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Data publikacji: 8 listopada 2023

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1

1954-, Dilcher Karl, Skula Ladislav i Slavutskiĭ Ilja Sh, red. Bernoulli numbers: Bibliography (1713-1990). Kingston, Ont: Queen's University, 1991.

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2

Arakawa, Tsuneo, Tomoyoshi Ibukiyama i Masanobu Kaneko. Bernoulli Numbers and Zeta Functions. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2.

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author, Ibukiyama Tomoyoshi, Kaneko Masanobu author i Zagier, Don, 1951- writer of supplementary textual content, red. Bernoulli numbers and Zeta functions. Tokyo: Springer, 2014.

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Kanemitsu, Shigeru. Vistas of special functions. Singapore: World Scientific, 2007.

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5

Invitation to classical analysis. Providence, R.I: American Mathematical Society, 2012.

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Vistas of Special Functions. World Scientific Publishing Company, 2007.

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7

Vorlesungen über die Bernoullischen zahlen: Ihren zusammenhang mit den secanten-coefficienten und ihre wichtigeren anwendungen. Berlin: J. Springer, 1991.

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Ibukiyama, Tomoyoshi, Masanobu Kaneko, Tsuneo Arakawa i Don B. Zagier. Bernoulli Numbers and Zeta Functions. Springer, 2016.

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9

Ibukiyama, Tomoyoshi, Masanobu Kaneko i Tsuneo Arakawa. Bernoulli Numbers and Zeta Functions. Springer, 2014.

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10

Franzosa, Marie M. Densities and dependence for point processes. 1988.

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11

Zabell, Sandy. Symmetry Arguments in Probability. Redaktorzy Alan Hájek i Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.15.

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The history of the use of symmetry arguments in probability theory is traced. After a brief consideration of why these did not occur in ancient Greece, the use of symmetry in probability, starting in the 17th century, is considered. Some of the contributions of Bernoulli, Bayes, Laplace, W. E. Johnson, and Bruno de Finetti are described. One important thread here is the progressive move from using symmetry to identify a single, unique probability function to using it instead to narrow the possibilities to a family of candidate functions via the qualitative concept of exchangeability. A number of modern developments are then discussed: partial exchangeability, the sampling of species problem, and Jeffrey conditioning. Finally, the use or misuse of seemingly innocent symmetry assumptions is illustrated, using a number of apparent paradoxes that have been widely discussed.

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Thurner, Stefan, Rudolf Hanel i Peter Klimekl. Probability and Random Processes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821939.003.0002.

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Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

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13

Escudier, Marcel. Bernoulli’s equation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0007.

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In this chapter Newton’s second law of motion is used to derive Euler’s equation for the flow of an inviscid fluid along a streamline. For a fluid of constant density ρ‎ Euler’s equation can be integrated to yield Bernoulli’s equation: p + ρ‎gz′ + ρ‎V2 = pT which shows that the sum of the static pressure p, the hydrostatic pressure ρ‎gz and the dynamic pressure ρ‎V2/2 is equal to the total pressure pT. The combination p + ρ‎V2/2 is an important quantity known as the stagnation pressure. Each of the terms on the left-hand side of Bernoulli’s equation can be regarded as representing different forms of mechanical energy and also equivalent to the hydrostatic pressure due to a vertical column of liquid. The dynamic pressure can be thought of as measuring the intensity or strength of a flow and is frequently combined with other fluid and flow properties to produce non-dimensional (or dimensionless) numbers which characterise various aspects of fluid motion.

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Skula, Ladislav, i Karl Dilcher. Bernoulli Numbers Bibliography (Queen's Papers in Pure and Applied Mathematics, No. 87). Queens Univ Campus, 1991.

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Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science. Columbia University Press, 2021.

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Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science. Columbia University Press, 2022.

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17

Dixon, Tim H., i Aubrey Clayton. Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science. Audible Studios on Brilliance Audio, 2021.

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