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

Brownian motion of a charged particle in electromagnetic fluctuations at finite temperature

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle's equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a suparohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed.Comment: accepter by Foundation of Physics, for IARD 6, 200

The entomopathogenic nematode Steinernema hermaphroditum is a self-fertilizing hermaphrodite and a genetically tractable system for the study of parasitic and mutualistic symbiosis

Entomopathogenic nematodes (EPNs), including Heterorhabditis and Steinernema, are parasitic to insects and contain mutualistically symbiotic bacteria in their intestines (Photorhabdus and Xenorhabdus, respectively) and therefore offer opportunities to study both mutualistic and parasitic symbiosis. The establishment of genetic tools in EPNs has been impeded by limited genetic tractability, inconsistent growth in vitro, variable cryopreservation, and low mating efficiency. We obtained the recently described Steinernema hermaphroditum strain CS34 and optimized its in vitro growth, with a rapid generation time on a lawn of its native symbiotic bacteria Xenorhabdus griffiniae. We developed a simple and efficient cryopreservation method. Previously, S. hermaphroditum isolated from insect hosts was described as producing hermaphrodites in the first generation. We discovered that CS34, when grown in vitro, produced consecutive generations of autonomously reproducing hermaphrodites accompanied by rare males. We performed mutagenesis screens in S. hermaphroditum that produced mutant lines with visible and heritable phenotypes. Genetic analysis of the mutants demonstrated that this species reproduces by self-fertilization rather than parthenogenesis and that its sex is determined chromosomally. Genetic mapping has thus far identified markers on the X chromosome and three of four autosomes. We report that S. hermaphroditum CS34 is the first consistently hermaphroditic EPN and is suitable for genetic model development to study naturally occurring mutualistic symbiosis and insect parasitism

Puzzles in BB physics

I discuss some puzzles observed in exclusive $B$ meson decays, concentrating on the large difference between the direct CP asymmetries in the $B^0\to \pi^\mp K^\pm$ and $B^\pm\to \pi^0 K^\pm$ modes, the large $B^0\to\pi^0\pi^0$ branching ratio, and the large deviation of the mixing-induced CP asymmetries in the $b\to sq\bar q$ penguins from those in the $b\to c\bar c s$ trees.Comment: 6 pages, 1 figure, talk presented at the 9th Workshop on High Energy Physics Phenomenology, Bhubaneswar, Orissa, India, Jan. 3-14, 2006; reference adde

Knaster's problem for (Z2)k(Z_2)^k-symmetric subsets of the sphere S2k−1S^{2^k-1}

We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about equipartition of a measures in $\mathbb R^{2^k}$ by $(Z_2)^{k+1}$-symmetric convex fans

GALEX J201337.6+092801: The lowest gravity subdwarf B pulsator

We present the recent discovery of a new subdwarf B variable (sdBV), with an exceptionally low surface gravity. Our spectroscopy of J20136+0928 places it at Teff = 32100 +/- 500, log(g) = 5.15 +/- 0.10, and log(He/H) = -2.8 +/- 0.1. With a magnitude of B = 12.0, it is the second brightest V361 Hya star ever found. Photometry from three different observatories reveals a temporal spectrum with eleven clearly detected periods in the range 376 to 566 s, and at least five more close to our detection limit. These periods are unusually long for the V361 Hya class of short-period sdBV pulsators, but not unreasonable for p- and g-modes close to the radial fundamental, given its low surface gravity. Of the ~50 short period sdB pulsators known to date, only a single one has been found to have comparable spectroscopic parameters to J20136+0928. This is the enigmatic high-amplitude pulsator V338 Ser, and we conclude that J20136+0928 is the second example of this rare subclass of sdB pulsators located well above the canonical extreme horizontal branch in the HR diagram.Comment: 5 pages, accepted for publication in ApJ Letter

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Procjena cito-/genotoksičnosti irinotekana u V79-stanicama primjenom komet-testa, mikronukleus-testa i testa kromosomskih aberacija

Irinotecan is a topoisomerase I interactive agent, widely used in the treatment of metastatic colorectal cancer. The genotoxic effects of the maximum single dose (18 μg mL-1), recommended monotherapy dose (9 μg mL-1), and recommended combined therapy dose (4.5 μg mL-1) of irinotecan were studied on V79 cells using the comet assay, chromosome aberration assay, and micronucleus test. The cells were treated with irinotecan for 2 h or 24 h. The statistical signifi cance of the results was determined using the one-way ANOVA test and a nonparametric Mann Whitney U test. The comet assay did not show dose-dependent or time-dependent effects. The chromosome aberration analysis showed large DNA rearrangements, i.e., chromosome exchanges. Although the exposed cultures showed a signifi cant increase in micronucleated cells in respect to control, no dose-dependent relation was established among the treated cultures. Timedependent effect was also not observed.Irinotekan je citotoksični lijek koji inhibira enzim DNA-topoizomerazu I. U širokoj je primjeni u terapiji metastatskog karcinoma kolona i rektuma. U uvjetima in vitro primjenom komet-testa, analize kromosomskih aberacija i mikronukleus-testa na V79-stanicama istražili smo genotoksični učinak maksimalne pojedinačne doze (18 μg mL-1), preporučene monoterapijske doze (9 μg mL-1) i preporučene doze irinotekana za kombiniranu terapiju (4,5 μg mL-1). Kulture stanica bile su tretirane irinotekanom 2 h i 24 h. Statistička značajnost određivana je jednosmjernim ANOVA-testom i neparametrijskim Mann Whitneyevim U-testom. Komet-testom nije utvrđen učinak koncentracije i/ili vremena izloženosti. Analiza kromosomskih aberacija pokazala je prisutnost izmjena kromatida, tj. porast broja triradijusa i tetraradijusa. Iako je u kulturama stanica izloženi irinotekanu opažen značajan porast broja mikronukleusa u odnosu na kontrolu, nije uočena ovisnost o dozi lijeka ni o vremenu izloženosti u opisanim eksperimentalnim uvjetima. Dobiveni rezultati upućuju na genotoksičnost irinotekana za V79-stanice. Nijednom od primijenjenih metoda nije utvrđena ovisnost učinka irinotekana o vremenu ili dozi

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

Perturbative QCD factorization of πγ∗→γ(π)\pi \gamma^*\to \gamma(\pi) and B→γ(π)lνˉB\to \gamma(\pi)l\bar \nu

We prove factorization theorem for the processes $\pi\gamma^*\to\gamma$ and $\pi\gamma^*\to\pi$ to leading twist in the covariant gauge by means of the Ward identity. Soft divergences cancel and collinear divergences are grouped into a pion wave function defined by a nonlocal matrix element. The gauge invariance and universality of the pion wave function are confirmed. The proof is then extended to the exclusive $B$ meson decays $B\to\gamma l\bar\nu$ and $B\to\pi l\bar\nu$ in the heavy quark limit. It is shown that a light-cone $B$ meson wave function, though absorbing soft dynamics, can be defined in an appropriate frame. Factorization of the $B\to\pi l\bar\nu$ decay in $k_T$ space, $k_T$ being parton transverse momenta, is briefly discussed. We comment on the extraction of the leading-twist pion wave function from experimental data.Comment: 21 pages in Latex file, version to appear in Phys. Rev.