scholarly journals A Generalized Coupon Collector Problem

2011 ◽  
Vol 48 (4) ◽  
pp. 1081-1094 ◽  
Author(s):  
Weiyu Xu ◽  
A. Kevin Tang
Keyword(s):  
Exact Algorithm ◽  
Numerical Examples ◽  
Asymptotic Case ◽  
Finite Case ◽  
Coupon Collector ◽  
Theoretical Predictions

This paper presents an analysis of a generalized version of the coupon collector problem, in which the collector receives d coupons each run and chooses the least-collected coupon so far. In the asymptotic case when the number of coupons n goes to infinity, we show that, on average, (nlogn) / d + (n / d)(m − 1)log logn + O(mn) runs are needed to collect m sets of coupons. An exact algorithm is also developed for any finite case to compute the exact mean number of runs. Numerical examples are provided to verify our theoretical predictions.

scholarly journals A Generalized Coupon Collector Problem

2011 ◽  
Vol 48 (04) ◽  
pp. 1081-1094 ◽  
Author(s):  
Weiyu Xu ◽  
A. Kevin Tang
Keyword(s):  
Exact Algorithm ◽  
Numerical Examples ◽  
Asymptotic Case ◽  
Finite Case ◽  
Coupon Collector ◽  
Theoretical Predictions

This paper presents an analysis of a generalized version of the coupon collector problem, in which the collector receives d coupons each run and chooses the least-collected coupon so far. In the asymptotic case when the number of coupons n goes to infinity, we show that, on average, (nlogn) / d + (n / d)(m − 1)log logn + O(mn) runs are needed to collect m sets of coupons. An exact algorithm is also developed for any finite case to compute the exact mean number of runs. Numerical examples are provided to verify our theoretical predictions.

scholarly journals An Efficient Numerical Procedure for Thermohydrodynamic Analysis of Cavitating Bearings

1996 ◽  
Vol 118 (3) ◽  
pp. 555-563 ◽  
Author(s):  
D. Vijayaraghavan
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Boundary Conditions ◽  
Radial Direction ◽  
Heat Dissipation ◽  
Numerical Procedure ◽  
Hydrodynamic Performance ◽  
Numerical Examples ◽  
Thermal Boundary Conditions ◽  
Theoretical Predictions

In this paper, an efficient and accurate numerical procedure to determine the thermo-hydrodynamic performance of cavitating bearings is described. This procedure is based on the earlier development of Elrod for lubricating films, in which the properties across the film thickness are determined at Lobatto points and their distributions are expressed by collocated polynomials. The cavitated regions and their boundaries are rigorously treated. Thermal boundary conditions at the surfaces, including heat dissipation through the metal to the ambient, are incorporated. Numerical examples are presented comparing the predictions using this procedure with earlier theoretical predictions and experimental data. With a few points across the film thickness and across the journal and the bearing in the radial direction, the temperature profile is very well predicted.

scholarly journals A Discontinuous Finite Volume Method for the Darcy-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhe Yin ◽  
Ziwen Jiang ◽  
Qiang Xu
Keyword(s):  
Error Estimate ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Numerical Examples ◽  
First Order ◽  
Theoretical Predictions ◽  
Volume Method

This paper proposes a discontinuous finite volume method for the Darcy-Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh-dependent norm. First-orderL2-error estimates are derived for the approximations of both velocity and pressure. Some numerical examples verifying the theoretical predictions are presented.

scholarly journals CRITÈRES D'IRRÉDUCTIBILITÉ POUR LES REPRÉSENTATIONS DES COURBES ELLIPTIQUES

2011 ◽  
Vol 07 (04) ◽  
pp. 1001-1032 ◽  
Author(s):  
NICOLAS BILLEREY
Keyword(s):  
Elliptic Curve ◽  
Prime Number ◽  
Number Field ◽  
Efficient Algorithm ◽  
Complex Multiplication ◽  
Prime Numbers ◽  
Prime Divisors ◽  
Numerical Examples ◽  
Finite Case ◽  
Courbe Elliptique

Soit E une courbe elliptique définie sur un corps de nombres K. On dit qu'un nombre premier p est réductible pour le couple (E, K) si E admet une p-isogénie définie sur K. L'ensemble de tous ces nombres premiers est fini si et seulement si E n'a pas de multiplication complexe définie sur K. Dans cet article, on montre que l'ensemble des nombres premiers réductibles pour le couple (E, K) est contenu dans l'ensemble des diviseurs premiers d'une liste explicite d'entiers (dépendant de E et de K) dont une infinité d'entre eux est non nulle. Cela fournit un algorithme efficace de calcul dans le cas fini. D'autres critères moins généraux, mais néanmoins utiles sont donnés ainsi que de nombreux exemples numériques. Let E be an elliptic curve defined over a number field K. We say that a prime number p is reducible for (E, K) if E admits a p-isogeny defined over K. The so-called reducible set of all such prime numbers is finite if and only if E does not have complex multiplication over K. In this paper, we prove that the reducible set is included in the set of prime divisors of an explicit list of integers (depending on E and K), infinitely many of them being non-zero. It provides an efficient algorithm for computing it in the finite case. Other less general but rather useful criteria are given, as well as many numerical examples.

Vortex-Induced Response of a Flexible Cylinder in a Constant Current

1985 ◽  
Vol 107 (2) ◽  
pp. 244-249 ◽  
Author(s):  
N. M. Patrikalakis ◽  
C. Chryssostomidis
Keyword(s):  
Theoretical Prediction ◽  
Constant Current ◽  
Induced Response ◽  
Flexible Cylinder ◽  
Response Frequency ◽  
Numerical Examples ◽  
Simultaneous Evaluation ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Uniform Stream

In this paper we develop a method for the theoretical prediction of the static and lift responses of a flexible cylinder in a unidirectional constant current. Our theoretical prediction is based on information derived from experimental results involving rigid cylinders forced to oscillate sinusoidally orthogonally to a uniform stream. Our approach allows the prediction of a number of, independently determined, monochromatic, and multimode dynamic solutions. For each such multimode solution our procedure allows the simultaneous evaluation of lift response frequency, amplitude and phase between modes. Numerical examples assuming monomodal solutions are included to allow comparison of our theoretical predictions with experimental and other published theoretical results.

Microcalorimeters for X-Ray Spectroscopy

1988 ◽  
Vol 102 ◽  
pp. 41
Author(s):  
E. Silver ◽  
C. Hailey ◽  
S. Labov ◽  
N. Madden ◽  
D. Landis ◽  
...  
Keyword(s):  
High Resolution ◽  
High Efficiency ◽  
Thermal Response ◽  
Low Noise ◽  
High Resolution Spectroscopy ◽  
Superconducting Transition ◽  
Sapphire Substrates ◽  
Laboratory Plasmas ◽  
Adiabatic Demagnetization ◽  
Theoretical Predictions

The merits of microcalorimetry below 1°K for high resolution spectroscopy has become widely recognized on theoretical grounds. By combining the high efficiency, broadband spectral sensitivity of traditional photoelectric detectors with the high resolution capabilities characteristic of dispersive spectrometers, the microcalorimeter could potentially revolutionize spectroscopic measurements of astrophysical and laboratory plasmas. In actuality, however, the performance of prototype instruments has fallen short of theoretical predictions and practical detectors are still unavailable for use as laboratory and space-based instruments. These issues are currently being addressed by the new collaborative initiative between LLNL, LBL, U.C.I., U.C.B., and U.C.D.. Microcalorimeters of various types are being developed and tested at temperatures of 1.4, 0.3, and 0.1°K. These include monolithic devices made from NTD Germanium and composite configurations using sapphire substrates with temperature sensors fabricated from NTD Germanium, evaporative films of Germanium-Gold alloy, or material with superconducting transition edges. A new approache to low noise pulse counting electronics has been developed that allows the ultimate speed of the device to be determined solely by the detector thermal response and geometry. Our laboratory studies of the thermal and resistive properties of these and other candidate materials should enable us to characterize the pulse shape and subsequently predict the ultimate performance. We are building a compact adiabatic demagnetization refrigerator for conveniently reaching 0.1°K in the laboratory and for use in future satellite-borne missions. A description of this instrument together with results from our most recent experiments will be presented.

A crystallographic analysis of the CoSi/Si(111) interface using Transmission Electron Microscopy

1990 ◽  
Vol 48 (4) ◽  
pp. 574-575
Author(s):  
A.C. Daykin ◽  
C.J. Kiely ◽  
R.C. Pond ◽  
J.L. Batstone
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Defect Structure ◽  
Room Temperature ◽  
Theoretical Method ◽  
Crystallographic Analysis ◽  
Si Substrate ◽  
Transmission Electron ◽  
Theoretical Predictions

When CoSi2 is grown onto a Si(111) surface it can form in two distinct orientations. A-type CoSi2 has the same orientation as the Si substrate and B-type is rotated by 180° degrees about the [111] surface normal.One method of producing epitaxial CoSi2 is to deposit Co at room temperature and anneal to 650°C.If greater than 10Å of Co is deposited then both A and B-type CoSi2 form via a number of intermediate silicides .The literature suggests that the co-existence of A and B-type CoSi2 is in some way linked to these intermediate silicides analogous to the NiSi2/Si(111) system. The phase which forms prior to complete CoSi2 formation is CoSi. This paper is a crystallographic analysis of the CoSi2/Si(l11) bicrystal using a theoretical method developed by Pond. Transmission electron microscopy (TEM) has been used to verify the theoretical predictions and to characterise the defect structure at the interface.

Combining Defaults and Transparency Information to Increase Policy Compliance

2020 ◽  
Vol 51 (5) ◽  
pp. 354-359 ◽  
Author(s):  
Yavor Paunov ◽  
Michaela Wänke ◽  
Tobias Vogel
Keyword(s):  
Independent Effect ◽  
Online Experiment ◽  
Policy Compliance ◽  
Empirical Question ◽  
Theoretical Predictions

Abstract. Combining the strengths of defaults and transparency information is a potentially powerful way to induce policy compliance. Despite negative theoretical predictions, a recent line of research revealed that default nudges may become more effective if people are informed why they should exhibit the targeted behavior. Yet, it is an open empirical question whether the increase in compliance came from setting a default and consequently disclosing it, or the provided information was sufficient to deliver the effect on its own. Results from an online experiment indicate that both defaulting and transparency information exert a statistically independent effect on compliance, with highest compliance rates observed in the combined condition. Practical and theoretical implications are discussed.

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