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Journal articles on the topic 'Bernoulli'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Kammeyer, Janet Whalen. "A classification of the isometric extensions of a multidimensional Bernoulli shift." Ergodic Theory and Dynamical Systems 12, no. 2 (1992): 267–82. http://dx.doi.org/10.1017/s014338570000674x.

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AbstractThe isometric extensions of a multidimensional Bernouli shift are classified completely, up to C-isomorphism, and up to isomorphism. If such an extension is weakly mixing then it must be Bernoulli; otherwise, it has a rotation factor, which has a Bernoulli complementary algebra. This result is extended to multidimensional Bernoulli flows and Bernoulli shifts of infinite entropy.

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2

Majdina, Nadhilah Idzni, Budi Pratikno, and Agustini Tripena. "PENENTUAN UKURAN SAMPEL MENGGUNAKAN RUMUS BERNOULLI DAN SLOVIN: KONSEP DAN APLIKASINYA." Jurnal Ilmiah Matematika dan Pendidikan Matematika 16, no. 1 (2024): 73. http://dx.doi.org/10.20884/1.jmp.2024.16.1.11230.

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ABSTRACT. The research discussed a sample survey to draw the population inference based on the sample from that population. There are several techniques to take a sample size, but here we focused to use the Bernoulli’s and Slovin’s formula. This study aims to: (1) reconstruct the Bernoulli’s and Slovin’s formula and (2) examine the conditions (properties) in using the Bernoulli’s and Slovin’s formula. Here, we used a simple random sampling (SRM). Furthermore, both the reconstruction of Bernoulli's and Slovin's formula used the SRM as a sampling technique. This is due to the simple random sampl

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3

Suryaningtyas, Wahyuni, Nur Iriawan, Heri Kuswanto, and Ismaini Zain. "On the Hierarchical Bernoulli Mixture Model Using Bayesian Hamiltonian Monte Carlo." Symmetry 13, no. 12 (2021): 2404. http://dx.doi.org/10.3390/sym13122404.

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The model developed considers the uniqueness of a data-driven binary response (indicated by 0 and 1) identified as having a Bernoulli distribution with finite mixture components. In social science applications, Bernoulli’s constructs a hierarchical structure data. This study introduces the Hierarchical Bernoulli mixture model (Hibermimo), a new analytical model that combines the Bernoulli mixture with hierarchical structure data. The proposed approach uses a Hamiltonian Monte Carlo algorithm with a No-U-Turn Sampler (HMC/NUTS). The study has performed a compatible syntax program computation ut

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4

Taylor, John A. "Marginal Utility and New Saint Petersburg Paradoxes." Vestnik of Saint Petersburg University. History 69, no. 3 (2024): 758–73. http://dx.doi.org/10.21638/spbu02.2024.313.

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Adam Smith may have read Daniel Bernoulli’s 1738 essay on risk, and Smith modified his view on risk while teaching jurisprudence to two Russian students, this essay argues. The matter is important because William Stanley Jevons read Adam Smith closely, of course, but Jevons did not read Daniel Bernoulli, and Jevons convinced Alfred Marshall that the concept of marginal utility did not need the advanced mathematical probability which they could have found in Bernoulli. Jevons thought arguments in English prose, like Smith’s arguments, together with the very simple mathematics of Gregory King we

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5

Bayad, Abdelmejid, and Yilmaz Simsek. "On Generating Functions for Parametrically Generalized Polynomials Involving Combinatorial, Bernoulli and Euler Polynomials and Numbers." Symmetry 14, no. 4 (2022): 654. http://dx.doi.org/10.3390/sym14040654.

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The aim of this paper is to give generating functions for parametrically generalized polynomials that are related to the combinatorial numbers, the Bernoulli polynomials and numbers, the Euler polynomials and numbers, the cosine-Bernoulli polynomials, the sine-Bernoulli polynomials, the cosine-Euler polynomials, and the sine-Euler polynomials. We investigate some properties of these generating functions. By applying Euler’s formula to these generating functions, we derive many new and interesting formulas and relations related to these special polynomials and numbers mentioned as above. Some s

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6

Sniecinski, Roman M. "Bernoulli." Anesthesia & Analgesia 119, no. 6 (2014): 1238–40. http://dx.doi.org/10.1213/ane.0000000000000490.

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7

Filipovic, Mirjana, and Ana Djuric. "Whole analogy between Daniel Bernoulli solution and direct kinematics solution." Theoretical and Applied Mechanics 37, no. 1 (2010): 49–78. http://dx.doi.org/10.2298/tam1001049f.

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In this paper, the relationship between the original Euler-Bernoulli's rod equation and contemporary knowledge is established. The solution which Daniel Bernoulli defined for the simplest conditions is essentially the solution of 'direct kinematics'. For this reason, special attention is devoted to dynamics and kinematics of elastic mechanisms configuration. The Euler-Bernoulli equation and its solution (used in literature for a long time) should be expanded according to the requirements of the mechanisms motion complexity. The elastic deformation is a dynamic value that depends on the total m

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8

Diniz, Marcio Alves. "Stop calling Bernoulli’s law of large numbers his "Golden Theorem" (Please?)." Revista Brasileira de História da Matemática 24, no. 48 (2024): 151–55. http://dx.doi.org/10.47976/rbhm2024v24n48151-155.

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Jakob Bernoulli (1655 - 1705) proved the first form of the law of large numbers before 1690 and realized the range of applications of probability calculus would be largely widened by the result. It is pretty common to find examples in the statistical literature referring to it as his “Golden Theorem”. But when did Jakob name his discovery? In fact, he never did, at least this one. A mistake in the translation of Bernoulli's major work, Ars Conjectandi (1713), and the fact that Bernoulli named another result as “Golden theorem” led us to propagate this mistake ... for almost 100 years.

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9

Sun, Zhi-Hong. "Congruences concerning Bernoulli numbers and Bernoulli polynomials." Discrete Applied Mathematics 105, no. 1-3 (2000): 193–223. http://dx.doi.org/10.1016/s0166-218x(00)00184-0.

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10

Sun, Zhi-Hong. "Congruences for Bernoulli numbers and Bernoulli polynomials." Discrete Mathematics 163, no. 1-3 (1997): 153–63. http://dx.doi.org/10.1016/s0012-365x(97)81050-3.

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11

Alzer, Horst, and Man Kam Kwong. "Identities for Bernoulli polynomials and Bernoulli numbers." Archiv der Mathematik 102, no. 6 (2014): 521–29. http://dx.doi.org/10.1007/s00013-014-0653-1.

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12

Ananjevskii, Sergey M., and Valery B. Nevzorov. "On series of successes in Bernoulli sequences of random variables." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 11, no. 4 (2024): 663–70. https://doi.org/10.21638/spbu01.2024.403.

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Some of the first studies in probability theory were associated with Bernoulli schemes - sequences of independent identically distributed random variables taking the values 1 with a certain probability 0 < p < 1 and 0 with a probability q = 1 - p. The study of sequences of such random variables led to the need to deal with a geometrically distributed random variable. Limit theorems for properly centered and normalized sums required the consideration and study of normally distributed random variables. Working with classical Bernoulli sequences and their other two-point generalizations led

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13

Kenyon, Kern E. "Believing Bernoulli." Natural Science 10, no. 04 (2018): 142–50. http://dx.doi.org/10.4236/ns.2018.104015.

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14

Deshmukh, Shailaja R. "BERNOULLI SAMPLING." Australian Journal of Statistics 33, no. 2 (1991): 167–76. http://dx.doi.org/10.1111/j.1467-842x.1991.tb00424.x.

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15

Hewitt, Paul. "BERNOULLI BUBBLES." Physics Teacher 57, no. 4 (2019): 212. http://dx.doi.org/10.1119/1.5095370.

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16

Gradl, Hans, and Sebastian Walcher. "Bernoulli algebras." Communications in Algebra 21, no. 10 (1993): 3503–20. http://dx.doi.org/10.1080/00927879308824745.

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17

Pizzo, Joe. "Bernoulli station." Physics Teacher 27, no. 4 (1989): 308–10. http://dx.doi.org/10.1119/1.2342770.

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18

Waltham, Chris, Sarah Bendall, and Andrzej Kotlicki. "Bernoulli levitation." American Journal of Physics 71, no. 2 (2003): 176–79. http://dx.doi.org/10.1119/1.1524162.

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19

Brusca, S. "Buttressing Bernoulli." Physics Education 21, no. 1 (1986): 14–18. http://dx.doi.org/10.1088/0031-9120/21/1/307.

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20

Murphy, A. B., and S. Brusca. "Bernoulli effect." Physics Education 21, no. 5 (1986): 262–63. http://dx.doi.org/10.1088/0031-9120/21/5/104.

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21

McCaughan, J. B. T., and S. Brusca. "Bernoulli bunkum." Physics Education 22, no. 1 (1987): 9–11. http://dx.doi.org/10.1088/0031-9120/22/1/102.

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22

Mukhopadhyay, Utpal. "Bernoulli brothers." Resonance 6, no. 10 (2001): 29–37. http://dx.doi.org/10.1007/bf02836965.

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23

Kowalski, Zbigniew S. "Bernoulli property of smooth extensions of Bernoulli shifts." Applicationes Mathematicae 46, no. 2 (2019): 275–82. http://dx.doi.org/10.4064/am2376-2-2019.

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24

Dilcher, Karl. "Zeros of Bernoulli, generalized Bernoulli and Euler polynomials." Memoirs of the American Mathematical Society 73, no. 386 (1988): 0. http://dx.doi.org/10.1090/memo/0386.

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25

Si, Do Tan. "The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked." Applied Mathematics 10, no. 03 (2019): 100–112. http://dx.doi.org/10.4236/am.2019.103009.

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26

R. Sivaraman. "On Class of Area Vanishing Functions on the Unit Interval." Journal of Information Systems Engineering and Management 10, no. 31s (2025): 1057–68. https://doi.org/10.52783/jisem.v10i31s.5206.

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Among several classes of Riemann integrable real valued functions we are interested in finding class of functions whose (signed) integral values over a compact interval vanishes. Determining such class of functions was one of the important objectives of this paper. We begin our quest by introducing Bernoulli numbers then extending them to Bernoulli polynomials. We observe that Bernoulli polynomials are generalized version of the most famous and notorious Bernoulli numbers introduced by Jacob Bernoulli in 1713. In particular, we see that Bernoulli numbers are simply the constant terms of Bernou

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27

Cao, Jian, José Luis López-Bonilla, and Feng Qi. "Three identities and a determinantal formula for differences between Bernoulli polynomials and numbers." Electronic Research Archive 32, no. 1 (2023): 224–40. http://dx.doi.org/10.3934/era.2024011.

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<abstract><p>In the paper, the authors simply review recent results of inequalities, monotonicity, signs of determinants, determinantal formulas, closed-form expressions, and identities of the Bernoulli numbers and polynomials, establish an identity involving the differences between the Bernoulli polynomials and the Bernoulli numbers, present two identities among the differences between the Bernoulli polynomials and the Bernoulli numbers in terms of a determinant and a partial Bell polynomial, and derive a determinantal formula of the differences between the Bernoulli polynomials a

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28

Kim, Taekyun. "On the Symmetries of theq-Bernoulli Polynomials." Abstract and Applied Analysis 2008 (2008): 1–7. http://dx.doi.org/10.1155/2008/914367.

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Kupershmidt and Tuenter have introduced reflection symmetries for theq-Bernoulli numbers and the Bernoulli polynomials in (2005), (2001), respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a symmetry of power sum polynomials and the classical Bernoulli numbers. In this paper, we study the new symmetries of theq-Bernoulli numbers and polynomials, which are different from Kupershmidt's and Tuenter's results. By using our symmetries for

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29

Jiu, Lin, Victor H. Moll, and Christophe Vignat. "A symbolic approach to some identities for Bernoulli–Barnes polynomials." International Journal of Number Theory 12, no. 03 (2016): 649–62. http://dx.doi.org/10.1142/s1793042116500421.

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The Bernoulli–Barnes polynomials are defined as a natural multidimensional extension of the classical Bernoulli polynomials. Many of the properties of the Bernoulli polynomials admit extensions to this new family. A specific expression involving the Bernoulli–Barnes polynomials has recently appeared in the context of self-dual sequences. The work presented here provides a proof of this self-duality using the symbolic calculus attached to Bernoulli numbers and polynomials. Several properties of the Bernoulli–Barnes polynomials are established by this procedure.

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30

Yushkevich, A. P. "Nicholas Bernoulli and the Publication of James Bernoulli’s Ars Conjectandi." Theory of Probability & Its Applications 31, no. 2 (1987): 286–303. http://dx.doi.org/10.1137/1131034.

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31

Porter, Christopher P. "Effective aspects of Bernoulli randomness." Journal of Logic and Computation 29, no. 6 (2019): 933–46. http://dx.doi.org/10.1093/logcom/exz021.

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Abstract In this paper, we study Bernoulli random sequences, i.e. sequences that are Martin-Löf random with respect to a Bernoulli measure $\mu _p$ for some $p\in [0,1]$, where we allow for the possibility that $p$ is noncomputable. We focus in particular on the case in which the underlying Bernoulli parameter $p$ is proper (i.e. Martin-Löf random with respect to some computable measure). We show for every Bernoulli parameter $p$, if there is a sequence that is both proper and Martin-Löf random with respect to $\mu _p$, then $p$ itself must be proper, and explore further consequences of this r

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32

Sharyn, Campbell A., Anant P. Godbole, and Stephanie Schaller. "Discriminating between sequences of bernoulli and markov-bernoulli trials." Communications in Statistics - Theory and Methods 23, no. 10 (1994): 2787–814. http://dx.doi.org/10.1080/03610929408831416.

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33

Kim, Dae San, and Taekyun Kim. "Bernoulli Basis and the Product of Several Bernoulli Polynomials." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/463659.

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34

Dilcher, Karl. "Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials." Journal of Approximation Theory 49, no. 4 (1987): 321–30. http://dx.doi.org/10.1016/0021-9045(87)90071-2.

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35

Ônishi, Yoshihiro. "Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers." Russian Mathematical Surveys 66, no. 5 (2011): 871–932. http://dx.doi.org/10.1070/rm2011v066n05abeh004763.

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36

Kargın, Levent. "p-Bernoulli and geometric polynomials." International Journal of Number Theory 14, no. 02 (2018): 595–613. http://dx.doi.org/10.1142/s1793042118500665.

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We relate geometric polynomials and [Formula: see text]-Bernoulli polynomials with an integral representation, then obtain several properties of [Formula: see text]-Bernoulli polynomials. These results yield new identities for Bernoulli numbers. Moreover, we evaluate a Faulhaber-type summation in terms of [Formula: see text]-Bernoulli polynomials. Finally, we introduce poly-[Formula: see text]-Bernoulli polynomials and numbers, then study some arithmetical and number theoretical properties of them.

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37

Bolthausen, Erwin, and Mario V. Wüthrich. "BERNOULLI'S LAW OF LARGE NUMBERS." ASTIN Bulletin 43, no. 2 (2013): 73–79. http://dx.doi.org/10.1017/asb.2013.11.

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AbstractThis year we celebrate the 300th anniversary of Jakob Bernoulli's path-breaking work Ars conjectandi, which appeared in 1713, eight years after his death. In Part IV of his masterpiece, Bernoulli proves the law of large numbers which is one of the fundamental theorems in probability theory, statistics and actuarial science. We review and comment on his original proof.

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38

Guan, Hao, Waseem Ahmad Khan, and Can Kızılateş. "On Generalized Bivariate (p,q)-Bernoulli–Fibonacci Polynomials and Generalized Bivariate (p,q)-Bernoulli–Lucas Polynomials." Symmetry 15, no. 4 (2023): 943. http://dx.doi.org/10.3390/sym15040943.

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Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties, have been studied in the literature with the help of generating functions and their functional equations. In this paper, we define the generalized (p,q)-Bernoulli–Fibonacci and generalized (p,q)-Bernoulli–Lucas polynomials and numbers by using the (p,q)-Bernoulli numbers, unified (p,q)-Bernoulli polynomials, h(x)-Fibonacci polynomials, and h(x)-Lucas polynomials. We also introduce the generalized bivariate (p,q)-Bernoulli–Fibonacci and generalized bivariate (p,q)-Bernoulli–Lucas polyno

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39

Filipovic, Mirjana. "New form of the Euler-Bernoulli rod equation applied to robotic systems." Theoretical and Applied Mechanics 35, no. 4 (2008): 381–406. http://dx.doi.org/10.2298/tam0804381f.

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This paper presents a theoretical background and an example of extending the Euler-Bernoulli equation from several aspects. Euler-Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. The stiffness matrix is a full matrix. Damping is an omnipresent elasticity characteristic of real systems, so that it is naturally included in the Euler-Bernoulli equation. It is shown that Daniel Bernoulli's particular integral is just one component of the total elastic deformation

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40

Phang, Chang, Yoke Teng Toh, and Farah Suraya Md Nasrudin. "An Operational Matrix Method Based on Poly-Bernoulli Polynomials for Solving Fractional Delay Differential Equations." Computation 8, no. 3 (2020): 82. http://dx.doi.org/10.3390/computation8030082.

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In this work, we derive the operational matrix using poly-Bernoulli polynomials. These polynomials generalize the Bernoulli polynomials using a generating function involving a polylogarithm function. We first show some new properties for these poly-Bernoulli polynomials; then we derive new operational matrix based on poly-Bernoulli polynomials for the Atangana–Baleanu derivative. A delay operational matrix based on poly-Bernoulli polynomials is derived. The error bound of this new method is shown. We applied this poly-Bernoulli operational matrix for solving fractional delay differential equat

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41

Ramadan, Mohamed Abdel Latif, and Mohamed R. Ali. "Application of Bernoulli wavelet method to solve a system of fuzzy integral equations." Journal of Modern Methods in Numerical Mathematics 9, no. 1-2 (2018): 16–27. http://dx.doi.org/10.20454/jmmnm.2018.1262.

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In this paper, an efficient numerical method to solve a system of linear fuzzy Fredholm integral equations of the second kind based on Bernoulli wavelet method (BWM) is proposed. Bernoulli wavelets have been generated by dilation and translation of Bernoulli polynomials. The aim of this paper is to apply Bernoulli wavelet method to obtain approximate solutions of a system of linear Fredholm fuzzy integral equations. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, then we used it to transform the integral equations to the system of algebraic equations. The error e

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42

Bayad, Abdelmejid, Daeyeoul Kim, and Yan Li. "Arithmetical properties of double Möbius-Bernoulli numbers." Open Mathematics 17, no. 1 (2019): 32–42. http://dx.doi.org/10.1515/math-2019-0006.

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Abstract Given positive integers n, n′ and k, we investigate the Möbius-Bernoulli numbers Mk(n), double Möbius-Bernoulli numbers Mk(n,n′), and Möbius-Bernoulli polynomials Mk(n)(x). We find new identities involving double Möbius-Bernoulli, Barnes-Bernoulli numbers and Dedekind sums. In part of this paper, the Möbius-Bernoulli polynomials Mk(n)(x), can be interpreted as critical values of the following Dirichlet type L-function $$\begin{array}{} \displaystyle L_{HM}(s;n,x):=\sum_{d|n} \sum_{m= 0}^\infty \frac{\mu(d)}{(md+x)^s} \, \, \text{(for Re} (s) \gt 1), \end{array} $$ which has analytic c

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43

Korkmaz, Mustafa Ç., Víctor Leiva, and Carlos Martin-Barreiro. "The Continuous Bernoulli Distribution: Mathematical Characterization, Fractile Regression, Computational Simulations, and Applications." Fractal and Fractional 7, no. 5 (2023): 386. http://dx.doi.org/10.3390/fractalfract7050386.

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The continuous Bernoulli distribution is defined on the unit interval and has a unique property related to fractiles. A fractile is a position on a probability density function where the corresponding surface is a fixed proportion. This article presents the derivation of properties of the continuous Bernoulli distribution and formulates a fractile or quantile regression model for a unit response using the exponentiated continuous Bernoulli distribution. Monte Carlo simulation studies evaluate the performance of point and interval estimators for both the continuous Bernoulli distribution and th

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44

Weinmann, Siegfried. "Entscheidungen über unsichere Gewinne und Verluste von Geld und Zeit." WiSt - Wirtschaftswissenschaftliches Studium 50, no. 12 (2021): 63–70. http://dx.doi.org/10.15358/0340-1650-2021-12-63.

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Wie bewertet ein Investor die Aussicht auf einen Geldgewinn oder ein Fahrer den Zeitverlust einer Route? Das normative Entscheidungsmodell von Bernoulli mit dem logarithmischen Ansatz hat den Vorteil, eine Ressource am Vermögen des Nutzers zu bewerten, doch in der Literatur über Bernoullis Prinzip des Erwartungsnutzens kommt dieser Ansatz zu kurz. Typische Beispiele zeigen, wie der logarithmische Nutzen ökonomisches Verhalten bei unsicheren Gewinnen abbildet, wie ursprünglich gedacht, doch auch Entscheidungen bei Verlusten plausibel darstellt.

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45

Kim, T., J. Choi, and Y. H. Kim. "Some Identities on theq-Bernoulli Numbers and Polynomials with Weight 0." Abstract and Applied Analysis 2011 (2011): 1–8. http://dx.doi.org/10.1155/2011/361484.

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Recently, Kim (2011) has introduced theq-Bernoulli numbers with weightα. In this paper, we consider theq-Bernoulli numbers and polynomials with weightα=0and givep-adicq-integral representation of Bernstein polynomials associated withq-Bernoulli numbers and polynomials with weight0. From these integral representation onℤp, we derive some interesting identities on theq-Bernoulli numbers and polynomials with weight0.

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46

Luo, Qiu-Ming, Bai-Ni Guo, Feng Qi, and Lokenath Debnath. "Generalizations of Bernoulli numbers and polynomials." International Journal of Mathematics and Mathematical Sciences 2003, no. 59 (2003): 3769–76. http://dx.doi.org/10.1155/s0161171203112070.

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The concepts of Bernoulli numbersBn, Bernoulli polynomialsBn(x), and the generalized Bernoulli numbersBn(a,b)are generalized to the oneBn(x;a,b,c)which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships betweenBn,Bn(x),Bn(a,b), andBn(x;a,b,c)are established.

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47

Lee, Si Hyeon, Li Chen, and Wonjoo Kim. "Probabilistic Type 2 poly-Bernoulli Polynomials." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 2336–48. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5275.

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The main purpose of this article is to introduce the probabilistic type 2 poly-Bernoulli polynomials under the condition that Y is a random variable. This means that we will consider the probabilistic extension of the type 2 poly-Bernoulli polynomials and study to obtain some new results. Furthermore, we also define the probabilistic unipoly-Bernoulli polynomials and numbers attached to p, and investigate their interesting basic properties. Based on these new definition, we derive some meaningful formulae of probabilistic type 2 poly-Bernoulli polynomials and probabilistic unipoly-Bernoulli po

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48

Sahu, P. K., and S. Saha Ray. "A New Bernoulli Wavelet Method for Numerical Solutions of Nonlinear Weakly Singular Volterra Integro-Differential Equations." International Journal of Computational Methods 14, no. 03 (2017): 1750022. http://dx.doi.org/10.1142/s0219876217500220.

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In this paper, Bernoulli wavelet method has been developed to solve nonlinear weakly singular Volterra integro-differential equations. Bernoulli wavelets are generated by dilation and translation of Bernoulli polynomials. The properties of Bernoulli wavelets and Bernoulli polynomials are first presented. The present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by Newton’s method. Convergence analysis of the present method has been discussed in this paper. Some illustrative examples ha

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49

Noh, Hae-Young, Anne Kiremidjian, Luis Ceferino, and Emily So. "Bayesian Updating of Earthquake Vulnerability Functions with Application to Mortality Rates." Earthquake Spectra 33, no. 3 (2017): 1173–89. http://dx.doi.org/10.1193/081216eqs133m.

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Vulnerability functions often rely on data from expert opinion, post-earthquake investigations, or analytical simulations. Combining the information can be particularly challenging. In this paper, a Bayesian statistical framework is presented to combining disparate information. The framework is illustrated through application to earthquake mortality data obtained from the 2005 Pakistan earthquake and from PAGER. Three different models are tested including an exponential, a combination of Bernoulli and exponential and Bernoulli and gamma fit to model respectively zero and non-zero mortality rat

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Wang, Caishi, and Beiping Wang. "Dirichlet Forms Constructed from Annihilation Operators on Bernoulli Functionals." Advances in Mathematical Physics 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/8278161.

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Abstract:

The annihilation operators on Bernoulli functionals (Bernoulli annihilators, for short) and their adjoint operators satisfy a canonical anticommutation relation (CAR) in equal-time. As a mathematical structure, Dirichlet forms play an important role in many fields in mathematical physics. In this paper, we apply the Bernoulli annihilators to constructing Dirichlet forms on Bernoulli functionals. Let w be a nonnegative function on N. By using the Bernoulli annihilators, we first define in a dense subspace of L2-space of Bernoulli functionals a positive, symmetric, bilinear form Ew associated wi

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