Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity

Saari's homographic conjecture in N-body problem under the Newton gravity is the following; configurational measure \mu=\sqrt{I}U, which is the product of square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and the potential function U=\sum m_i m_j/r_{ij}, is constant if and only if the motion is homographic. Where m_k represents mass of body k and r_{ij} represents distance between bodies i and j. We prove this conjecture for planar equal-mass three-body problem. In this work, we use three sets of shape variables. In the first step, we use \zeta=3q_3/(2(q_2-q_1)) where q_k \in \mathbb{C} represents position of body k. Using r_1=r_{23}/r_{12} and r_2=r_{31}/r_{12} in intermediate step, we finally use \mu itself and \rho=I^{3/2}/(r_{12}r_{23}r_{31}). The shape variables \mu and \rho make our proof simple

41Ca in tooth enamel. part I: A biological signature of neutron exposure in atomic bomb survivors

The detection of 41Ca atoms in tooth enamel using accelerator mass spectrometry is suggested as a method capable of reconstructing thermal neutron exposures from atomic bomb survivors in Hiroshima and Nagasaki. In general, 41Ca atoms are produced via thermal neutron capture by stable 40Ca. Thus any 41Ca atoms present in the tooth enamel of the survivors would be due to neutron exposure from both natural sources and radiation from the bomb. Tooth samples from five survivors in a control group with negligible neutron exposure were used to investigate the natural 41Ca content in tooth enamel, and 16 tooth samples from 13 survivors were used to estimate bomb-related neutron exposure. The results showed that the mean 41Ca/Ca isotope ratio was (0.17 ± 0.05) × 10-14 in the control samples and increased to 2 × 10-14 for survivors who were proximally exposed to the bomb. The 41Ca/Ca ratios showed an inverse correlation with distance from the hypocenter at the time of the bombing, similar to values that have been derived from theoretical free-in-air thermal-neutron transport calculations. Given that γ-ray doses were determined earlier for the same tooth samples by means of electron spin resonance (ESR, or electron paramagnetic resonance, EPR), these results can serve to validate neutron exposures that were calculated individually for the survivors but that had to incorporate a number of assumptions (e.g. shielding conditions for the survivors).Fil: Wallner, A.. Ludwig Maximilians Universitat; Alemania. Universitat Technical Zu Munich; Alemania. Universidad de Viena; AustriaFil: Ruhm, W.. Helmholtz Center Munich German Research Center For Environmental Health; Alemania. Ludwig Maximilians Universitat; AlemaniaFil: Rugel, G.. Ludwig Maximilians Universitat; Alemania. Universitat Technical Zu Munich; AlemaniaFil: Nakamura, N.. Radiation Effects Research Foundation; JapónFil: Arazi, Andres. Universitat Technical Zu Munich; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Faestermann, T.. Universitat Technical Zu Munich; AlemaniaFil: Knie, K.. Universitat Technical Zu Munich; Alemania. Ludwig Maximilians Universitat; AlemaniaFil: Maier, H. J.. Ludwig Maximilians Universitat; AlemaniaFil: Korschinek, G.. Universitat Technical Zu Munich; Alemani

Memberships and CM Diagrams of the Open Cluster NGC 7243

The results of astrometric and photometric investigations of the open cluster NGC 7243 are presented. Proper motions of 2165 stars with root-mean-square error of 1.1 mas/yr were obtained by means of PDS scanning of astrometric plates covering the time interval of 97 years. A total of 211 cluster members down to V=15.5 mag have been identified. V and B magnitudes have been determined for 2118 and 2110 stars respectively. Estimations of mass (348Mo < M < 522Mo), age (t=2.5x10^8 yr), distance (r=698 pc) and reddening (E(B-V)=0.24) of the cluster NGC 7243 have been made.Comment: 24 pages, 15 figures. Submitted to Astronomy and Astrophysic

Tumor necrosis is associated with increased alphavbeta3 integrin expression and poor prognosis in nodular cutaneous melanomas

<p>Abstract</p> <p>Background</p> <p>Tumor necrosis and apoptotic activity are considered important in cancer progression, but these features have not been much studied in melanomas. Our hypothesis was that rapid growth in cutaneous melanomas of the vertical growth phase might lead to tissue hypoxia, alterations in apoptotic activity and tumor necrosis. We proposed that these tumor characteristics might be associated with changes in expression of cell adhesion proteins leading to increased invasive capacity and reduced patient survival.</p> <p>Methods</p> <p>A well characterized series of nodular melanoma (originally 202 cases) and other benign and malignant melanocytic tumors (109 cases) were examined for the presence of necrosis, apoptotic activity (TUNEL assay), immunohistochemical expression of hypoxia markers (HIF-1 α, CAIX, TNF-α, Apaf-1) and cell adhesion proteins (α_vβ₃integrin, CD44/HCAM and osteopontin). We hypothesized that tumor hypoxia and necrosis might be associated with increased invasiveness in melanoma through alterations of tumor cell adhesion proteins.</p> <p>Results</p> <p>Necrosis was present in 29% of nodular melanomas and was associated with increased tumor thickness, tumor ulceration, vascular invasion, higher tumor proliferation and apoptotic index, increased expression of α_vβ₃integrin and poor patient outcome by multivariate analysis. Tumor cell apoptosis did also correlate with reduced patient survival. Expression of TNF-α and Apaf-1 was significantly associated with tumor thickness, and osteopontin expression correlated with increased tumor cell proliferation (Ki-67).</p> <p>Conclusion</p> <p>Tumor necrosis and apoptotic activity are important features of melanoma progression and prognosis, at least partly through alterations in cell adhesion molecules such as increased α_vβ₃integrin expression, revealing potentially important targets for new therapeutic approaches to be further explored.</p

Ki-67 expression is superior to mitotic count and novel proliferation markers PHH3, MCM4 and mitosin as a prognostic factor in thick cutaneous melanoma

<p>Abstract</p> <p>Background</p> <p>Tumor cell proliferation is a predictor of survival in cutaneous melanoma. The aim of the present study was to evaluate the prognostic impact of mitotic count, Ki-67 expression and novel proliferation markers phosphohistone H3 (PHH3), minichromosome maintenance protein 4 (MCM4) and mitosin, and to compare the results with histopathological variables.</p> <p>Methods</p> <p>202 consecutive cases of nodular cutaneous melanoma were initially included. Mitotic count (mitosis per mm²) was assessed on H&E sections, and Ki-67 expression was estimated by immunohistochemistry on standard sections. PHH3, MCM4 and mitosin were examined by staining of tissue microarrays (TMA) sections.</p> <p>Results</p> <p>Increased mitotic count and elevated Ki-67 expression were strongly associated with increased tumor thickness, presence of ulceration and tumor necrosis. Furthermore, high mitotic count and elevated Ki-67 expression were also associated with Clark's level of invasion and presence of vascular invasion. High expression of PHH3 and MCM4 was correlated with high mitotic count, elevated Ki-67 expression and tumor ulceration, and increased PHH3 frequencies were associated with tumor thickness and presence of tumor necrosis. Univariate analyses showed a worse outcome in cases with elevated Ki-67 expression and high mitotic count, whereas PHH3, MCM4 and mitosin were not significant. Tumor cell proliferation by Ki-67 had significant prognostic impact by multivariate analysis.</p> <p>Conclusions</p> <p>Ki-67 was a stronger and more robust prognostic indicator than mitotic count in this series of nodular melanoma. PHH3, MCM4 and mitosin did not predict patient survival.</p