Weight function for the quantum affine algebra Uq(A2(2))U_q(A_2^{(2)})

In this article, we give an explicit formula for the universal weight function of the quantum twisted affine algebra $U_q(A_2^{(2)})$. The calculations use the technique of projecting products of Drinfeld currents onto the intersection of Borel subalgebras of different types.Comment: 25 page

Charmonium properties in hot quenched lattice QCD

We study the properties of charmonium states at finite temperature in quenched QCD on large and fine isotropic lattices. We perform a detailed analysis of charmonium correlation and spectral functions both below and above $T_c$. Our analysis suggests that both S wave states ($J/\psi$ and $\eta_c$) and P wave states ($\chi_{c0}$ and $\chi_{c1}$) disappear already at about $1.5 T_c$. The charm diffusion coefficient is estimated through the Kubo formula and found to be compatible with zero below $T_c$ and approximately $1/\pi T$ at $1.5 T_c\lesssim T\lesssim 3 T_c$.Comment: 32 pages, 19 figures, typo corrected, discussions on isotropic vs anisotropic lattices expanded, published versio

Manin-Olshansky triples for Lie superalgebras

Following V. Drinfeld and G. Olshansky, we construct Manin triples (\fg, \fa, \fa^*) such that \fg is different from Drinfeld's doubles of \fa for several series of Lie superalgebras \fa which have no even invariant bilinear form (periplectic, Poisson and contact) and for a remarkable exception. Straightforward superization of suitable Etingof--Kazhdan's results guarantee then the uniqueness of $q$-quantization of our Lie bialgebras. Our examples give solutions to the quantum Yang-Baxter equation in the cases when the classical YB equation has no solutions. To find explicit solutions is a separate (open) problem. It is also an open problem to list (\`a la Belavin-Drinfeld) all solutions of the {\it classical} YB equation for the Poisson superalgebras \fpo(0|2n) and the exceptional Lie superalgebra \fk(1|6) which has a Killing-like supersymmetric bilinear form but no Cartan matrix

Estimating Minimum Sum-rate for Cooperative Data Exchange

This paper considers how to accurately estimate the minimum sum-rate so as to reduce the complexity of solving cooperative data exchange (CDE) problems. The CDE system contains a number of geographically close clients who send packets to help the others recover an entire packet set. The minimum sum-rate is the minimum value of total number of transmissions that achieves universal recovery (the situation when all the clients recover the whole packet set). Based on a necessary and sufficient condition for a supermodular base polyhedron to be nonempty, we show that the minimum sum-rate for a CDE system can be determined by a maximization over all possible partitions of the client set. Due to the high complexity of solving this maximization problem, we propose a deterministic algorithm to approximate a lower bound on the minimum sum-rate. We show by experiments that this lower bound is much tighter than those lower bounds derived in the existing literature. We also show that the deterministic algorithm prevents from repetitively running the existing algorithms for solving CDE problems so that the overall complexity can be reduced accordingly.Comment: 6 pages, 6 figure

One-dimentional magnonic crystal as a medium with magnetically tunable disorder on a periodical lattice

We show that periodic magnetic nanostructures (magnonic crystals) represent an ideal system for studying excitations on disordered periodical lattices because of the possibility of controlled variation of the degree of disorder by varying the applied magnetic field. Ferromagnetic resonance (FMR) data collected inside minor hysteresis loops for a periodic array of Permalloy nanowires of alternating width and magnetic force microscopy images of the array taken after running each of these loops were used to establish convincing evidence that there is a strong correlation between the type of FMR response and the degree of disorder of the magnetic ground state. We found two types of dynamic responses: anti-ferromagnetic (AFM) and ferromagnetic (FM), which represent collective spin wave modes or collective magnonic states. Depending on the history of sample magnetization either AFM or FM state is either the fundamental FMR mode or represents a state of a magnetic defect on the artificial crystal. A fundamental state can be transformed into a defect one and vice versa by controlled magnetization of the sample.Comment: 4 pages, 3 figures, Letter paper, already submitted to PR

A Practical Approach for Successive Omniscience

The system that we study in this paper contains a set of users that observe a discrete memoryless multiple source and communicate via noise-free channels with the aim of attaining omniscience, the state that all users recover the entire multiple source. We adopt the concept of successive omniscience (SO), i.e., letting the local omniscience in some user subset be attained before the global omniscience in the entire system, and consider the problem of how to efficiently attain omniscience in a successive manner. Based on the existing results on SO, we propose a CompSetSO algorithm for determining a complimentary set, a user subset in which the local omniscience can be attained first without increasing the sum-rate, the total number of communications, for the global omniscience. We also derive a sufficient condition for a user subset to be complimentary so that running the CompSetSO algorithm only requires a lower bound, instead of the exact value, of the minimum sum-rate for attaining global omniscience. The CompSetSO algorithm returns a complimentary user subset in polynomial time. We show by example how to recursively apply the CompSetSO algorithm so that the global omniscience can be attained by multi-stages of SO