An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion

We apply the theory of algebraic polynomials to analytically study the transonic properties of general relativistic hydrodynamic axisymmetric accretion onto non-rotating astrophysical black holes. For such accretion phenomena, the conserved specific energy of the flow, which turns out to be one of the two first integrals of motion in the system studied, can be expressed as a 8$^{th}$ degree polynomial of the critical point of the flow configuration. We then construct the corresponding Sturm's chain algorithm to calculate the number of real roots lying within the astrophysically relevant domain of $\mathbb{R}$. This allows, for the first time in literature, to {\it analytically} find out the maximum number of physically acceptable solution an accretion flow with certain geometric configuration, space-time metric, and equation of state can have, and thus to investigate its multi-critical properties {\it completely analytically}, for accretion flow in which the location of the critical points can not be computed without taking recourse to the numerical scheme. This work can further be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical system can have in general. We also demonstrate how the transition from a mono-critical to multi-critical (or vice versa) flow configuration can be realized through the saddle-centre bifurcation phenomena using certain techniques of the catastrophe theory.Comment: 19 pages, 2 eps figures, to appear in "General Relativity and Gravitation

Collaborative multidisciplinary management and expertise of cT2-3 locally advanced operable esophageal squamous cell carcinoma:two case reports

Background: The accurate clinical staging of esophageal squamous cell carcinoma (ESCC) is pivotal for guiding treatment strategies. However, the current precision in staging for clinical T (cT)2 and cT3 stages remains unsatisfactory. This article discusses the role of multidisciplinary teams (MDTs) in the clinical staging and formulation of neoadjuvant treatment strategies for locally advanced operable ESCC. These challenges underscore the importance of precise staging in the decision-making process for appropriate therapeutic interventions.Case Description: Through the lens of two patient case studies with locally advanced resectable ESCC, the article showcases the intricate process of treatment planning undertaken by MDTs. It captures a range of expert perspectives from Japan, China, Hong Kong (China), Korea, the USA, and Europe, focusing on the challenges of differentiating between cT2 and cT3 stages of the disease, which is a critical determinant in the management and therapeutic approach for patients.Conclusions: The article concludes that the accurate staging of ESCC is a cornerstone in determining the most suitable treatment strategies. It underscores the vital role that MDTs play in both clinical staging and the decision-making process for treatment. Highlighting the limitations in current diagnostic methods, the article emphasizes the urgent need for advanced research and the refinement of diagnostic tools to improve the precision of staging, particularly between the cT2 and cT3 stages. It suggests that future research should consider whether a reclassification of these stages could be warranted to enhance treatment planning and outcomes for patients with ESCC.<br/

[Review] Keiichi Tsumori (2014) Proust et le paysage: des écrits de jeunesse à la ‘Recherche du temps perdu’

Infrared spectroscopy has been used to investigate the temperature dependence and c-axis magnetic field dependence of the Josephson plasma resonance in optimally doped Tl2Ba2CaCu2O8 thin films, and underdoped YBa2Cu3O6.5 ortho - II single crystals. The resonances are directly related to the c-axis penetration depths, yielding low temperature, zero fields values of about 20 micrometer, and 7 micrometer respectively. While the temperature dependencies of the resonances in the two compounds are very similar, the magnetic field dependence in YBCO is much weaker. We attribute this weak magnetic field dependence to the lower anisotropy of YBCO, and discuss the observed behaviours in terms of thermal fluctuations and pinning of pancake vortices, valid for highly anisotropic layered superconductors.Comment: 4 pages, ReVTeX, 5 eps figures, PRL, in pres

Quantum oscillations and the Fermi surface of high-temperature cuprate superconductors

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