Invariance Principle Under Self-Normalization for Nonidentically Distributed Random Variables

Let V _n ^–1 _n be the adaptive process of self-normalized partial sums S _k of independent random variables X _i , defined by linear interpolation between the points (V _k ²/V _n ²,S _k /V _n ), kn, where V _k ²= _ik X _i ². We prove that if the X _k 's are symmetric, V _n ^–1 _n converges weakly to the Brownian motion W in each Hölder space supporting W if and only if V _n ^–1 max _kn |X _k |=o _P (1). We give some partial extension to the non symmetric case.     

Hölderian Invariance Principle for Triangular Arrays of Random Variables

In this paper, we extend the Hölderian invariance principle of Lamperti [6] to the case of partial-sum processes based on a triangular array of row-wise independent random variables. As an application, we obtain necessary and sufficient conditions for the almost sure (resp. in probability) weak Hölder convergence of partial-sum processes based on bootstrapped samples.     

Green's temperature functions of massive scalar particles for finite matter density

An explicit expression is obtained for the Green's functions of a massive scalar field for nonnull temperatures and density in the form of a series in powers of m/T. The equivalence of the spectral-geometric approach and the temperature technique of Matsubara and Bernard is demonstrated. Corrections to the Stefan-Boltzmann law are obtained on the basis of the calculated Green's functions. The energy density is calculated in regions of high and low temperatures. The formulas obtained can prove to be useful in the discussion of the phase transition hadrons-quark-gluon plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 32–40, July, 1991.     

Influence of crystal defects on the irreversibility line of YBa2Cu3O7-x single crystals

High quality flux grown and defect enriched peritectically grown YBa₂Cu₃O_7–x single crystals have been investigated by an ac-susceptibility technique. This method allows to determine an irreversibility line from the temperature and field dependence of the peaked imaginary part of the susceptibility, which is due to magnetic losses. For magnetic fieldsH _ac perpendicular to thec-axis of the crystal, the irreversibility line of the defect enriched crystal shows a shift to higher field values as compared to the perfect crystal, a sign that crystal defects like Y₂BaCuO₅(211)-precipitates and microcracks act as strong pinning centers. ForH _ac parallel to thec-axis no clear evidence for a stronger pinning is found. From these results we conclude that different pinning mechanisms are dominating at different field orientations.     

Efficiency of the multiwave method of determination of the ozone content in the atmosphere by UV spectrometry-ozonometry

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 3, pp. 472–477, September, 1991.     

Kink propagation induced by multiplicative noise

The influence of spatio-temporal external multiplicative fluctuations on a single kink in a bistable distributed system is studied. For this purpose we derive a stochastic dynamic equation for the position of the shifted kink. An analytical estimate for spatio-temporally uncorrelated fluctuations is represented and discussed. We draw the conclusion that multiplicative noise induces a propagation of the most probable kink into the region of larger noise. This effect is demonstrated in numerical simulations.     

Radiationless transition probabilities in muonic208Pb,232Th,and238U

The probabilities for non-radiative (n.r.) excitationsP _n.r. in the muonic nuclides²⁰⁸Pb,²³²Th, and²³⁸U have been determined from (μ^?,γγ)-measurements by comparing the intensities of muonic X-ray transitions in single and coincidence spectra. The value ofP _n.r. (3p→1s), measured for the first time, is about 90% for the actinides²³²Th and²³⁸U, but only about 8% for²⁰⁸Pb. The value ofP _n.r. (3d→1s) is found to be 10 % for²³³Th, 13% for²³⁸U, and about 4% for²⁰⁸Pb. For²⁰⁸Pb a vanishing strength of the n.r. decay of the 2p-level is found, while for²³²Th and for²³⁸U n.r. strengths of about 20% and 26%, respectively, are observed. By regarding two subcomplexes of the 2p→1s transitions leading to different mean excitation energies the n.r. transition probabilities were found to be different for²³⁸U only, 21.6% and 31.1.%, respectively.     

Finite element solutions for laminar flow and combined convection around a square prism

The finite element solutions of the full Navier-Stokes and energy equations for steady laminar flow and combined convection around square prisms with attack angles of 0° and 45° are obtained for a gas having Pr=0.7. The variations of surface shear stress, local pressure and Nusselt number are obtained over the entire prism surface including the zone beyond the point of the separation. The predicted values of drag coefficients, the location of separation, average Nusselt number and the plots of velocity flow fields and isotherms are also presented. The trend of the present numerical results seems reasonable.

---

Finite-Elemente-Verfahren für laminare Strömung und kombinierte Naturkonvektion um ein quadratisches Prisma

Zusammenfassung Es wird über Lösungen der Navier-Stokesund der Energiegleichungen mit Hilfe der Finite-Elemente-Methode für stationäre laminare Strömung, kombiniert mit Naturkonvektion, um ein quadratisches Prisma berichtet, wobei als Anströmwinkel 0° und 45° gewählt wurden und Gasströmung mitPr=0,7 angenommen wurde. Die Rechnung ergibt den Verlauf der Wandschubspannungen, des örtlichen Druckes und der Nusselt-Zahl über die gesamte Oberfläche des Prismas, einschließlich des Bereiches hinter dem Ablösepunkt. Weiterhin werden in dem Aufsatz Angaben gemacht über die Widerstandskoeffizienten, die Lage des Ablösepunktes, der mittleren Nusselt-Zahl sowie der Geschwindigkeits- und Temperaturfelder. Die numerischen Ergebnisse erscheinen im Trend vernünftig zu sein.

---

Nomenclature a side length of square - C _f friction drag coefficient - C _p pressure drag coefficient - C _D total drag coefficient - F _f total friction drag force - F _P total pressure drag force - Gr Groshoff number,g (T _w -T )a ³/v ² - g gravitational acceleration - h local heat transfer coefficient - K thermal conductivity - L dimensionless location of surface from the front stagna tion point,L ^*/a - L ^* dimension location of prism surface - Lc location of separation - N _j shape function - Nu, local and average Nusselt numbers - M _l shape function - P dimensionless pressure,p ^*/u ² - P ^* pressure - p _x ^* x-componentP ^* - Pe Peclet number,Re Pr - Pr Prandtl number, c/K - Ra Rayleigh number,Gr Pr - Re Reynolds number,a u /v - s direction along the sides of prism - u dimensionlessX-direction component of velocity,u ^*/u - u ^* X-direction component of velocity - u free stream velocity - dimensionlessY-direction component of velocity,v*/u - ^* Y-direction component of velocity - X X-direction axis - x dimensionlessX-direction coordinate,x ^*/a - x ^* X- direction coordinate - Y Y-direction axis - y ^* dimensionless 7-direction coordinate,y ^*/a - y ^* Y-direction coordinate Greek symbols coefficient of volumetric thermal expansion - attack angle - dynamic viscosity - kinematic viscosity,/ - density of fluid - _w dimensionless surface shear stress, _w ^* /u ² - _w ^* surface shear stress - _wx ^* x-component of _w ^/* - dimensionless temperature,      

In-beam spectroscopy of 253, 254No

In-beam conversion electron spectroscopy experiments have been performed on the transfermium nuclei ^{253, 254}No using the conversion electron spectrometer SACRED in nearly collinear geometry in conjunction with the gas-filled separator RITU at the University of Jyv?skyl?. The experimental setup is discussed and the spectra are compared to Monte Carlo simulations. The implications for the ground-state configuration of ²⁵³No are discussed. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: rdh@ns.ph.liv.ac.uk RID="b" ID="b"Present address: GANIL, F-14021 Caen, France. RID="c" ID="c"Permanent address: IReS Strasbourg, IN2P3-CNRS, F-67037-Strasbourg, France. RID="d" ID="d"Present address: CEA/DIF DCRE/SDE/LDN F-91680 Bruyeres-le-Chatel. RID="e" ID="e"Present address: Daresbury Laboratory, Daresbury WA4 4AD, UK. RID="f" ID="f"Permanent address: IPN Lyon, IN2P3-CNRS, F-69037 Lyon, France.