Some asymptotic expansions of moments of order statistics

Series expansions of moments of order statistics are obtained from expansions of the inverse of the distribution function. They are valid for certain types of distributions with regularly varying tails. We show that the expansions converge quickly when the sample size is moderate to large, and we obtain bounds on the rate of convergence. The special case of the Cauchy distribution is treated in more detail.     

On low order moments of the homodyned-K distribution

Fractional low order moments have been reported as beneficial for sampling computations using the K distribution. However, it has been recently pointed out that this it not the case for the homodyned-K distribution for a tissue discrimination problem. In this paper we show that such an statement is not fully justified. To that end, we follow a standard pattern recognition procedure both to determine class separability measures and to classify data with several classifiers. We conclude that the optimum order of the moments is intimately linked to the specific statistical properties of the tissues to be discriminated. Some ideas on how to choose the optimum order are discussed.     

Lifetime measurements in Tm I,Tm II,and Tm III by time-resolved laser spectroscopy

Natural radiative lifetimes of eight levels in Tm I ( 4f ¹³5d6p and 4f ¹²5d6s ² configurations), two levels in Tm II ( 4f ¹²5d6s configuration) and three levels in Tm III (4f ¹²5d configuration) have been measured by using time-resolved laser spectroscopy. Free thulium atoms, as well as singly and doubly ionized ions, were obtained in a laser-induced thulium plasma and the investigated states were selectively populated by a single-step excitation process with a tunable narrow-band laser pulse. Received 20 August 2002 / Received in final form 7 January 2003 Published online 4 March 2003 RID="a" ID="a"e-mail: huailiang.xu@fysik.lth.se     

Compactly Supported Tight Affine Frames with Integer Dilations and Maximum Vanishing Moments

When a cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L ²=L ²(R) with dilation integer factor M2, the standard matrix extension approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The notion of vanishing moment recovery (VMR) was introduced in our earlier work (and independently by Daubechies et al.) for dilation M=2 to increase the order of vanishing moments. This present paper extends the tight frame results in the above mentioned papers from dilation M=2 to arbitrary integer M2 for any compactly supported M-dilation scaling functions. It is shown, in particular, that M compactly supported tight frame generators suffice, but not M–1 in general. A complete characterization of the M-dilation polynomial symbol is derived for the existence of M–1 such frame generators. Linear spline examples are given for M=3,4 to demonstrate our constructive approach.     

A novel approach to separating EPR lines arising from species with different transition moments

In pulsed EPR, spectral contributions from several species in one sample can be separated based on different EPR transition probabilities. This is usually done by monitoring the Rabi nutations in a 2D experiment. By using long pulses, the FID and echo shapes of species with different transition probabilities differ significantly, including temporal shifts of the observed echo signals in a two-pulse ESE experiment. These shifts can be used to disentangle spectral components in a 1D field-swept ESE experiment by choosing an appropriate detection time. This approach is demonstrated by experiments on a sample containing Mn(2+) and Cr(3+) centers as well as on an exchange-coupled Mn(III)/Mn(IV) system with Mn(2+) contaminations.     

Numerical Analysis of Electromagnetic Fields in Multiscale Model

Modeling technique for electromagnetic fields excited by antennas is an important topic in computational electromagnetics, which is concerned with the numerical solution of Maxwell's equations. In this paper, a novel hybrid technique that combines method of moments(MoM) with finite-difference time-domain(FDTD) method is presented to handle the problem. This approach employed Huygen's principle to realize the hybridization of the two classical numerical algorithms. For wideband electromagnetic data, the interpolation scheme is used in the MoM based on the dyadic Green's function. On the other hand, with the help of equivalence principle, the scattered electric and magnetic fields on the Huygen's surface calculated by MoM are taken as the sources for FDTD. Therefore, the electromagnetic fields in the environment can be obtained by employing finite-difference time-domain method. Finally, numerical results show the validity of the proposed technique by analyzing two canonical samples.     

Spectral,thermal and magnetic investigations of Mn(II), Co(II), Ni(II), Cu(II), Zn(II) and Cd(II) 4-methylphthalates

Conditions for the preparation of Mn(II), Co(II), Ni(II), Cu(II), Zn(II) and Cd(II) 4-methylphthalates were investigated and their composition, solubility in water at 295 K and magnetic moments were determined. IR spectra and powder diffraction patterns of the complexes prepared with molar ratio of metal to organic ligand of 1.0:1.0 and general formula: M [ CH₃C₆H₃(CO₂)₂]·nH₂o (n=1-3) were recorded and their decomposition in air were studied. During heating the hydrated complexes are dehydrated in one (Mn, Co, Ni, Zn, Cd) or two steps (Cu) and next the anhydrous complexes decompose to oxides directly (Cu, Zn), with intermediate formation of carbonates (Mn, Cd), oxocarbonates (Ni) or carbonate and free metal (Co). The carboxylate groups in the complexes studied are mono- and bidentate (Co, Ni), bidentate chelating and bridging (Zn) or bidentate chelating (Mn, Cu, Cd). The magnetic moments for paramagnetic complexes of Mn(II), Co(II), Ni(II) and Cu(II) attain values 5.92, 5.05, 3.36 and 1.96 M.B., respectively. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electromagnetic form factors of nucleons in a relativistic square-root potential model of independent quarks

The nucleon electromagnetic form factorsG _E ^P (q²),G _M ^P (q²) and the axial-vector form factor G_A(q²) are studied in a relativistic model of independent quarks confined by an equally mixed scalar-vector square root potentialV _q(r)=1/2(1+γ ⁰)(ar ^1/2+ν ₀) taking into account the appropriate centre-of-mass corrections. The respective root-mean-square radii associated withG _E ^P (q²) and G _A (q²) come out as [〈r ²〉 _E ^P ]^1/2=0.86 fm and 〈r _A ² 〉^1/2=0.88 fm. Restoration of chiral symmetry in this model is discussed to derive the pion-nucleon form factorG _πNN(q²) and consequently the pion-nucleon coupling constant is obtained asg _πNN(q²)=12.81 as compared tog _πNN(q²)_exp⋍13.     

二维轴对称图象高阶胡氏不变矩快速算法的改进

提出了基于二维轴对称性目标图象矩快速算法的实用化改进方案.算法实用化改进是通过两个命题的证明实现的.一是通过轴对称目标图象质心在对称轴上的命题证明,实现了将二维轴对称图象矩快速算法用于轴对称性图象中心矩的计算;二是通过目标图象以坐标系中任意两点为圆心,旋转相同角度,结果图象具有平移性的命题证明,实现了算法用于对旋转不同角度的对称目标图象的中心矩的计算改进.在此基础上,完成了二维轴对称目标图象高阶胡氏不变矩实用化快速算法的实现.实验证明,该算法具有较好的实时性能,且具有较小的引入误差.