Counterexample of loss of regularity for fractional order evolution equations with both degenerating and oscillating coefficients

For weak evolution models of fractional order with singularity near the origin, the joint influence from the principal σ-Laplacian operator, degenerating part and oscillating part is of prime concern in the discussion of regularity behavior of the solutions. We apply the techniques from the micro-local analysis to explore the upper bound of loss of regularity. Furthermore, in order to demonstrate the optimality of the estimates, a delicate counterexample with periodic coefficients will be constructed to show the lower bound of loss of regularity by the application of harmonic analysis and instability arguments. This optimality discussion develops the theory in Cicognani and Colombini (2006), Cicognani et al. (2008), Lu and Reissig (2009) and Lu and Reissig (2009) by combining both oscillation and degeneracy of the coefficients

An Investigation into the Case of Multi-interpretation in Poetry Translation

In translating poems, it is very common that different people have quite different versions of the same poem. It therefore intends to expound upon its underlying factors from the perspective of Hermeneutics, by exploring the relation between the textual meaning and the textual significance of a poem, the relation between the author’s intention and the textual intention of a poem, aiming to explain the key element in translating poems—multi-interpretation.     Keywords: poetry translation, Hermeneutics, the textual meaning, the textual significance, the author’s intention, the textual intention, multi-interpretatio

Chirality Dependence of the KK-Momentum Dark Excitons in Carbon Nanotubes

Using a collection of twelve semiconducting carbon nanotube samples, each highly enriched in a single chirality, we study the chirality dependence of the $K$-momentum dark singlet exciton using phonon sideband optical spectroscopy. Measurements of bright absorptive and emissive sidebands of this finite momentum exciton identify its energy as 20 - 38 meV above the bright singlet exciton, a separation that exhibits systematic dependencies on tube diameter, $2n+m$ family, and semiconducting type. We present calculations that explain how chiral angle dependence in this energy separation relates to the Coulomb exchange interaction, and elaborate the dominance of the $K_{A_1'}$ phonon sidebands over the zone-center phonon sidebands over a wide range of chiralities. The Kataura plot arising from these data is qualitatively well described by theory, but the energy separation between the sidebands shows a larger chiral dependence than predicted. This latter observation may indicate a larger dispersion for the associated phonon near the $K$ point than expected from finite distance force modeling.Comment: 24 pages, 12 figures, 1 table; slight title change, Figures 1 and 11 added, reference added, presentation improved throughout documen

A Coupled AKNS-Kaup-Newell Soliton Hierarchy

A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS-Kaup-Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of the systems lead to the AKNS hierarchy and the Kaup-Newell hierarchy, and thus those two soliton hierarchies also possess tri-Hamiltonian structures.Comment: 15 pages, late

Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study

Recently, entropy corrections on nonorientable manifolds such as the Klein bottle are proposed as a universal characterization of critical systems with an emergent conformal field theory (CFT). We show that entropy correction on the Klein bottle can be interpreted as a boundary effect via transforming the Klein bottle into an orientable manifold with nonlocal boundary interactions. The interpretation reveals the conceptual connection of the Klein bottle entropy with the celebrated Affleck-Ludwig entropy in boundary CFT. We propose a generic scheme to extract these universal boundary entropies from quantum Monte Carlo calculation of partition function ratios in lattice models. Our numerical results on the Affleck-Ludwig entropy and Klein bottle entropy for the $q$-state quantum Potts chains with $q=2,3$ show excellent agreement with the CFT predictions. For the quantum Potts chain with $q=4$, the Klein bottle entropy slightly deviates from the CFT prediction, which is possibly due to marginally irrelevant terms in the low-energy effective theory.Comment: 10 pages, 4 figures. Published versio

Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton Hierarchy

Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense, which also provides us with new examples of finite dimensional integrable Hamiltonian systems. A sort of involutive solutions to the Kaup-Newell hierarchy are exhibited through the obtained finite dimensional integrable systems and the general involutive system engendered by binary nonlinearization is reduced to a specific involutive system generated by mono-nonlinearization.Comment: 15 pages, plain+ams tex, to be published in Il Nuovo Cimento

Deranged calcium signaling and neurodegeneration in spinocerebellar ataxia type 3

Spinocerebellar ataxia type 3 (SCA3), also known as Machado-Joseph disease (MJD), is an autosomal-dominant neurodegenerative disorder caused by a polyglutamine expansion in ataxin-3 (SCA3, MJD1) protein. In biochemical experiments we demonstrate that mutant SCA3exp specifically associated with the type 1 inositol 1,4,5-trisphosphate receptor (InsP3R1), an intracellular calcium (Ca2+) release channel. In electrophysiological and Ca2+ imaging experiments we show that InsP3R1 are sensitized to activation by InsP3 in the presence of mutant SCA3exp. We found that feeding SCA3-YAC-84Q transgenic mice with dantrolene, a clinically relevant stabilizer of intracellular Ca2+ signaling, improved their motor performance and prevented neuronal cells loss in pontine nuclei and substantia nigra regions. Our results indicate that deranged Ca2+ signaling may play an important role in SCA3 pathology and that Ca2+ signaling stabilizers such as dantrolene may be considered as potential therapeutic drugs for treatment of SCA3 patients