shannon channel capacity. In the end, numerical examples are presented, which demonstrate that the causal encoders/decoders render less restrictive stabilizability conditions than those under linear encoders/decoders studied in the existing works.Comment: Accepted by the 54th IEEE Conference on Decision and Contro

Predictive CPCP Violating Relations for Charmless Two-body Decays of Beauty Baryons Ξb−, 0\Xi^{-,\;0}_b and Λb0\Lambda_b^0 With Flavor SU(3)SU(3) Symmetry

Several baryons containing a heavy b-quark have been discovered. The decays of these states provide new platform for testing the standard model (SM). We study $CP$ violation in SM for charmless two-body decays of the flavor $SU(3)$ anti-triplet beauty baryon (b-baryon) ${\cal B} = (\Xi^-_b,\;\Xi^0_b,\;\Lambda_b^0)$ in a model independent way. We found, in the flavor $SU(3)$ symmetry limit, a set of new predictive relations among the branching ratio $Br$ and $CP$ asymmetry $A_{CP}$ for $\cal B$ decays, such as $A_{CP}(\Xi_b^-\to K^0 \Xi^-)/A_{CP}(\Xi_b^-\to \bar K^0 \Sigma^-) = - Br(\Xi_b^- \to \bar K^0 \Sigma^-)/Br(\Xi_b^- \to K^0 \Sigma^-)$, $A_{CP}(\Lambda_b^0 \to \pi^- p)/A_{CP} (\Xi^0_b \to K^- \Sigma^+) = -Br(\Xi^0_b \to K^- \Sigma^+)\tau_{\Lambda_b^0}/Br(\Lambda_b^0 \to \pi^- p)\tau_{\Xi^0_b}$,and $A_{CP}(\Lambda_b^0 \to K^- p)/ A_{CP} (\Xi^0_b \to \pi^- \Sigma^+) = -Br(\Xi^0_b \to \pi^- \Sigma^+)\tau_{\Lambda_b^0}/ Br(\Lambda_b^0 \to K^- p)\tau_{\Xi^0_b}$. Future data from LHCb can test these relations and also other relations found.Comment: 13 pages, no figure, 6 tables, several missing terms in eq.11 are adde

CP violation in neutrino mixing with δ=−π/2\delta = -\pi/2 in A4A_4 Type-II seesaw model

We study a class of models for neutrino mass matrix in Type-II seesaw with $A_4$ family symmetry. The resulting neutrino mass matrix can be naturally made to respect a $\mu-\tau$ exchange plus CP conjugate symmetry (GLS) with the CP violating phase $\delta$ and the mixing angle $\theta_{23}$ predicted to be $\pm\pi/2$ and $\pi/4$, respectively. When GLS is explicitly broken by complex Yukawa couplings, the model predictions for $\delta$ and $\theta_{23}$ can be significantly modified. Should future experiments will indeed determine $\theta_{23}$ and $\delta_{CP}$ away from the GLS limit values, one then had to consider models with broken GLS. We study several simple scenarios to show how the modifications arise when GLS is broken and how future experiments can test this class of models.Comment: 15 pages, 3 figures, minor errors corrected. Version appeared in Phys.Lett.B. arXiv admin note: text overlap with arXiv:1504.0156

Economic Transition and the Motherhood Wage Penalty in Urban China: Investigation using Panel Data

China’s economic transition has fundamentally changed the mechanisms for allocating and compensating labor. This paper investigates how the economic transition has affected the wage gap between mothers and childless women in urban China using panel data for the period 1990-2005. The results show that overall, mothers earned considerably less than childless women; additionally, the wage penalties for motherhood went up substantially from the gradualist reform period (1990-1996) to the radical reform period (1999-2005). The results also show that that although motherhood does not appear to have a significant wage effect for the state sector, it imposes substantial wage losses for mothers in the non-state sector. These findings suggest that the economic transition has shifted part of the cost of child-bearing and -rearing from the state and employers back to women in the form of lower earnings for working mothers.

Some Predictions of Diquark Model for Hidden Charm Pentaquark Discovered at the LHCb

The LHCb has discovered two new states with preferred $J^P$ quantum numbers $3/2^-$ and $5/2^+$ from $\Lambda_b$ decays. These new states can be interpreted as hidden charm pentaquarks. It has been argued that the main features of these pentaquarks can be described by diquark model. The diquark model predicts that the $3/2^-$ and $5/2^+$ are in two separate octet multiplets of flavor $SU(3)$ and there is also an additional decuplet pentaquark multiplet. Finding the states in these multiplets can provide crucial evidence for this model. The weak decays of b-baryon to a light meson and a pentaquark can have Cabibbo allowed and suppressed decay channels. We find that in the $SU(3)$ limit, for $U$-spin related decay modes the ratio of the decay rates of Cabibbo suppressed to Cabibbo allowed decay channels is given by $|V_{cd}|^2/|V_{cs}|^2$. There are also other testable relations for b-baryon weak decays into a pentaquark and a light pseudoscalar. These relations can be used as tests for the diquark model for pentaquark.Comment: revtex, 19 pages, 3 figures. one reference added and some typos correcte