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

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

Physical Insights of Low Thermal Expansion Coefficient Electrode Stress Effect on Hafnia-Based Switching Speed

In this report, we investigate the effect of low coefficient of thermal expansion (CTE) metals on the operating speed of hafnium-based oxide capacitance. We found that the cooling process of low CTE metals during rapid thermal annealing (RTA) generates in-plane tensile stresses in the film, This facilitates an increase in the volume fraction of the o-phase and significantly improves the domain switching speed. However, no significant benefit was observed at electric fields less than 1 MV/cm. This is because at low voltage operation, the defective resistance (dead layer) within the interface prevents electron migration and the increased RC delay. Minimizing interface defects will be an important key to extending endurance and retention

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.

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

Unified Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Five Dimensions

Unified N=2 Maxwell-Einstein supergravity theories (MESGTs) are supergravity theories in which all the vector fields, including the graviphoton, transform in an irreducible representation of a simple global symmetry group of the Lagrangian. As was established long time ago, in five dimensions there exist only four unified Maxwell-Einstein supergravity theories whose target manifolds are symmetric spaces. These theories are defined by the four simple Euclidean Jordan algebras of degree three. In this paper, we show that, in addition to these four unified MESGTs with symmetric target spaces, there exist three infinite families of unified MESGTs as well as another exceptional one. These novel unified MESGTs are defined by non-compact (Minkowskian) Jordan algebras, and their target spaces are in general neither symmetric nor homogeneous. The members of one of these three infinite families can be gauged in such a way as to obtain an infinite family of unified N=2 Yang-Mills-Einstein supergravity theories, in which all vector fields transform in the adjoint representation of a simple gauge group of the type SU(N,1). The corresponding gaugings in the other two infinite families lead to Yang-Mills-Einstein supergravity theories coupled to tensor multiplets.Comment: Latex 2e, 28 pages. v2: reference added, footnote 14 enlarge

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

Fractionated administration of irinotecan and cisplatin for treatment of lung cancer: a phase I study

A combination chemotherapy of irinotecan (CPT-11) and cisplatin (CDDP) has been reported to be active for lung cancer. In the previous trial, however, diarrhoea and leucopenia became the major obstacle for sufficient dose escalation of CPT-11 to improve the treatment outcome. We conducted a phase I study to investigate whether the fractionated administration of CDDP and CPT-11 at escalated dose was feasible and could improve the treatment outcome. Twenty-four previously untreated patients with unresectable non-small-cell lung cancer (NSCLC) or extensive disease of small-cell lung cancer (SCLC) were eligible. Both CDDP and CPT-11 were given on days 1 and 8, and repeated every 4 weeks. The dose of CDDP was fixed at 60 mg m−2 and given by 1-h infusion before CPT-11 administration. The starting dose of CPT-11 was 40 mg m−2, and the dose was escalated by an increase of 10 mg m−2. The maximally tolerated dose of CPT-11 was determined as 60 mg m−2 because grade 4 haematological or grade 3 or 4 non-haematological toxicities developed in six patients out of 11 patients evaluated. Diarrhoea became a dose-limiting toxicity. The objective response rates were 76% for NSCLC and 100% for SCLC. The recommended dose of CPT-11 and CDDP in a phase II study will be 50 mg m−2 and 60 mg m−2 respectively. © 1999 Cancer Research Campaig