Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type III. The Heun Case

The Heun equation can be rewritten as an eigenvalue equation for an ordinary differential operator of the form $-d^2/dx^2+V(g;x)$, where the potential is an elliptic function depending on a coupling vector $g\in{\mathbb R}^4$. Alternatively, this operator arises from the $BC_1$ specialization of the $BC_N$ elliptic nonrelativistic Calogero-Moser system (a.k.a. the Inozemtsev system). Under suitable restrictions on the elliptic periods and on $g$, we associate to this operator a self-adjoint operator $H(g)$ on the Hilbert space ${\mathcal H}=L^2([0,\omega_1],dx)$, where $2\omega_1$ is the real period of $V(g;x)$. For this association and a further analysis of $H(g)$, a certain Hilbert-Schmidt operator ${\mathcal I}(g)$ on ${\mathcal H}$ plays a critical role. In particular, using the intimate relation of $H(g)$ and ${\mathcal I}(g)$, we obtain a remarkable spectral invariance: In terms of a coupling vector $c\in{\mathbb R}^4$ that depends linearly on $g$, the spectrum of $H(g(c))$ is invariant under arbitrary permutations $\sigma(c)$, $\sigma\in S_4$

A note on the Gauss decomposition of the elliptic Cauchy matrix

Explicit formulas for the Gauss decomposition of elliptic Cauchy type matrices are derived in a very simple way. The elliptic Cauchy identity is an immediate corollary.Comment: 5 page

Arthrectomy for traumatic proximal interphalangeal arthritis in the lateral digit in a heifer

ΔΕΝ ΔΙΑΤΙΘΕΤΑΙ ΠΕΡΙΛΗΨΗInstructive information on the treatment for chronic deep infections of digital joints in a 9-month-old Holstein heifer is described in this report. Preoperative ultrasonographic and radiographic examinations revealed soft tissue swelling and subchondral bone lysis at the distal part of the proximal phalanx in the lateral digit. Arthrectomy was performed under xylazine sedation to remove infectious articular cartilage tissues. Immature callus formation was observed via radiography at the surgical site by the 28th postoperative day. On the 48th postoperative day, callus fellinto disrepair on the radiographs along with aggravation of the locomotion score. After the application of a half-limb cast, the immature callus formed again by the 62nd postoperative day (11 months), and bony callus formation was observed by the 74th postoperative day. Thereafter, the heifer could walk well with marked improvement in the locomotion score. The withers height of the heifer at 13 months (136 cm) was within the range of that in control heifers of the same age on this farm (133 ± 3 cm); however, the body weight (BW) of this heifer (322 kg) was lower than the BW of controls (384 ± 26 kg). The BW gain from 11 to 13 months of age seemed to be higher in the present heifer (+76 kg) than in controls (+55±20 kg), suggesting that BW of the present heifer was returning to the original BW. Based on these observations, we suggested that arthrectomy was an effective treatment option for the present case of digital joint arthritis

High temperature optical absorption investigation into the electronic transitions in sol–gel derived C12A7 thin films

Optical absorption into 6 mm thick sol–gel derived films, annealed at 1300 °C of 12CaO·7Al2O3 calcium aluminate binary compound on MgO〈100〉 single crystal substrates was studied at temperatures ranging from room temperature to 300 °C. Experimental data were analysed in both Tauc and Urbach regions. The optical band gap decreased from 4.088 eV at 25 °C to 4.051 eV at 300 °C, while Urbach energy increased from 0.191 eV at 25 °C to 0.257 eV at 300 °C. The relationship between the optical band gap and the Urbach energy at different temperatures showed an almost linear relationship from which the theoretical values of 4.156 and 0.065 eV were evaluated for the band gap energy and Urbach energy of a 12CaO·7Al2O3 crystal with zero structural disorder at 0 K

Parton energy loss at strong coupling and the universal bound

The apparent universality of jet quenching observed in heavy ion collisions at RHIC for light and heavy quarks, as well as for quarks and gluons, is very puzzling and calls for a theoretical explanation. Recently it has been proposed that the synchrotron--like radiation at strong coupling gives rise to a universal bound on the energy of a parton escaping from the medium. Since this bound appears quite low, almost all of the observed particles at high transverse momentum have to originate from the surface of the hot fireball. Here I make a first attempt of checking this scenario against the RHIC data and formulate a "Universal Bound Model" of jet quenching that can be further tested at RHIC and LHC.Comment: 8 pages, 2 figures, invited plenary talk given at "Hard Probes 2008" Conference, 8-14 June 2008, Illa da Toxa, Galicia, Spai

Neuroinflammation, Mast Cells, and Glia: Dangerous Liaisons

The perspective of neuroinflammation as an epiphenomenon following neuron damage is being replaced by the awareness of glia and their importance in neural functions and disorders. Systemic inflammation generates signals that communicate with the brain and leads to changes in metabolism and behavior, with microglia assuming a pro-inflammatory phenotype. Identification of potential peripheral-to-central cellular links is thus a critical step in designing effective therapeutics. Mast cells may fulfill such a role. These resident immune cells are found close to and within peripheral nerves and in brain parenchyma/meninges, where they exercise a key role in orchestrating the inflammatory process from initiation through chronic activation. Mast cells and glia engage in crosstalk that contributes to accelerate disease progression; such interactions become exaggerated with aging and increased cell sensitivity to stress. Emerging evidence for oligodendrocytes, independent of myelin and support of axonal integrity, points to their having strong immune functions, innate immune receptor expression, and production/response to chemokines and cytokines that modulate immune responses in the central nervous system while engaging in crosstalk with microglia and astrocytes. In this review, we summarize the findings related to our understanding of the biology and cellular signaling mechanisms of neuroinflammation, with emphasis on mast cell-glia interactions

First COVID-19 Case in Zambia - Comparative phylogenomic analyses of SARS-CoV-2 detected in African countries

Since its first discovery in December 2019 in Wuhan, China, COVID-19, caused by the novel coronavirus SARS-CoV-2, has spread rapidly worldwide. Whilst African countries were relatively spared initially, the initial low incidence of COVID-19 cases was not sustained for long due to continuing travel links between China, Europe and Africa.. In preparation, Zambia had applied a multisectoral national epidemic disease surveillance and response system resulting in the identification of the first case within 48 hours of the individual entering the country by air travel from a trip to France. Contact tracing showed that SARS-CoV-2 infection was contained within the patient's household, with no further spread to attending health care workers or community members. Phylogenomic analysis of the patient's SARS-CoV-2 strain showed it belonged to lineage B.1.1., sharing the last common ancestor with SARS-CoV-2 strains recovered from South Africa. At the African continental level, our analysis showed that lineage B.1 and B.1.1 lineages appear to be predominant in Africa. Whole genome sequence analysis should be part of all surveillance and case detection activities in order to monitor the origin and evolution of SARS-CoV-2 lineages across Africa

Azimuthal Angle Correlations for Rapidity Separated Hadron Pairs in d+Au Collisions at sqrt(s_NN) = 200 GeV

We report on two-particle azimuthal angle correlations between charged hadrons at forward/backward (deuteron/gold going direction) rapidity and charged hadrons at mid-rapidity in deuteron-gold (d+Au) and proton-proton (p+p) collisions at sqrt(s_NN) = 200 GeV. Jet structures are observed in the correlations which we quantify in terms of the conditional yield and angular width of away side partners. The kinematic region studied here samples partons in the gold nucleus carrying nucleon momentum fraction x~0.1 to x~0.01. Within this range, we find no x dependence of the jet structure in d+Au collisions.Comment: 330 authors, 6 pages text, 4 figures, no tables. Submitted to Phys. Rev. Lett. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm

Centrality dependence of charged hadron production in deuteron+gold and nucleon+gold collisions at sqrt(s_NN)=200 GeV

We present transverse momentum (p_T) spectra of charged hadrons measured in deuteron-gold and nucleon-gold collisions at \sqrts = 200 GeV for four centrality classes. Nucleon-gold collisions were selected by tagging events in which a spectator nucleon was observed in one of two forward rapidity detectors. The spectra and yields were investigated as a function of the number of binary nucleon-nucleon collisions, \nu, suffered by deuteron nucleons. A comparison of charged particle yields to those in p+p collisions show that the yield per nucleon-nucleon collision saturates with \nu for high momentum particles. We also present the charged hadron to neutral pion ratios as a function of p_T.Comment: 330 authors, 15 pages text, 16 figures, 3 tables. Submitted to Phys. Rev. Lett. v2 has minor changes to reflect revisions during review process. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm