A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations

A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that one operator of the Hamiltonian pair is invertible. Through our formulation, four examples of triangular systems are exhibited, which also show that bi-Hamiltonian systems in both lower dimensions and higher dimensions are many and varied. Two of four examples give local 2+1 dimensional bi-Hamiltonian systems and illustrate that multi-scale perturbations can lead to higher-dimensional bi-Hamiltonian systems.Comment: 16 pages, to appear in J. Math. Phy

Elliptic gradient estimates and Liouville theorems for a weighted nonlinear parabolic equation

Let $(M^N, g, e^{-f}dv)$ be a complete smooth metric measure space with $\infty$-Bakry-\'Emery Ricci tensor bounded from below. We derive elliptic gradient estimates for positive solutions of a weighted nonlinear parabolic equation \begin{align*} \displaystyle \Big(\Delta_f - \frac{\partial}{\partial t}\Big) u(x,t) +q(x,t)u^\alpha(x,t) = 0, \end{align*} where $(x,t) \in M^N \times (-\infty, \infty)$ and $\alpha$ is an arbitrary constant. As Applications we prove a Liouville-type theorem for positive ancient solutions and Harnack-type inequalities for positive bounded solutions.Comment: 18 page

From carbon nanotubes and silicate layers to graphene platelets for polymer nanocomposites

In spite of extensive studies conducted on carbon nanotubes and silicate layers for their polymer-based nanocomposites, the rise of graphene now provides a more promising candidate due to its exceptionally high mechanical performance and electrical and thermal conductivities. The present study developed a facile approach to fabricate epoxy–graphene nanocomposites by thermally expanding a commercial product followed by ultrasonication and solution-compounding with epoxy, and investigated their morphologies, mechanical properties, electrical conductivity and thermal mechanical behaviour. Graphene platelets (GnPs) of 3.5

Assessing health and well-being among older people in rural South Africa

Background: The population in developing countries is ageing, which is likely to increase the burden of noncommunicable diseases and disability. Objective: To describe factors associated with self-reported health, disability and quality of life (QoL) of older people in the rural northeast of South Africa. Design: Cross-sectional survey of 6,206 individuals aged 50 and over. We used multivariate analysis to examine relationships between demographic variables and measures of self-reported health (Health Status), functional ability (WHODASi) and quality of life (WHOQoL). Results: About 4,085 of 6,206 people eligible (65.8%) completed the interview. Women (Odds Ratio (OR) 1.30, 95% CI 1.09, 1.55), older age (OR2.59, 95% CI 1.97, 3.40), lower education (OR1.62, 95% CI 1.31,2.00), single status (OR1.18, 95% CI 1.01, 1.37) and not working at present (OR1.29, 95% CI 1.06, 1.59) were associated with a low health status. Women were also more likely to report a higher level of disability (OR1.38, 95% CI 1.14, 1.66), as were older people (OR2.92, 95% CI 2.25, 3.78), those with no education (OR1.57, 95% CI 1.26, 1.97), with single status (OR1.25, 95% CI 1.06, 1.46) and not working at present (OR1.33, 95% CI 1.06, 1.66). Older age (OR1.35, 95% CI 1.06, 1.74), no education (OR1.39, 95% CI 1.11, 1.73), single status (OR1.28, 95% CI 1.10, 1.49), a low household asset score (OR1.52, 95% CI 1.19, 1.94) and not working at present (OR1.32; 95% CI 1.07, 1.64) were all associated with lower quality of life. Conclusions: This study presents the first population-based data from South Africa on health status, functional ability and quality of life among older people. Health and social services will need to be restructured to provide effective care for older people living in rural South Africa with impaired functionality and other health problems

Higher Order Potential Expansion for the Continuous Limits of the Toda Hierarchy

A method for introducing the higher order terms in the potential expansion to study the continuous limits of the Toda hierarchy is proposed in this paper. The method ensures that the higher order terms are differential polynomials of the lower ones and can be continued to be performed indefinitly. By introducing the higher order terms, the fewer equations in the Toda hierarchy are needed in the so-called recombination method to recover the KdV hierarchy. It is shown that the Lax pairs, the Poisson tensors, and the Hamiltonians of the Toda hierarchy tend towards the corresponding ones of the KdV hierarchy in continuous limit.Comment: 20 pages, Latex, to be published in Journal of Physics

The regulatory subunit of PKA-I remains partially structured and undergoes β-aggregation upon thermal denaturation

Background: The regulatory subunit (R) of cAMP-dependent protein kinase (PKA) is a modular flexible protein that responds with large conformational changes to the binding of the effector cAMP. Considering its highly dynamic nature, the protein is rather stable. We studied the thermal denaturation of full-length RIα and a truncated RIα(92-381) that contains the tandem cyclic nucleotide binding (CNB) domains A and B. Methodology/Principal Findings: As revealed by circular dichroism (CD) and differential scanning calorimetry, both RIα proteins contain significant residual structure in the heat-denatured state. As evidenced by CD, the predominantly α-helical spectrum at 25°C with double negative peaks at 209 and 222 nm changes to a spectrum with a single negative peak at 212-216 nm, characteristic of β-structure. A similar α→β transition occurs at higher temperature in the presence of cAMP. Thioflavin T fluorescence and atomic force microscopy studies support the notion that the structural transition is associated with cross-β-intermolecular aggregation and formation of non-fibrillar oligomers. Conclusions/Significance: Thermal denaturation of RIα leads to partial loss of native packing with exposure of aggregation-prone motifs, such as the B' helices in the phosphate-binding cassettes of both CNB domains. The topology of the β-sandwiches in these domains favors inter-molecular β-aggregation, which is suppressed in the ligand-bound states of RIα under physiological conditions. Moreover, our results reveal that the CNB domains persist as structural cores through heat-denaturation. © 2011 Dao et al

ff-minimal surface and manifold with positive mm-Bakry-\'{E}mery Ricci curvature

In this paper, we first prove a compactness theorem for the space of closed embedded $f$-minimal surfaces of fixed topology in a closed three-manifold with positive Bakry-\'{E}mery Ricci curvature. Then we give a Lichnerowicz type lower bound of the first eigenvalue of the $f$-Laplacian on compact manifold with positive $m$-Bakry-\'{E}mery Ricci curvature, and prove that the lower bound is achieved only if the manifold is isometric to the $n$-shpere, or the $n$-dimensional hemisphere. Finally, for compact manifold with positive $m$-Bakry-\'{E}mery Ricci curvature and $f$-mean convex boundary, we prove an upper bound for the distance function to the boundary, and the upper bound is achieved if only if the manifold is isometric to an Euclidean ball.Comment: 15 page

Galactic and Extragalactic Samples of Supernova Remnants: How They Are Identified and What They Tell Us

Supernova remnants (SNRs) arise from the interaction between the ejecta of a supernova (SN) explosion and the surrounding circumstellar and interstellar medium. Some SNRs, mostly nearby SNRs, can be studied in great detail. However, to understand SNRs as a whole, large samples of SNRs must be assembled and studied. Here, we describe the radio, optical, and X-ray techniques which have been used to identify and characterize almost 300 Galactic SNRs and more than 1200 extragalactic SNRs. We then discuss which types of SNRs are being found and which are not. We examine the degree to which the luminosity functions, surface-brightness distributions and multi-wavelength comparisons of the samples can be interpreted to determine the class properties of SNRs and describe efforts to establish the type of SN explosion associated with a SNR. We conclude that in order to better understand the class properties of SNRs, it is more important to study (and obtain additional data on) the SNRs in galaxies with extant samples at multiple wavelength bands than it is to obtain samples of SNRs in other galaxiesComment: Final 2016 draft of a chapter in "Handbook of Supernovae" edited by Athem W. Alsabti and Paul Murdin. Final version available at https://doi.org/10.1007/978-3-319-20794-0_90-

GLAST: Understanding the High Energy Gamma-Ray Sky

We discuss the ability of the GLAST Large Area Telescope (LAT) to identify, resolve, and study the high energy gamma-ray sky. Compared to previous instruments the telescope will have greatly improved sensitivity and ability to localize gamma-ray point sources. The ability to resolve the location and identity of EGRET unidentified sources is described. We summarize the current knowledge of the high energy gamma-ray sky and discuss the astrophysics of known and some prospective classes of gamma-ray emitters. In addition, we also describe the potential of GLAST to resolve old puzzles and to discover new classes of sources.Comment: To appear in Cosmic Gamma Ray Sources, Kluwer ASSL Series, Edited by K.S. Cheng and G.E. Romer

An Alternative Interpretation of Statistical Mechanics

In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics