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Progressive Randomization of a Deck of Playing Cards: Experimental Tests and Statistical Analysis of the riffle Shuffle

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Open Journal of Statistics 2019年第2期9卷 268-298页

作者： M. P. Silverman Department of Physics Trinity College Hartford CT USA

The question of how many shuffles are required to randomize an initially ordered deck of cards is a problem that has fascinated mathematicians, scientists, and the general public. The two principal theoretical approaches to the problem, which differed in how each defined randomness, has led to statistically different threshold numbers of shuffles. This paper reports a comprehensive experimental analysis of the card randomization problem for the purposes of determining 1) which of the two theoretical approaches made the more accurate prediction, 2) whether different statistical tests yield different threshold numbers of randomizing shuffles, and 3) whether manual or mechanical shuffling randomizes a deck more effectively for a given number of shuffles. Permutations of 52-card decks, each subjected to sets of 19 successive riffle shuffles executed manually and by an auto-shuffling device were recorded sequentially and analyzed in respect to 1) the theory of runs, 2) rank ordering, 3) serial correlation, 4) theory of rising sequences, and 5) entropy and information theory. Among the outcomes, it was found that: 1) different statistical tests were sensitive to different patterns indicative of residual order;2) as a consequence, the threshold number of randomizing shuffles could vary widely among tests;3) in general, manual shuffling randomized a deck better than mechanical shuffling for a given number of shuffles;and 4) the mean number of rising sequences as a function of number of manual shuffles matched very closely the theoretical predictions based on the Gilbert-Shannon-Reed (GSR) model of riffle shuffles, whereas mechanical shuffling resulted in significantly fewer rising sequences than predicted.

关键词： Randomization of Cards Number of riffle Shuffles Rising Sequences GSR Model Entropy and Information

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Environmental Characterization of Periphyton Community

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Journal of Ocean University of China 2006年第4期5卷 305-310页

作者： Y. M. Jo J. M. Oh J.G.Yoo Department of Environmental Science & Engineering Center for Environmental Studies Kyunghee University Kyunggido 449-701 Kore Department of Chemical Engineering Hanseo University Chungcheongnamdo Korea

The present paper deals with the behavior of the Attached Microbial Community (AMC) for water self-purification at different riverbeds in a typical local river. The study quantitatively investigated the problem starting with in-situ sampling. It was found that more biomass of AMC was at riffles with wider distribution than in pools. High current velocity (HCV) plays a negative role at the initial stage of attachment on the riverbed, but HCV aids the community proliferation after stable attachment. External disturbances such as rainfalls and discharges from dams or reservoirs would detach the periphyton depending on the intensity of turbulence in water. However, it was discovered that the flock of periphyton could be restored very quickly because it was not completely removed. Thus, in order to enhance self-purification by periphyton, a suitable configuration of the riverbed must be constructed, and occasional appropriate repair along the channels would improve the decontamination of the river.

关键词： periphyton riffle pool riverbed self-purification

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Study on the Utilization of Low Grade Tin Ore Results Washing(SHP)with a Shaking Table to Improve Recovery and Grade of Tin Ore:Case Study in Toboali Washing Plant PT Timah Tbk Bangka

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Journal of Environmental Science and Engineering(A) 2022年第5期11卷 171-181页

作者： Taufik Arief Fajri Vidian Nina Tanzerina Department of Mining Engineering Faculty of EngineeringSriwijaya UniversityPalembang City 30139South SumateraIndonesia Mechanical Engineering Department Faculty of EngineeringSriwijaya UniversityPalembang City 30139South SumateraIndonesia Biology Department Faculty of Mathematics and EducationSriwijaya UniversityPalembang City 30139South SumateraIndonesia

Shaking table is a technology that is still used in processing of tin ore using water as a *** the application at PT Timah Tbk,the shaking table is still used to process low grade tin ore into tin ore with a standard smelting grade of PT Timah(72%-74%Sn).In processing tin ore using a shaking table,valuable minerals and impurity minerals are separated based on differences in specific gravity,size and shape of the *** get the recovery of valuable minerals(recovery)and optimal grades,it is strongly influenced by the separation variables of tin ore *** variables include riffle,slope of deck,washing water rate,stroke length,and deck movement *** study aims to vary the number of riffles,table slope and time in a laboratory scale to obtain optimal recovery and grade of tin *** ore samples were obtained from the washing residue of the Toboali Washing Plant tin *** the experiment,the numbers of riffles set were 16(R1),24(R2)and 34(R3).The table slopes were 2°(S1),3°(S2),and 4°(S3).Time variations were 15(T1),20(T2)and 25 min(T3).The relationship between the number of riffles and the grade can be determined through quadratic polynomial regression analysis with the functionŶ=-20.60+2.26X+(-0.04X2),while the relationship between the number of riffles and recovery is determined by the functionŶ=-173.33+17.376 X+(-0.315X2).Optimal levels are obtained at variations in the number of riffle 26 by 66.43%,with levels of 8.45%*** recovery is obtained on the variation of the number of riffle 28 with a recovery of 66.43%.

关键词： Tin ore shaking table riffle content recovery

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