Degenerate principal series representations and their holomorphic extensions

AbstractLet X=H/L be an irreducible real bounded symmetric domain realized as a real form in an Hermitian symmetric domain D=G/K. The intersection S of the Shilov boundary of D with X defines a distinguished subset of the topological boundary of X and is invariant under H. It can be realized as S=H/P for certain parabolic subgroup P of H. We study the spherical representations IndPH(λ) of H induced from P. We find formulas for the spherical functions in terms of the Macdonald F12 hypergeometric function. This generalizes the earlier result of Faraut–Koranyi for Hermitian symmetric spaces D. We consider a class of H-invariant integral intertwining operators from the representations IndPH(λ) on L2(S) to the holomorphic representations of G restricted to H. We construct a new class of complementary series for the groups H=SO(n,m), SU(n,m) (with n−m>2) and Sp(n,m) (with n−m>1). We realize them as discrete components in the branching rule of the analytic continuation of the holomorphic discrete series of G=SU(n,m), SU(n,m)×SU(n,m) and SU(2n,2m) respectively

On cost-effective communication network designing

How to efficiently design a communication network is a paramount task for network designing and engineering. It is, however, not a single objective optimization process as perceived by most previous researches, i.e., to maximize its transmission capacity, but a multi-objective optimization process, with lowering its cost to be another important objective. These two objectives are often contradictive in that optimizing one objective may deteriorate the other. After a deep investigation of the impact that network topology, node capability scheme and routing algorithm as well as their interplays have on the two objectives, this letter presents a systematic approach to achieve a cost-effective design by carefully choosing the three designing aspects. Only when routing algorithm and node capability scheme are elegantly chosen can BA-like scale-free networks have the potential of achieving good tradeoff between the two objectives. Random networks, on the other hand, have the built-in character for a cost-effective design, especially when other aspects cannot be determined beforehand.Comment: 6 pages, 4 figure

Using Microsatellites to Assess Genetic Variation in a Selective Breeding Program of Chinese Bay Scallop (Argopecten irradians irradians)

This study aimed to improve our understanding of the genetics of the Chinese bay scallop (Argopecten irradians irradians), one of the most important maricultured shellfish in China. Ten polymorphic microsatellite loci were examined to assess the allelic diversity, heterozygosity, and genetic variation between two domesticated populations selected for fast growth in breeding programs, and their base population. Forty-one alleles were found throughout the loci and the mean number of alleles per locus ranged 3.30-3.50. The average heterozygosity ranged 0.38-0.45, whereas the polyamorphic information content ranged 0.1504-0.7518. Genetic differences between the three populations were detected based on the number of alleles per locus, effective number of alleles, Shannon index, inbreeding coefficient (Fis), p values, genetic distance, and pairwise Fst values. There was no significant loss of genetic variability in the breeding program but changes in gene frequencies were detectable over the populations, implying that thea loci were saffected by the pressures of selective culture

A derivative formula for the free energy function

We consider bond percolation on the ${\bf Z}^d$ lattice. Let $M_n$ be the number of open clusters in $B(n)=[-n, n]^d$. It is well known that $E_pM_n / (2n+1)^d$ converges to the free energy function $\kappa(p)$ at the zero field. In this paper, we show that $\sigma^2_p(M_n)/(2n+1)^d$ converges to $-(p^2(1-p)+p(1-p)^2)\kappa'(p)$.Comment: 8 pages 1 figur

Understanding the performance of the electric power industry in China

© 2012 The Earth Institute at Columbia University and the Massachusetts Institute of Technology.Despite three decades of reform, China's electricity sector is still organized by a “new reformed plan” where capacity investment has been liberalized but prices and production remain controlled. This paper examines the impact of the current plan prices on end-users with reference to the OECD and how the plan price of electricity supply is formed. We argue that the plan price is set in an attempt to balance the interests of the public and the power industry. We find that China's industries do not pay a cheaper price for electricity than the West, and the plan price is formed through bargain between the firm and the state, which allows the firm to have a soft price constraint on its costs

Precise Algorithm to Generate Random Sequential Addition of Hard Hyperspheres at Saturation

Random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time {\it saturation} limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for near-saturation configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. Uche, and F.~H. Stillinger, Phys. Rev. E {\bf 74}, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space using finite computational time with heretofore unattained precision and across the widest range of dimensions ($2 \le d \le 8$). We have also calculated the packing and covering densities, pair correlation function $g_2(r)$ and structure factor $S(k)$ of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed "decorrelation" principle, and the degree of "hyperuniformity" (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average Voronoi cell. Our algorithm is easily generalizable to generate saturated RSA packings of nonspherical particles