Theorie und Optimierung der radiometrischen Absorptionsmethode zur Analyse von Binärsystemen

Die Arbeit behandelt theoretisch das Auflösungsvermögen der Absorptionsmethode zur Analyse von Binārsystemen bei Anwendung von monoenergetischer Gamma- und Rötgenstrahlung. Es wird eine analytische Beziehung für die Funktion Δp abgeleitet, die die kleinstmöglichen Veränderung in der Zusammensetzung des Systems chgarakterisiert und die wir noch mittelts dieser Methode in Abhängigkeit von allen zu berückischtigenden Faktoren bestimmen könne. Aus den Extremwerten der Funktion Δp werden dann die optimalen Werte der Energine, der Schichtdicke, der Strahlungshäufigkeit und die Optimalwerte der restlichen Parameter so bestimmt, daβ das Auflösungsvermögen der Methode maximal ist. Die Theorie wird auf eine Ag-Cu-Legierung angewendet.     

A Note on a Paper by P. Amodio and F. Mazzia

In 1999 Amodio and Mazzia presented a new backward error analysis for LU factorization and introduced a new growth factor _n . Their very interesting approach allowed them to obtain sharp error bounds. In particular, they derive nice results assuming that partial pivoting is used. However, the forward error bound for the solution of a linear system whose coefficient matrix A is an M-atrix given in Theorem 4.1 of that paper is not correct. They first obtain a bound for the condition number (U) assuming that one has the LU factorization of an M-matrix and then they apply the bounds obtained when partial pivoting is used. But if P is the permutation associated with partial pivoting then PA = LU can fail to be an M-atrix and the bound for (U) can be false, as shown in our Example 1.1. We also prove that, for a pivoting strategy presented in the paper, the growth factor of an M-matrix A is _n(A) = 1 and (U) (A), where U is the upper triangular matrix obtained after applying such a pivoting strategy.This revised version was published online in October 2005 with corrections to the Cover Date.     

Effect of Co2+ on the growth,optical properties and laser damage threshold of potential nonlinear optical l-alanine single crystal

Good transparent bulk single crystals of pure l-alanine (LA) and cobalt doped LA crystals have been synthesized and successfully grown by slow-cooling method from their aqueous solutions. The concentration of metal dopants in the mother solution with 0.5 mol% for cobalt was carried out individually and crystals were obtained with well defined morphology. The as grown metal doped and pure single crystals were characterized by single crystal XRD studies which confirm that the incorporation of metallic dopants has not changed the basic structure of the parent crystal. The absorption of these crystals was analyzed and the result confirms that they possess low absorption in the range 230–1100 nm. Fourier transform infrared (FTIR) spectroscopy was carried out to investigate the molecular vibrations of these crystals and to confirm the incorporation of the dopants. The thermal properties have been studied by TGA/DTA curves. The EDAX measurement and surface morphology were studied for pure and metal doped LA crystals. The second harmonic generation (SHG) signals were observed using Nd: YAG laser with fundamental wavelength of 1064 nm in pure and metal doped crystals. The laser damage threshold was measured for pure and metal doped LA crystals and also tested by using a Q-switched Nd: YAG laser showed enhanced LDT value for metal (Co²⁺) doped LA crystal compared to pure LA crystal due to the metallic substitutions thus proving their useful candidature for nonlinear optical applications.     

Goodness-Of-Fit Tests Based on Estimated Expectations of Probability Integral Transformed Order Statistics

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the location-scale model. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesized distribution. The limiting null distributions of the test statistics are derived in terms of functionals of a certain Gaussian process, and the tests are shown to be consistent against a broad family of alternatives. Critical points for all sample sizes are provided for tests of normality. A simulation study shows that the proposed tests are more powerful than established tests such as Shapiro-Wilk, Cramér-von Mises and Anderson-Darling, for a wide range of alternative distributions.     

Some Results for the Compound Poisson Process That Is Perturbed by Diffusion

Abstract In the present paper surplus process perturbed by diffusion are considered.The distributions ofthe surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation andruin caused by a claim are studied.Some joint distribution densities are obtained.Techniques from martingaletheory and renewal theory are used.     

分布变点模型的非参数检验和区间估计

提 要设　是定义在［０,１］上的随机过程Ｘ（ｔ）的ｎ个等距独立观察值,其中,　服从公共连续分布Ｆ;,服从公共连续分布 Ｆ＊,Ｆ与Ｆ＊不同;其中,是过程 Ｘ（ｔ）的变点．用ＣＵＳＵＭ及Ｂｒｏｗｎｉａｎ Ｓｈｅｅｔ方法给出了检测变点τ位置的一个程序,并证明了所得结果是强相合的;同时也讨论了τ的假设检验和区间估计．     

Asymptotically minimax testing ofr>2 simple hypotheses

In this paper, we consider the problem of asymptotically minimax testing ofr≥2 simple hypotheses when a general stochastic process is observed. We establish general conditions for the exponential decrease of maximal probability errors of minimax tests as the number of observations increases. At the present time, similar results for testing several multinomial schemes were obtained by Salihov [8]. Similar results for testing two simple hypotheses were obtained in [5]. In the proofs of the main results, we use the theory of large deviations ([3], [2]). In Sec. 1, the main result is proved. In Secs. 2–4, we analyze the i.i.d. case, nonhomogeneous Poisson processes, and renewal processes as examples. Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 313–320, July–September, 2000.     

关于非负下半连续函数最优可测耦合的存在性及其应用

本文证明了两个转移概率关于非负下半连续函数最优可测耦合的存在性定理．作为对这一结果的应用,推广了Ｓｔｒａｓｓｅｎ定理,进而证明了跳过程的随机可比性等价于保序耦合的存在性．     

Ultra-thin film growth of titanium dioxide on W(1 0 0)

We have employed low energy electron diffraction (LEED) and X-ray photoelectron spectroscopy to follow the epitaxial growth of thin films of TiO₂ on W(1 0 0). The films were grown both by metal vapour deposition of titanium onto the substrate in UHV with subsequent annealing in a low partial pressure of oxygen, and by metal vapour deposition in a low partial pressure of oxygen. LEED patterns showed the characteristic patterns of (1 1 0) oriented rutile. A systematic spot splitting was observed and attributed to a stepped surface. The calculated step height was found to be in good agreement with that expected for rutile TiO₂(1 1 0), 3.3 Å. Titanium core level shifts were used to identify oxidation states as a function of film thickness allowing the interpretation in terms of a slightly sub-stoichiometric interface layer in contact with the substrate. In combination with the LEED patterns, the film structure is therefore determined to be (1 1 0) oriented rutile with a comparable level of stoichiometry to UHV prepared bulk crystals. The ordered step structure indicates considerable structural complexity of the surface.