Additive results for the generalized Drazin inverse in a Banach algebra

In this paper we investigate additive properties of the generalized Drazin inverse in a Banach algebra. We find some new conditions under which the generalized Drazin inverse of the sum a + b could be explicitly expressed in terms of a, a^d, b, b^d. Also, some recent results of Castro and Koliha [New additive results for the g-Drazin inverse, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004) 1085-1097] are extended.     

The Matsumoto-Yor property and the structure of the Wishart distribution

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart.     

CRYRING at the LSR at FLAIR

FLAIR will be the next-generation facility for physics with low-energy antiprotons, providing antiprotons at energies from tens of MeV down to rest. It will also offer unique possibilities for physics with highly charged ions at very low energies. The FLAIR facility will have two deceleration rings, the LSR which will decelerate antiprotons to 300 keV and the USR which will bring them down further to 20 keV. The LSR will consist of the present CRYRING at the Manne Siegbahn Laboratory. During the next few years, CRYRING will be modified with respect to injection and extraction, to allow injection of 30 MeV antiprotons and to provide it with both fast (single-turn) and slow (resonant) extraction at a variable energy. We here describe plans and preparations for the transfer of CRYRING to FLAIR, giving, in particular, an overview of new components for injection and extraction.     

Long alternating paths in bicolored point sets

Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length . We disprove a conjecture of Erd?s by constructing an example without any such path of length greater than .     

The increment ratio statistic

We introduce a new statistic written as a sum of certain ratios of second-order increments of partial sums process of observations, which we call the increment ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d-integrated () behavior of time series X_t, including short memory (d=0), (stationary) long-memory and unit roots (d=1). If S_n behaves asymptotically as an (integrated) fractional Brownian motion with parameter , the IR statistic converges to a monotone function Λ(d) of as both the sample size N and the window parameter m increase so that N/m→∞. For Gaussian observations X_t, we obtain a rate of decay of the bias EIR-Λ(d) and a central limit theorem (N/m)^1/2(IR-EIR)→N(0,σ²(d)), in the region . Graphs of the functions Λ(d) and σ(d) are included. A simulation study shows that the IR test for short memory (d=0) against stationary long-memory alternatives has good size and power properties and is robust against changes in mean, slowly varying trends and nonstationarities. We apply this statistic to sequences of squares of returns on financial assets and obtain a nuanced picture of the presence of long-memory in asset price volatility.     

Hydrothermal Synthesis and Vacuum Ultraviolet-Excited Luminescence Properties of Novel Dy^3＋-doped GdPO4 White Light Phosphors

Novel Dy^3＋-doped GdPO4 white light phosphors with a monoclinic system are successfully synthesized by the hydrothermal method at 240℃. The strong absorption at around 147nm in the excitation spectrum is assigned to the host absorption. It is suggested that the vacuum ultraviolet excited energy is transferred from the host to the Dy^3＋ ions. The f - d transition of the Dy^3＋ ion is observed to be located at 182nm, which is consistent with the calculated value using Dorenbos＇s expression. Under 147nm excitation, Gd0.92PO4：0.08Dy^3＋ phosphor exhibits two emission bands located at 572 nm （yellow） and 478 nm （blue）, which correspond to the hypersensitive transitions ^4 F9/2-^6 H13/2 and ^4 F9/2-^6 H15/2. The two emission bands lead to the white light. Because of the strong absorption at about 147nm, Gd0.92PO4：0.08Dy^3＋ under vacuum ultraviolet excitation is an effective white light phosphor, and has promising applications to mercury-free lamps.     

A Note on the Game Chromatic Index of Graphs

In this note we prove that the game chromatic index χ _g ^′(G) of a graph G of arboricity k is at most Δ + 3k − 1. This improves a bound obtained by Cai and Zhu [J. Graph Theory 36 (2001), 144–155] for k-degenerate graphs. Tomasz Bartnicki: Research of the first author is supported by a PhD grant from Polish Ministry of Science and Higher Education N201 2128 33. Received: November 1, 2006. Final version received: December 22, 2007.     

Feasibility of using ultrasound contrast agents to increase the size of thermal lesions induced by non-focused transducers: in vitro demonstration in tissue mimicking phantom

Miniature flat ultrasound transducers have shown to be effective for a large variety of thermal therapies, but the associated superficial heating implicates developing original strategies in order to extend therapeutic depth. The goal of the present paper is to use ultrasound contrast agents (UCA) to increase remote attenuation and heating. Theoretical simulations demonstrated that increasing attenuation from 0.27 to 0.8 Np/cm at 10 MHz beyond a distance of 18 mm from the transducer should result in longer thermal damages due to protein coagulation in a tissue mimicking phantom. Contrast agents (BR14, Bracco, Plan-les-Ouates, Switzerland) were embedded in thermo-sensitive gel and attenuations ranging from 0.27 to 1.33 Np/cm were measured at 10 MHz for concentrations of BR14 between 0 and 4.8%. Thermal damages were then induced in several gels, which had different layering configurations. Thermal damages, 12.8 mm in length, were obtained in homogeneous gels. When mixing contrast agents at a concentration of 3.2% beyond a first 18 mm-thick layer of homogeneous gel, the thermal damages reached 21.5 mm in length. This work demonstrated that contrast agents can be used for increasing attenuation remotely and extending therapeutic depth induced by a non-focused transducer. Additional work must be done in vivo in order to verify the remote-only distribution of bubbles and associated increase in attenuation.     

逐步增加的Ⅱ型截尾下冷贮备串联系统可靠性指标的Bayes估计

在逐步增加的Ⅱ型截尾模型下,运用Bayes方法,研究部件寿命服从双参数指数分布的冷贮备串联系统可靠性指标的近似置信区间问题.在两个参数均未知的情形下,给出了失效率,系统可靠度及平均寿命的Bayes近似置信区间的计算公式;对于超参数的确定,给出一种新的方法;最后进行了随机模拟,并对近似置信区间的精度进行了讨论.     

Link Homologies and the Refined Topological Vertex

We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the Hopf link, whose components are colored by arbitrary representations of sl(N). At present, the mathematical formulation of such homological invariants is available only for the fundamental representation (the Khovanov-Rozansky theory) and the relation with the refined topological vertex should be useful for categorizing quantum group invariants associated with other representations (R ₁, R ₂). Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert space of BPS states in the presence of branes, where the physical interpretation of gradings is in terms of charges of the branes ending on Lagrangian branes.