Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterisations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained.Comment: LaTex 18 pages, to appear in J. Math. Phys. (To compile, need pb-diagram.sty, pb-lams.sty, pb-xy.sty and lamsarrow.sty

Internet-induced marketing techniques: Critical factors in viral marketing campaigns

The rapid diffusion of the Internet and the emergence of various social constructs facilitated by Internet technologies are changing the drivers that define how marketing techniques are developed and refined. This paper identifies critical factors for viral marketing, an Internet-based ‘word-of-mouth’ marketing technique. Based on existing knowledge, five types of viral marketing factors that may critically influence the success of viral marketing campaigns are identified. These factors are the overall structure of the campaign, the characteristics of the product or service, the content of the message, the characteristics of the diffusion and, the peer-to-peer information conduit. The paper discusses three examples of viral marketing campaigns and identifies the specific factors in each case that influence its success. The paper concludes with a viral marketing typology differentiating between viral marketing communications, unintended viral marketing and commercial viral marketing. This is still a rapidly evolving area and further research is clearly needed to monitor new developments and make sense of the radical changes these developments bring to the market

Coronal Electron Confinement by Double Layers

In observations of flare-heated electrons in the solar corona, a longstanding problem is the unexplained prolonged lifetime of the electrons compared to their transit time across the source. This suggests confinement. Recent particle-in-cell (PIC) simulations, which explored the transport of pre-accelerated hot electrons through ambient cold plasma, showed that the formation of a highly localized electrostatic potential drop, in the form of a double layer (DL), significantly inhibited the transport of hot electrons (T.C. Li, J.F. Drake, and M. Swisdak, 2012, ApJ, 757, 20). The effectiveness of confinement by a DL is linked to the strength of the DL as defined by its potential drop. In this work, we investigate the scaling of the DL strength with the hot electron temperature by PIC simulations, and find a linear scaling. We demonstrate that the strength is limited by the formation of parallel shocks. Based on this, we analytically determine the maximum DL strength, and find also a linear scaling with the hot electron temperature. The DL strength obtained from the analytic calculation is comparable to that from the simulations. At the maximum strength, the DL is capable of confining a significant fraction of hot electrons in the source

X(1812) in Quarkonia-Glueball-Hybrid Mixing Scheme

Recently a $J^{PC}=0^{++}$ (X(1812)) state with a mass near the threshold of $\omega$ and $\phi$ has been observed by the BES collaboration in $J/\psi \to \gamma \omega \phi$ decay. It has been suggested that it is a $I^G = 0^+$ state. If it is true, this state fits in a mixing scheme based on quarkonia, glueball and hybrid (QGH) very nicely where five physical states are predicted. Together with the known $f_0(1370)$, $f_0(1500)$, $f_0(1710)$, and $f_0(1790)$ states, X(1812) completes the five members in this family. Using known experimental data on these particles we determine the ranges of the mixing parameters and predict decay properties for X(1812). We also discuss some features which may be able to distinguish between four-quark and hybrid mixing schemes.Comment: 15 pages, 2 figures, 3 table