On the Head and the Tail of the Colored Jones Polynomial

The colored Jones polynomial is a series of one variable Laurent polynomials J(K,n) associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coefficients of J(K,n) are independent of n when n is sufficiently large. Computation of sample knots indicates that this should be true for any fixed leading coefficient of the colored Jones polynomial for alternating knots. As a corollary we get a Volume-ish Theorem for the colored Jones Polynomial.Comment: 14 pages, 6 figure

Universal thermodynamics of the one-dimensional attractive Hubbard model

The one-dimensional (1D) Hubbard model, describing electrons on a lattice with an on-site repulsive interaction, provides a paradigm for the physics of quantum many-body phenomena. Here by solving the thermodynamic Bethe ansatz equations we study the universal thermodynamics, quantum criticality and magnetism of the 1D attractive Hubbard model. We show that the compressibility and the susceptibility of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state obey simple additivity rules at low temperatures, indicating an existence of two free quantum fluids. The magnetic properties, such as magnetization and susceptibility, reveal three physical regions: quantum fluids at low temperatures, a non-Fermi liquid at high temperatures and the quantum fluid to non-Fermi liquid crossover in between. The lattice interaction is seen to significantly influence the nature of the FFLO-like state in 1D. Furthermore, we show that the dimensionless Wilson ratio provides an ideal parameter to map out the various phase boundaries and to characterize the two free fluids of the FLLO-like state. The quantum scaling functions for the thermal and magnetic properties yield the same dynamic critical exponent $z=2$ and correlation critical exponent $\nu=1/2$ in the quantum critical region whenever a phase transition occurs. Our results provide a rigorous understanding of quantum criticality and free fluids of many-body systems on a 1D lattice.Comment: revised version, 23 pages, 9 figures, The detailed analysis for the previous short paper. Another long paper on the correlation functions will be presented in Null. Phys. B, see arXiv:1710.0874

Performance analysis of time slicing in DVB-H

TV is the biggest media and the last one missing from mobile phones. Digital Video Broadcasting for Handhelds (DVB-H) is the latest development from the DVB Project targeting handheld, battery powered devices such as mobile telephones, PDAs(Personal Digital Assistants), etc. Time Division Multiplexing (TDM) is the technology that is usually used in computer and telecommunication systems. Time slicing is one of the characteristics that makes it possible to broadcast high resolution TV programes and fast IP data services to battery powered handheld terminals. This paper discusses the characteristics and advantages of Time slicing algorithm in DVB-H and presents the performance analysis of time slicing in DVB-H through both theoretical analysis and software simulation

Incorporating Digital Repeaters into the Soft Handover Standard in Digital Video Broadcasting Handheld

Digital Video Broadcasting for Handhelds (DVB-H) is a standard for broadcasting IP data services to portable devices. Handover in unidirectional broadcast networks is a novel issue introduced by this technology. This paper proposes and analyses the Repeater Aided Soft Handover (RA_handover) algorithm for a DVB-H receiver with MIMO antennas and presents the benefits of implementing RA_handover compared with a handover process without repeaters. For network planning and optimisation purposes simulation models are developed to analyse the RA_handover approach. It is shown that RA_handover could greatly improve the quality of service and consume much less front-end battery power than a handover method without repeaters. In addition, the cost introduced by the algorithm is briefly estimated. In conclusion, curves are given that show the relationship between quality of service and consumed battery power, which provide further support for including RA_handover in the DVB-H soft handover standard. The paper provides valuable outcomes for service providers and standard policy makers