Super-rigidity for CR embeddings of real hypersurfaces into hyperquadrics

Let Q^N_l\subset \bC\bP^{N+1} denote the standard real, nondegenerate hyperquadric of signature $l$ and M\subset \bC^{n+1} a real, Levi nondegenerate hypersurface of the same signature $l$. We shall assume that there is a holomorphic mapping H_0\colon U\to \bC\bP^{N_0+1}, where $U$ is some neighborhood of $M$ in \bC^{n+1}, such that $H_0(M)\subset Q^{N_0}_l$ but $H(U)\not\subset Q^{N_0}_l$. We show that if $N_0-n<l$ then, for any $N\geq N_0$, any holomorphic mapping H\colon U\to \bC\bP^{N+1} with $H(M)\subset Q^{N}_l$ and $H(U)\not\subset Q^{N_0}_l$ must be the standard linear embedding of $Q^{N_0}_l$ into $Q^N_l$ up to conjugation by automorphisms of $Q^{N_0}_l$ and $Q^N_l$

A review of personal communications services

This article can be accessed from the link below - Copyright @ 2009 Nova Science Publishers, LtdPCS is an acronym for Personal Communications Service. PCS has two layers of meaning. At the low layer, from the technical perspective, PCS is a 2G mobile communication technology operating at the 1900 MHz frequency range. At the upper layer, PCS is often used as an umbrella term that includes various wireless access and personal mobility services with the ultimate goal of enabling users to freely communicate with anyone at anytime and anywhere according to their demand. Ubiquitous PCS can be implemented by integrating the wireless and wireline systems on the basis of intelligent network (IN), which provides network functions of terminal and personal mobility. In this chapter, we focus on various aspects of PCS except location management. First we describe the motivation and technological evolution for personal communications. Then we introduce three key issues related to PCS: spectrum allocation, mobility, and standardization efforts. Since PCS involves several different communication technologies, we introduce its heterogeneous and distributed system architecture. IN is also described in detail because it plays a critical role in the development of PCS. Finally, we introduce the application of PCS and its deployment status since the mid-term of 1990’s.This work was supported in part by the National Natural Science Foundation of China under Grant No. 60673159 and 70671020; the National High-Tech Research and Development Plan of China under Grant No. 2006AA01Z214, and the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1

Multivariate adaptive regression splines for estimating riverine constituent concentrations

Regression-based methods are commonly used for riverine constituent concentration/flux estimation, which is essential for guiding water quality protection practices and environmental decision making. This paper developed a multivariate adaptive regression splines model for estimating riverine constituent concentrations (MARS-EC). The process, interpretability and flexibility of the MARS-EC modelling approach, was demonstrated for total nitrogen in the Patuxent River, a major river input to Chesapeake Bay. Model accuracy and uncertainty of the MARS-EC approach was further analysed using nitrate plus nitrite datasets from eight tributary rivers to Chesapeake Bay. Results showed that the MARS-EC approach integrated the advantages of both parametric and nonparametric regression methods, and model accuracy was demonstrated to be superior to the traditionally used ESTIMATOR model. MARS-EC is flexible and allows consideration of auxiliary variables; the variables and interactions can be selected automatically. MARS-EC does not constrain concentration-predictor curves to be constant but rather is able to identify shifts in these curves from mathematical expressions and visual graphics. The MARS-EC approach provides an effective and complementary tool along with existing approaches for estimating riverine constituent concentrations

Entropy and specific heat for open systems in steady states

The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics can be built. In this paper, we show that the Boltzmann distribution in general can not describe the steady state of open system. Based on the effective Hamiltonian approach, we calculate the specific heat, the free energy and the entropy for an open system in steady states. Examples are illustrated and discussed.Comment: 4 pages, 7 figure