Factorization of the current algebra and integrable top-like systems

A hierarchy of integrable hamiltonian nonlinear ODEs is associated with any decomposition of the Lie algebra of Laurent series with coefficients being elements of a semi-simple Lie algebra into a sum of the subalgebra consisting of the Taylor series and some complementary subalgebra. In the case of the Lie algebra $so(3)$ our scheme covers all classical integrable cases in the Kirchhoff problem of the motion of a rigid body in an ideal fluid. Moreover, the construction allows us to generate integrable deformations for known integrable models.Comment: 21 page

Integrable matrix equations related to pairs of compatible associative algebras

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we investigate in details the multiplications of the A-type and integrable matrix ODEs and PDEs generated by them.Comment: 12 pages, Late

Optical Conductivity of the Trellis-Lattice t-J Model: Charge Fluctuations in NaV_2O_5

Optical conductivity of the trellis lattice t-J model at quarter filling is calculated by an exact-diagonalization technique on small clusters, whereby the valence state of V ions of NaV_2O_5 is considered. We show that the experimental features at \sim 1 eV, including peak positions, presence of shoulders, and anisotropic spectral weight, can be reproduced in reasonable range of parameter values, only by assuming that the system is in the charge disproportionated ground state. Possible reconciliation with experimental data suggesting the presence of uniform ladders at T>T_c is discussed.Comment: 4 pages, 4 gif figures. Minor revisions have been made. Hardcopies of figures (or the entire manuscript) can be obtained by e-mail request to [email protected]

"Doubled" generalized Landau-Lifshiz hierarchies and special quasigraded Lie algebras

Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This hierarchy can be also interpreted as an anisotropic vector generalization of "modified" Sine-Gordon hierarchy or as a very special vector generalization of so(3) anisotropic chiral field hierarchy.Comment: 16 pages, no figures, submitted to Journal of Physics

Design of Scalable Continuous Media Servers with Dynamic Replication

Multimedia applications place high demands for quality-of-service (QoS), performance, and reliability on systems. These stringent requirements make design of cost-effective and scalable systems difficult. Therefore efficient adaptive and dynamic resource management techniques in conjunction with data placement techniques can be of great help in improving performance, scalability and reliability of such systems. In this paper, we first focus on data placement. In the recent past, a great deal of work has focused on "wide" data striping as a way of dealing with load imbalance problems caused by skews in data access patterns. Another approach to dealing with load imbalance problems is replication. The appropriate compromise between the degree of striping and the degree of replication is key to the design of scalable continuous media (CM) servers. In this work we focus on evaluation of this compromise in the context of a hybrid CM server design. Changes in data access patterns lead to other questions: (1) when should the system alter the number of copies of a CM object, and (2) how to accomplish this change. We address (1) through an adaptive threshold-based approach, and we use dynamic replication policies in conjunction with a mathematical model of user behavior to address (2). We do this without any knowledge of data access patterns and with provisions for full use of VCR functionality. Through a performance study, we show that not only does the use of this mathematical model in conjunction with dynamic resource management policies improves the system's performance but that it also facilitates reduced sensitivity to changes in:(a) workload characteristics, (b) skewness of data access patterns, and (c) frequency of changes in data access patterns. We believe that not only is this a desirable property for a CM server, in general, but that furthermore, it suggests the usefulness of these techniques across a wide range of continuous media applications. (Cross-referenced as UMIACS-TR-2001-21

From AKNS to derivative NLS hierarchies via deformations of associative products

Using deformations of associative products, derivative nonlinear Schrodinger (DNLS) hierarchies are recovered as AKNS-type hierarchies. Since the latter can also be formulated as Gelfand-Dickey-type Lax hierarchies, a recently developed method to obtain 'functional representations' can be applied. We actually consider hierarchies with dependent variables in any (possibly noncommutative) associative algebra, e.g., an algebra of matrices of functions. This also covers the case of hierarchies of coupled DNLS equations.Comment: 22 pages, 2nd version: title changed and material organized in a different way, 3rd version: introduction and first part of section 2 rewritten, taking account of previously overlooked references. To appear in J. Physics A: Math. Ge

High frequency dielectric and magnetic anomaly at the phase transition in NaV2O5

We found anomalies in the temperature dependence of the dielectric and the magnetic susceptibiliy of NaV_2O_5 in the microwave and far infrared frequency ranges. The anomalies occur at the phase transition temperature T_c, at which the spin gap opens. The real parts of the dielectric constants epsilon_a and epsilon_c decrease below T_c. The decrease of epsilon_a (except for the narrow region close to T_c) is proportional to the intensity of the x-ray reflection appearing at T_c. The dielectric constant anomaly can be explained by the zigzag charge ordering in the ab-plane appearing below T_c. The anomaly of the microwave magnetic losses is probably related to the coupling between the spin and charge degrees of freedom in vanadium ladders.Comment: 3 PS-figures, LATEX-text, new experimental data added, typos correcte

Postpandemic rebound of adeno-associated virus type 2 (AAV2) infections temporally associated with an outbreak of unexplained severe acute hepatitis in children in the United Kingdom

Over 1000 cases of unexplained severe acute hepatitis in children have been reported to date worldwide. An association with adeno-associated virus type 2 (AAV2) infection, a human parvovirus, prompted us to investigate the epidemiology of AAV in the United Kingdom. Three hundred pediatric respiratory samples collected before (April 03, 2009–April 03, 2013) and during (April 03, 2022) the COVID-19 pandemic were obtained. Wastewater samples were collected from 50 locations in London (August 2021–March 2022). Samples were tested for AAV using real-time polymerase chain reaction followed by sequencing. Selected adenovirus (AdV)-positive samples were also sequenced. The detection frequency of AAV2 was a sevenfold higher in 2022 samples compared with 2009–2013 samples (10% vs. 1.4%) and highest in AdV-positive samples compared with negatives (10/37, 27% vs. 5/94, 5.3%, respectively). AAV2-positive samples displayed high genetic diversity. AAV2 sequences were either very low or absent in wastewater collected in 2021 but increased in January 2022 and peaked in March 2022. AAV2 was detected in children in association with AdV of species C, with a highest frequency in 2022. Our findings are consistent with the expansion of the population of children unexposed to AAV2, leading to greater spread of the virus once distancing restrictions were lifted

Folded modes in the infrared spectra of the spin-Peierls phase of CuGeO_3

Polarized far-infrared transmittance spectra of CuGeO_3 single crystals were measured at different temperatures (6K < T < 300K). Two spectral lines, at 284.2 cm-1 in E||c polarization and at 311.7 cm-1 in E||b polarization, appear at the temperature of the spin-Peierls transition and grow in intensity with decreasing temperature. Both of them are, most probably, folded modes of the dimerized lattice. We discuss a possible role of the spin-phonon interaction in the formation of the 311.7 cm-1 feature.Comment: 4 pages, 5 figures, 1 table; Submitted to Phys.Rev.B Second revision. Figures and text were slightly change

One-dimensional dynamics of the d-electrons in α′\alpha'-NaV2_{2}O5_{5}

We have studied the electronic properties of the ladder compound $\alpha'$-NaV$_{2}$O$_{5}$, adopting a joint experimental and theoretical approach. The momentum-dependent loss function was measured using electron energy-loss spectroscopy in transmission. The optical conductivity derived from the loss function by a Kramers-Kronig analysis agrees well with our results from LSDA+U band-structure calculations upon application of an antiferromagnetic alignment of the V~3$d_{xy}$ spins along the legs and an on-site Coulomb interaction U of between 2 and 3 eV. The decomposition of the calculated optical conductivity into contributions from transitions between selected energy regions of the DOS reveals the origin of the observed anisotropy of the optical conductivity. In addition, we have investigated the plasmon excitations related to transitions between the vanadium states within an effective 16 site vanadium cluster model. Good agreement between the theoretical and experimental loss function was obtained using the hopping parameters derived from the tight binding fit to the band-structure and moderate Coulomb interactions between the electrons within the ab plane.Comment: 23 pages, 8 figures; submitted to PR