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Journal articles on the topic 'Probabilistic number theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Stakėnas, Vilius. "The probabilistic number theory and continuum." Lietuvos matematikos rinkinys, no. III (December 17, 1999): 93–99. http://dx.doi.org/10.15388/lmr.1999.35485.

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Let bn be a sequence of real numbers increasing unboundedly, α > 0 and B(n, α) = [bn α]. The conditions on bn are considered, which imply the regularity of distribution of B(n, α) in arithmetic progressions for almost all α > 0. This allows to develop a piece of probabilistic number theory on sequences B(n, α) for almost all α > 0.

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2

Indlekofer, K. H. "Number theory—probabilistic, heuristic, and computational approaches." Computers & Mathematics with Applications 43, no. 8-9 (2002): 1035–61. http://dx.doi.org/10.1016/s0898-1221(02)80012-8.

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3

Stakėnas, V. "On some inequalities of probabilistic number theory." Lithuanian Mathematical Journal 46, no. 2 (2006): 208–16. http://dx.doi.org/10.1007/s10986-006-0022-2.

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4

Erdõs, P. "Recent problems in probabilistic number theory and combinatorics." Advances in Applied Probability 24, no. 4 (1992): 766–67. http://dx.doi.org/10.1017/s0001867800024654.

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5

Stakėnas, Vilius. "Jonas Kubilius and genesis of probabilistic number theory." Lithuanian Mathematical Journal 55, no. 1 (2015): 25–47. http://dx.doi.org/10.1007/s10986-015-9263-2.

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6

Zhang, Wen-Bin. "Probabilistic number theory in additive arithmetic semigroups II." Mathematische Zeitschrift 235, no. 4 (2000): 747–816. http://dx.doi.org/10.1007/s002090000165.

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7

Kátai, Imre, Bui Minh Phong, and Le Manh Thanh. "Some results and problems in probabilistic number theory." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 43 (2014): 253–65. https://doi.org/10.71352/ac.43.253.

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8

Elliott, P. D. T. A. "Jonas Kubilius and Probabilistic Number Theory Some Personal Reflections." Lithuanian Mathematical Journal 55, no. 1 (2015): 2–24. http://dx.doi.org/10.1007/s10986-015-9262-3.

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9

Daili, Noureddine. "DENSITIES AND NATURAL INTEGRABILITY. APPLICATIONS IN PROBABILISTIC NUMBER THEORY." JP Journal of Algebra, Number Theory and Applications 47, no. 1 (2020): 51–65. http://dx.doi.org/10.17654/nt047010051.

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10

Lokutsievskiy, Lev V. "Optimal probabilistic search." Sbornik: Mathematics 202, no. 5 (2011): 697–719. http://dx.doi.org/10.1070/sm2011v202n05abeh004162.

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11

Aistleitner, Christoph, and Christian Elsholtz. "The Central Limit Theorem for Subsequences in Probabilistic Number Theory." Canadian Journal of Mathematics 64, no. 6 (2012): 1201–21. http://dx.doi.org/10.4153/cjm-2011-074-1.

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Abstract Let (nk)k≥1 be an increasing sequence of positive integers, and let f (x) be a real function satisfyingIf the distribution ofconverges to a Gaussian distribution. In the casethere is a complex interplay between the analytic properties of the function f , the number-theoretic properties of (nk)k≥1, and the limit distribution of (2).In this paper we prove that any sequence (nk)k≥1 satisfying lim contains a nontrivial subsequence (mk)k≥1 such that for any function satisfying (1) the distribution ofconverges to a Gaussian distribution. This result is best possible: for any ε > 0 there

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12

Haik, Sumayra. "AFFINE LINES AND ADVANCED PROBABILISTIC MODEL THEORY." Mathematical Statistician and Engineering Applications 70, no. 2 (2021): 01–14. http://dx.doi.org/10.17762/msea.v70i2.8.

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Letjbe an almost surely algebraic, meromorphic domain.Recent developments in singular logic [36, 22] have raised the question ofwhether every pseudo-Dedekind number is ultra-Gaussian and singular.We show tha

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13

Barát, Anna, and Erdener Kaya. "On the models of Indlekofer and Kubilius in probabilistic number theory." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 39 (2013): 17–34. https://doi.org/10.71352/ac.39.017.

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14

Keller, Frank, and Ash Asudeh. "Probabilistic Learning Algorithms and Optimality Theory." Linguistic Inquiry 33, no. 2 (2002): 225–44. http://dx.doi.org/10.1162/002438902317406704.

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This article provides a critical assessment of the Gradual Learning Algorithm (GLA) for probabilistic optimality-theoretic (OT) grammars proposed by Boersma and Hayes (2001). We discuss the limitations of a standard algorithm for OT learning and outline how the GLA attempts to overcome these limitations. We point out a number of serious shortcomings with the GLA: (a) A methodological problem is that the GLA has not been tested on unseen data, which is standard practice in computational language learning. (b) We provide counterexamples, that is, attested data sets that the GLA is not able to le

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15

Lazorec, Mihai-Silviu. "Probabilistic aspects of ZM-groups." Communications in Algebra 47, no. 2 (2018): 541–52. http://dx.doi.org/10.1080/00927872.2018.1482310.

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16

Heijungs, Reinout. "On the number of Monte Carlo runs in comparative probabilistic LCA." International Journal of Life Cycle Assessment 25, no. 2 (2019): 394–402. http://dx.doi.org/10.1007/s11367-019-01698-4.

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Abstract Introduction The Monte Carlo technique is widely used and recommended for including uncertainties LCA. Typically, 1000 or 10,000 runs are done, but a clear argument for that number is not available, and with the growing size of LCA databases, an excessively high number of runs may be a time-consuming thing. We therefore investigate if a large number of runs are useful, or if it might be unnecessary or even harmful. Probability theory We review the standard theory or probability distributions for describing stochastic variables, including the combination of different stochastic variabl

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17

Corob Cook, Ged, and Matteo Vannacci. "Probabilistic finiteness properties for profinite groups." Journal of Algebra 574 (May 2021): 584–616. http://dx.doi.org/10.1016/j.jalgebra.2021.01.026.

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18

Ragot, Jean-François. "Probabilistic absolute irreducibility test for polynomials." Journal of Pure and Applied Algebra 172, no. 1 (2002): 87–107. http://dx.doi.org/10.1016/s0022-4049(01)00165-7.

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19

Dvurecenskij, Anatolij, та Jiri Rachunek. "Probabilistic Averaging in Bounded Rℓ-Monoids". Semigroup Forum 72, № 2 (2006): 191–206. http://dx.doi.org/10.1007/s00233-005-0545-6.

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20

Guralnick, Robert M., and William M. Kantor. "Probabilistic Generation of Finite Simple Groups." Journal of Algebra 234, no. 2 (2000): 743–92. http://dx.doi.org/10.1006/jabr.2000.8357.

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21

KUBOTA, Hisayoshi, and Hiroshi SUGITA. "PROBABILISTIC PROOF OF LIMIT THEOREMS IN NUMBER THEORY BY MEANS OF ADELES." Kyushu Journal of Mathematics 56, no. 2 (2002): 391–404. http://dx.doi.org/10.2206/kyushujm.56.391.

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22

Thiagarajan, P. S., and Shaofa Yang. "A Theory of Distributed Markov Chains." Fundamenta Informaticae 175, no. 1-4 (2020): 301–25. http://dx.doi.org/10.3233/fi-2020-1958.

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We present the theory of distributed Markov chains (DMCs). A DMC consists of a collection of communicating probabilistic agents in which the synchronizations determine the probability distribution for the next moves of the participating agents. The key feature of a DMC is that the synchronizations are deterministic, in the sense that any two simultaneously enabled synchronizations involve disjoint sets of agents. Using our theory of DMCs we show how one can analyze the behavior using the interleaved semantics of the model. A key point is, the transition system which defines the interleaved sem

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23

Chan, Yu, Emelie Curl, Jesse Geneson, et al. "Using Markov Chains to Determine Expected Propagation Time for Probabilistic Zero Forcing." Electronic Journal of Linear Algebra 36, no. 36 (2020): 318–33. http://dx.doi.org/10.13001/ela.2020.5127.

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Zero forcing is a coloring game played on a graph where each vertex is initially colored blue or white and the goal is to color all the vertices blue by repeated use of a (deterministic) color change rule starting with as few blue vertices as possible. Probabilistic zero forcing yields a discrete dynamical system governed by a Markov chain. Since in a connected graph any one vertex can eventually color the entire graph blue using probabilistic zero forcing, the expected time to do this is studied. Given a Markov transition matrix for a probabilistic zero forcing process, an exact formula is es

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24

Pfeifer, Dietmar. "A probabilistic variant of Chernoff's product formula." Semigroup Forum 46, no. 1 (1993): 279–85. http://dx.doi.org/10.1007/bf02573572.

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25

Morillas, Patricia. "Optimal dual fusion frames for probabilistic erasures." Electronic Journal of Linear Algebra 32 (February 6, 2017): 191–203. http://dx.doi.org/10.13001/1081-3810.3267.

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For any fixed fusion frame, its optimal dual fusion frames for reconstruction is studied in case of erasures of subspaces. It is considered that a probability distribution of erasure of subspaces is given and that a blind reconstruction procedure is used, where the erased data are set to zero. It is proved that there are always optimal duals. Sufficient conditions for the canonical dual fusion frame being either the unique optimal dual, a non-unique optimal dual, or a non optimal dual, are obtained. The reconstruction error is analyzed, using the optimal duals in the probability model consider

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26

Damian, E., and A. Lucchini. "Finite Groups withp-Multiplicative Probabilistic Zeta Function." Communications in Algebra 35, no. 11 (2007): 3451–72. http://dx.doi.org/10.1080/00927870701509313.

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27

Breuer, Thomas, Robert M. Guralnick, and William M. Kantor. "Probabilistic generation of finite simple groups, II." Journal of Algebra 320, no. 2 (2008): 443–94. http://dx.doi.org/10.1016/j.jalgebra.2007.10.028.

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28

HIRTH, ULRICH MARTIN. "Probabilistic Number Theory, the GEM/Poisson-Dirichlet Distribution and the Arc-sine Law." Combinatorics, Probability and Computing 6, no. 1 (1997): 57–77. http://dx.doi.org/10.1017/s0963548396002805.

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The prime factorization of a random integer has a GEM/Poisson-Dirichlet distribution as transparently proved by Donnelly and Grimmett [8]. By similarity to the arc-sine law for the mean distribution of the divisors of a random integer, due to Deshouillers, Dress and Tenenbaum [6] (see also Tenenbaum [24, II.6.2, p. 233]), – the ‘DDT theorem’ – we obtain an arc-sine law in the GEM/Poisson-Dirichlet context. In this context we also investigate the distribution of the number of components larger than ε which correspond to the number of prime factors larger than nε.

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29

Yee, Eugene. "Theory for Reconstruction of an Unknown Number of Contaminant Sources using Probabilistic Inference." Boundary-Layer Meteorology 127, no. 3 (2008): 359–94. http://dx.doi.org/10.1007/s10546-008-9270-5.

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30

Zhang, Wenyu, and Yuting Zhu. "The Probabilistic Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Cumulative Prospect Theory and Its Application." Axioms 12, no. 10 (2023): 925. http://dx.doi.org/10.3390/axioms12100925.

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Addressing the complex issue of multi-attribute decision-making within a probabilistic dual hesitant fuzzy context, where attribute weights are unknown, a novel decision-making method based on cumulative prospect theory is proposed, named the probabilistic dual hesitant fuzzy multi-attribute decision-making method based on cumulative prospect theory. Firstly, a decision matrix is formulated, representing probabilistic dual hesitant fuzzy information. Secondly, according to the decision maker’s authentic preference and non-membership information sensitivity, a comprehensive score function suita

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31

DAMIAN, ERIKA, and ANDREA LUCCHINI. "A PROBABILISTIC GENERALIZATION OF SUBNORMALITY." Journal of Algebra and Its Applications 04, no. 03 (2005): 313–23. http://dx.doi.org/10.1142/s0219498805001204.

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A subnormal subgroup X of G has the following property: there exists a Dirichlet polynomial Q(s) with integer coefficients such that, for each t ∈ ℕ, Q(t) is the conditional probability that t random elements generate G given that they generate G together with the elements of X In this paper we analyze how far can a subgroup X be with this property from being a subnormal subgroup.

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32

Matera, Guillermo. "Probabilistic Algorithms for Geometric Elimination." Applicable Algebra in Engineering, Communication and Computing 9, no. 6 (1999): 463–520. http://dx.doi.org/10.1007/s002000050115.

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33

Shareshian, John. "On the Probabilistic Zeta Function for Finite Groups." Journal of Algebra 210, no. 2 (1998): 703–7. http://dx.doi.org/10.1006/jabr.1998.7560.

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34

Damian, Erika, and Andrea Lucchini. "The probabilistic zeta function of finite simple groups." Journal of Algebra 313, no. 2 (2007): 957–71. http://dx.doi.org/10.1016/j.jalgebra.2007.02.055.

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35

Mosbah, Mohamed. "PROBABILISTIC GRAPH GRAMMARS." Fundamenta Informaticae 26, no. 3,4 (1996): 341–62. http://dx.doi.org/10.3233/fi-1996-263406.

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36

Alon, Noga. "Choice Numbers of Graphs: a Probabilistic Approach." Combinatorics, Probability and Computing 1, no. 2 (1992): 107–14. http://dx.doi.org/10.1017/s0963548300000122.

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The choice number of a graph G is the minimum integer k such that for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). By applying probabilistic methods, it is shown that there are two positive constants c1 and c2 such that for all m ≥ 2 and r ≥ 2 the choice number of the complete r-partite graph with m vertices in each vertex class is between c1r log m and c2r log m. This supplies the solutions of two problems of Erdős, Rubin and Taylor, as it implies that the choice number of almost all the gra

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37

Sproston, Jeremy. "Probabilistic Timed Automata with Clock-Dependent Probabilities." Fundamenta Informaticae 178, no. 1-2 (2021): 101–38. http://dx.doi.org/10.3233/fi-2021-2000.

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Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition probabilities can depend linearly on clock values. Clock-dependent probabilistic timed automata allow the modelling of a continuous relationship between time passage and the likelihood of system events. We show that the problem of deciding whether the maximum probability of reaching a certain location is above a threshold is undecidable for clock-dependent p

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38

Brennan, Zachary. "Probabilistic zero forcing with vertex reversion." Electronic Journal of Linear Algebra 41 (January 21, 2025): 49–73. https://doi.org/10.13001/ela.2025.8653.

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Probabilistic zero forcing is a graph coloring process in which blue vertices "infect" (color blue) white vertices with a probability proportional to the number of neighboring blue vertices. This paper introduces reversion probabilistic zero forcing (RPZF), which shares the same infection dynamics but also allows for blue vertices to revert to being white in each round. A threshold number of blue vertices is produced such that the complete graph is entirely blue in the next round of RPZF with high probability. Utilizing Markov chain theory, a tool is formulated which, given a graph's RPZF Mark

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39

FREIVALDS, RŪSIŅŠ. "NON-CONSTRUCTIVE METHODS FOR FINITE PROBABILISTIC AUTOMATA." International Journal of Foundations of Computer Science 19, no. 03 (2008): 565–80. http://dx.doi.org/10.1142/s0129054108005826.

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Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. However, the proof is non-constructive. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures not proved but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these

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40

Liu, Yuqi, Xuehua Li, and Huan Li. "N-Widths of Multivariate Sobolev Spaces with Common Smoothness in Probabilistic and Average Settings in the Sq Norm." Axioms 12, no. 7 (2023): 698. http://dx.doi.org/10.3390/axioms12070698.

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In this article, we give the sharp bounds of probabilistic Kolmogorov N,δ-widths and probabilistic linear N,δ-widths of the multivariate Sobolev space W2A with common smoothness on a Sq norm equipped with the Gaussian measure μ, where A⊂Rd is a finite set. And we obtain the sharp bounds of average width from the results of the probabilistic widths. These results develop the theory of approximation of functions and play important roles in the research of related approximation algorithms for Sobolev spaces.

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41

Bukovics, István, and István Kun. "Non-probabilistic hazard evaluation." Opuscula Theologica et Scientifica 1, no. 1 (2023): 131–42. http://dx.doi.org/10.59531/ots.2023.1.1.131-142.

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Quantitative analysis of complex risk systems often faces three major problems. The first problem is the size of the system to be examined, since the number of possible system states increases exponentially with system size. The second problem is the topology of the system which may not be tree-like. The third problem is the consideration of randomness, since risk events are in many cases single, non-repetitive, therefore probability theory is inadequate. In order to handle this deficiency we suggest to apply logical risk analysis which traces back the main risk event to elementary, controllab

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42

Abbes, Samy. "Introduction to Probabilistic Concurrent Systems." Fundamenta Informaticae 187, no. 2-4 (2022): 71–102. http://dx.doi.org/10.3233/fi-222133.

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The first part of the paper is an introduction to the theory of probabilistic concurrent systems under a partial order semantics. Key definitions and results are given and illustrated on examples. The second part includes contributions. We introduce deterministic concurrent systems as a subclass of concurrent systems. Deterministic concurrent system are “locally commutative” concurrent systems. We prove that irreducible and deterministic concurrent systems have a unique probabilistic dynamics, and we characterize these systems by means of their combinatorial properties. ACM CSS: G.2.1; F.1.1

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43

Beyerlein, I. J., and C. N. Tomé. "A probabilistic twin nucleation model for HCP polycrystalline metals." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2121 (2010): 2517–44. http://dx.doi.org/10.1098/rspa.2009.0661.

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This article presents a basic probabilistic theory for the nucleation of deformation twins in hexagonal close packed (HCP) metals. Twin nucleation is assumed to rely on the dissociation of grain boundary defects (GBDs) under stress into the required number of twinning partials to create a twin nucleus. The number of successful conversion events is considered to follow a stochastic Poisson process where the rate is assumed to increase with local stress. From this concept, the probability distribution for the critical stress to form a twin nucleus is derived wherein the parameters of the distrib

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44

SHAKERI, S. "A CONTRACTION THEOREM IN MENGER PROBABILISTIC METRIC SPACES." Journal of Nonlinear Sciences and Applications 01, no. 03 (2008): 189–93. http://dx.doi.org/10.22436/jnsa.001.03.07.

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45

Shatanawi, Wasfi, and Mihai Postolache. "Mazur-Ulam theorem for probabilistic 2-normed spaces." Journal of Nonlinear Sciences and Applications 08, no. 06 (2015): 1228–33. http://dx.doi.org/10.22436/jnsa.008.06.29.

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46

Krejsa, Martin, Petr Janas, Işık Yilmaz, Marian Marschalko, and Tomas Bouchal. "The Use of the Direct Optimized Probabilistic Calculation Method in Design of Bolt Reinforcement for Underground and Mining Workings." Scientific World Journal 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/267593.

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The load-carrying system of each construction should fulfill several conditions which represent reliable criteria in the assessment procedure. It is the theory of structural reliability which determines probability of keeping required properties of constructions. Using this theory, it is possible to apply probabilistic computations based on the probability theory and mathematic statistics. Development of those methods has become more and more popular; it is used, in particular, in designs of load-carrying structures with the required level or reliability when at least some input variables in t

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47

Bruce, Juliette, and Daniel Erman. "A probabilistic approach to systems of parameters and Noether normalization." Algebra & Number Theory 13, no. 9 (2019): 2081–102. http://dx.doi.org/10.2140/ant.2019.13.2081.

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48

Ben-Ari, Iddo, and Michael Neumann. "Probabilistic approach to Perron root, the group inverse, and applications." Linear and Multilinear Algebra 60, no. 1 (2012): 39–63. http://dx.doi.org/10.1080/03081087.2011.559167.

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49

Huynh, Dung T., and Lu Tian. "On Some Equivalence Relations for Probabilistic Processes1." Fundamenta Informaticae 17, no. 3 (1992): 211–34. http://dx.doi.org/10.3233/fi-1992-17304.

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In this paper, we investigate several equivalence relations for probabilistic labeled transition systems: bisimulation equivalence, readiness equivalence, failure equivalence, trace equivalence, maximal trace equivalence and finite trace equivalence. We formally prove the inclusions (equalities) among these equivalences. We also show that readiness, failure, trace, maximum trace and finite trace equivalences for finite probabilistic labeled transition systems are decidable in polynomial time. This should be contrasted with the PSPACE completeness of the same equivalences for classical labeled

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50

Markov, Boris A., and Yury I. Sukharev. "Probabilistic and dynamic colloid equations." Butlerov Communications 57, no. 3 (2019): 33–41. http://dx.doi.org/10.37952/roi-jbc-01/19-57-3-33.

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We obtained two equations that characterize the structure of the colloid: the equation of the Schrodinger type that specifies the redistribution of heat and potential energy in the colloid and material equation – the diffusion equation with the operator of Liesegang associated directly with a substance that allows you to find the discontinuities of the structures caused by the vibrations of electrically charged particles. This procedure based on the assumption of the instability of the colloidal state, caused by the movement of charged particles. The reality is not collected in parts from the

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