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Journal articles on the topic '0-1 law'

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Published: 10 December 2022
Last updated: 29 January 2023

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1

Jones, Colin P. A. "Law and morality in evolutionary competition: Law: 1, morality: 0." Think 5, no. 14 (2007): 93–102. http://dx.doi.org/10.1017/s1477175600001937.

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2

Malyshkin, Y. A., and M. E. Zhukovskii. "MSO 0-1 law for recursive random trees." Statistics & Probability Letters 173 (June 2021): 109061. http://dx.doi.org/10.1016/j.spl.2021.109061.

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3

Járai, Antal. "A 0–1 law for multiplicative functional equations." Aequationes mathematicae 90, no. 1 (February 2016): 147–61. http://dx.doi.org/10.1007/s00010-016-0407-1.

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4

Zimand, Marius. "A High-Low Kolmogorov Complexity Law equivalent to the 0–1 Law." Information Processing Letters 57, no. 2 (January 1996): 59–64. http://dx.doi.org/10.1016/0020-0190(95)00201-4.

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5

Blaho, Peter. "Karol Rebro ( 2 7.1 0.1 9 1 2 - 3 1.1 0.2 0 0 0 )." Zeitschrift der Savigny-Stiftung für Rechtsgeschichte. Romanistische Abteilung 119, no. 1 (August 1, 2002): 680–82. http://dx.doi.org/10.7767/zrgra.2002.119.1.680.

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6

Kolaitis, Ph G., H. J. Promel, and B. L. Rothschild. "K l+1 -Free Graphs: Asymptotic Structure and a 0-1 Law." Transactions of the American Mathematical Society 303, no. 2 (October 1987): 637. http://dx.doi.org/10.2307/2000689.

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7

Berti, Patrizia, and Pietro Rigo. "A Conditional 0–1 Law for the Symmetric σ-field." Journal of Theoretical Probability 21, no. 3 (June 10, 2008): 517–26. http://dx.doi.org/10.1007/s10959-008-0174-6.

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8

Rodriguez, Pierre-François. "A 0–1 law for the massive Gaussian free field." Probability Theory and Related Fields 169, no. 3-4 (October 6, 2016): 901–30. http://dx.doi.org/10.1007/s00440-016-0743-z.

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9

Baláž, V., K. Nagasaka, and O. Strauch. "Benford’s law and distribution functions of sequences in (0, 1)." Mathematical Notes 88, no. 3-4 (October 2010): 449–63. http://dx.doi.org/10.1134/s0001434610090178.

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10

Brightwell, Graham. "Random graph orders do not satisfy a 0-1 law." Random Structures & Algorithms 6, no. 2-3 (March 1995): 231–38. http://dx.doi.org/10.1002/rsa.3240060211.

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11

Kolaitis, Ph G., H. J. Pr{ömel, and B. L. Rothschild. "$K\sb {l+1}$-free graphs: asymptotic structure and a $0$-$1$ law." Transactions of the American Mathematical Society 303, no. 2 (February 1, 1987): 637. http://dx.doi.org/10.1090/s0002-9947-1987-0902790-6.

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12

Burris, Stanley, Kevin Compton, Andrew Odlyzko, and Bruce Richmond. "Fine Spectra and Limit Laws, II First-Order 0–1 Laws." Canadian Journal of Mathematics 49, no. 4 (August 1, 1997): 641–52. http://dx.doi.org/10.4153/cjm-1997-030-6.

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AbstractUsing Feferman-Vaught techniques a condition on the fine spectrum of an admissible class of structures is found which leads to a first-order 0–1 law. The condition presented is best possible in the sense that if it is violated then one can find an admissible class with the same fine spectrum which does not have a first–order 0–1 law.If the condition is satisfied (and hence we have a first-order 0–1 law) we give a natural model of the limit law theory; and show that the limit law theory is decidable if the theory of the directly indecomposables is decidable. Using asymptotic methods from the partition calculus a useful test is derived to show several admissible classes have a first–order 0–1 law.
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13

Popova, S. N. "Zero-one law for random distance graphs with vertices in {−1, 0, 1} n." Problems of Information Transmission 50, no. 1 (January 2014): 57–78. http://dx.doi.org/10.1134/s0032946014010049.

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14

PHILLIPS, JAKE. "Desistance and Societies in Comparative Perspective D.Segev. Abingdon: Routledge (2020) 238pp. £120hb, £25.89e‐book ISBN 978‐0‐367‐25369‐1; I978‐0‐429‐28741‐1." Howard Journal of Crime and Justice 60, no. 3 (September 2021): 453–55. http://dx.doi.org/10.1111/hojo.12447.

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15

Akhmejanova, Margarita, and Maksim Zhukovskii. "EMSO(FO$^2$) 0-1 Law Fails for All Dense Random Graphs." SIAM Journal on Discrete Mathematics 36, no. 3 (August 2, 2022): 1788–99. http://dx.doi.org/10.1137/21m1429655.

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16

Kolaitis, Ph G., H. J. Prömel, and B. L. Rothschild. "Asymptotic enumeration and a 0-1 law for $m$-clique free graphs." Bulletin of the American Mathematical Society 13, no. 2 (October 1, 1985): 160–63. http://dx.doi.org/10.1090/s0273-0979-1985-15403-5.

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17

Höhnle, R., and K. TH Sturm. "A multidimensional analogue to the 0-1-law of engelbert and Schmidt." Stochastics and Stochastic Reports 44, no. 1-2 (September 1993): 27–41. http://dx.doi.org/10.1080/17442509308833840.

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18

SHELAH, SAHARON. "On the Very Weak 0–1 Law for Random Graphs with Orders." Journal of Logic and Computation 6, no. 1 (1996): 137–59. http://dx.doi.org/10.1093/logcom/6.1.137.

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19

Shelah, S. "On the very weak 0-1 law for random graphs with orders." Journal of Logic and Computation 6, no. 1 (February 1, 1996): 139–61. http://dx.doi.org/10.1093/logcom/6.1.139.

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20

Rodger, Alan. "David Daube ( 8. 2. 1 9 0 9 - 2 4. 2. 1 9 9 9)." Zeitschrift der Savigny-Stiftung für Rechtsgeschichte. Romanistische Abteilung 118, no. 1 (August 1, 2001): XIV—LII. http://dx.doi.org/10.7767/zrgra.2001.118.1.xiv.

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21

Vanistendael, Professor Frans. "BA + MA = (3+2 = 5+0 = 4+1) × 60 ECTS > (3+1) × 60 ECTS." European Journal of Legal Education 2, no. 2 (January 2005): 111–22. http://dx.doi.org/10.1080/16841360600844549.

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22

Niemistö, Hannu. "Zero-one law and definability of linear order." Journal of Symbolic Logic 74, no. 1 (March 2009): 105–23. http://dx.doi.org/10.2178/jsl/1231082304.

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§1. Introduction. A logic ℒ has a limit law, if the asymptotic probability of every query definable in ℒ converges. It has a 0–1-law if the probability converges to 0 or 1. The 0–1-law for first-order logic on relational vocabularies was independently found by Glebski et al. [6] and Fagin [5]. Later it has been shown for many other logics, for instance for fragments of second order logic [12], for finite variable logic [13] and for FO extended with the rigidity quantifier [3]. Lynch [14] has shown a limit law for first-order logic on vocabularies with unary functions.We say that two formulas or two logics are almost everywhere equivalent, if they are equivalent on a class of structures whose asymptotic probability measure is one [7]. A 0–1-law is usually proved by showing that every quantifier of the logic has almost everywhere quantifier elimination, i.e., every formula with just one quantifier in front of it is almost everywhere equivalent to a quantifier-free formula. Besides proving 0–1-law, this implies that the logic is (weakly) almost everywhere equivalent to first-order logic.The aim of this paper is to study, whether a logic with a 0–1-law can have greater expressive power than FO in the almost everywhere sense and to what extent. In particular, we are interested on the definability of linear order. Because a 0–1-law determines the almost everywhere expressive power of the sentences of the logic completely, but does not say anything about formulas explicitly, we have to assume some regularity on logics. We will therefore mostly consider extensions of first-order logic with generalized quantifiers.
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23

Getoor, R. K., and M. J. Sharpe. "On the arc-sine laws for Lévy processes." Journal of Applied Probability 31, no. 01 (March 1994): 76–89. http://dx.doi.org/10.1017/s002190020010734x.

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Let X be a Lévy process on the real line, and let Fc denote the generalized arcsine law on [0, 1] with parameter c. Then t −1 ⨍0 t P 0(X s > 0) ds → c as t → ∞ is a necessary and sufficient condition for t —1 ⨍0 t 1{Xs >0} ds to converge in P 0 law to Fc. Moreover, P 0(Xt > 0) = c for all t > 0 is a necessary and sufficient condition for t —1 ⨍0 t 1{Xs >0} ds under P 0 to have law Fc for all t > 0. We give an elementary proof of these results, and show how to derive Spitzer's theorem for random walks in a simple way from the Lévy process version.
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24

Bars, Jean-Marie Le. "Counterexamples of the 0-1 Law for Fragments of Existential Second-Order Logic: an Overview." Bulletin of Symbolic Logic 6, no. 1 (March 2000): 67–82. http://dx.doi.org/10.2307/421076.

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AbstractWe propose an original use of techniques from random graph theory to find a Monadic(Minimal Scott without equality) sentence without an asymptotic probability. Our result implies that the 0-1 law fails for the logics(FO2) and](Minimal Gödel without equality). Therefore we complete the classification of first-order prefix classes with or without equality, according to the existence of the 0-1 law for the correspondingfragment. In addition, our counterexample can be viewed as a single explanation of the failure of the 0-1 law of all the fragments of existential second-order logic for which the failure is already known.
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25

Getoor, R. K., and M. J. Sharpe. "On the arc-sine laws for Lévy processes." Journal of Applied Probability 31, no. 1 (March 1994): 76–89. http://dx.doi.org/10.2307/3215236.

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Let X be a Lévy process on the real line, and let Fc denote the generalized arcsine law on [0, 1] with parameter c. Then t−1 ⨍0tP0(Xs > 0) ds → c as t → ∞ is a necessary and sufficient condition for t—1 ⨍0t1{Xs>0}ds to converge in P0 law to Fc. Moreover, P0(Xt > 0) = c for all t > 0 is a necessary and sufficient condition for t—1 ⨍0t1{Xs>0}ds under P0 to have law Fc for all t > 0. We give an elementary proof of these results, and show how to derive Spitzer's theorem for random walks in a simple way from the Lévy process version.
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26

Harte, David. "Ecclesiastical LawMark Hill Oxford University Press, Oxford, 2007, lxiii + 730 (hardback £95.00)1 ISBN: 978-0-19-921712-0." Ecclesiastical Law Journal 10, no. 3 (August 12, 2008): 365–66. http://dx.doi.org/10.1017/s0956618x08001506.

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27

Le Bars, Jean-Marie. "The 0–1 law fails for monadic existential second-order logic on undirected graphs." Information Processing Letters 77, no. 1 (January 2001): 43–48. http://dx.doi.org/10.1016/s0020-0190(00)00149-6.

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28

Armacost, Robert L. "A 0–1 nonlinear programming model for coast guard fisheries law enforcement aircraft patrols." European Journal of Operational Research 56, no. 2 (January 1992): 134–45. http://dx.doi.org/10.1016/0377-2217(92)90217-w.

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29

Lacoste, Thierry. "A Simplified Proof of the 0–1 Law for Existential Second-Order Ackermann Sentences." Mathematical Logic Quarterly 43, no. 3 (1997): 413–18. http://dx.doi.org/10.1002/malq.19970430314.

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30

Ouedraogo, Awalou. "The International Law of Migrant Smuggling." Refuge: Canada's Journal on Refugees 30, no. 2 (November 19, 2014): 105–7. http://dx.doi.org/10.25071/1920-7336.39623.

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31

Corradi, Valentina. "DECIDING BETWEEN I(0) AND I(1) VIA FLIL-BASED BOUNDS." Econometric Theory 15, no. 5 (October 1999): 643–63. http://dx.doi.org/10.1017/s0266466699155014.

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We construct properly scaled functions of Rp-valued partial sums of demeaned data and derive bounds via the functional law of the iterated logarithm for strong mixing processes. If we obtain a value below or equal to the bound we decide in favor of I(0); otherwise we decide in favor of I(1). This provides a consistent rule for classifying time series as being I(1) or I(0). The nice feature of the procedure lies in the almost sure nature of the bound, guaranteeing a lim sup–type result. We finally provide conditions for the strong consistency of estimators of the variance in the dependent and heterogeneous case.
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32

BERGER, ARNO. "BENFORD'S LAW IN POWER-LIKE DYNAMICAL SYSTEMS." Stochastics and Dynamics 05, no. 04 (December 2005): 587–607. http://dx.doi.org/10.1142/s0219493705001602.

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A generalized shadowing lemma is used to study the generation of Benford sequences under non-autonomous iteration of power-like maps Tj : x ↦ αjxβj (1 - fj(x)), with αj, βj > 0 and fj ∈ C1, fj(0) = 0, near the fixed point at x = 0. Under mild regularity conditions almost all orbits close to the fixed point asymptotically exhibit Benford's logarithmic mantissa distribution with respect to all bases, provided that the family (Tj) is contracting on average, i.e. [Formula: see text]. The technique presented here also applies if the maps are chosen at random, in which case the contraction condition reads 𝔼 log β > 0. These results complement, unify and widely extend previous work. Also, they supplement recent empirical observations in experiments with and simulations of deterministic as well as stochastic dynamical systems.
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33

PERES, YUVAL, and PERLA SOUSI. "Brownian motion with variable drift: 0-1 laws, hitting probabilities and Hausdorff dimension." Mathematical Proceedings of the Cambridge Philosophical Society 153, no. 2 (July 4, 2012): 215–34. http://dx.doi.org/10.1017/s0305004112000217.

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AbstractBy the Cameron–Martin theorem, if a function f is in the Dirichlet space D, then B + f has the same a.s. properties as standard Brownian motion, B. In this paper we examine properties of B + f when fD. We start by establishing a general 0-1 law, which in particular implies that for any fixed f, the Hausdorff dimension of the image and the graph of B + f are constants a.s. (This 0-1 law applies to any Lévy process.) Then we show that if the function f is Hölder(1/2), then B + f is intersection equivalent to B. Moreover, B + f has double points a.s. in dimensions d ≤ 3, while in d ≥ 4 it does not. We also give examples of functions which are Hölder with exponent less than 1/2, that yield double points in dimensions greater than 4. Finally, we show that for d ≥ 2, the Hausdorff dimension of the image of B + f is a.s. at least the maximum of 2 and the dimension of the image of f.
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34

Choi, Bong Dae, and Soo Hak Sung. "On Chung's strong law of large numbers in general Banach spaces." Bulletin of the Australian Mathematical Society 37, no. 1 (February 1988): 93–100. http://dx.doi.org/10.1017/s0004972700004184.

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Let { Xn, n ≥ 1 } be a sequence of independent Banach valued random variables and { an, n, ≥ 1 } a sequence of real numbers such that 0 < an ↑ ∞. It is shown that, under the assumption with some restrictions on φ, Sn/an → 0 a.s. if and only if Sn/an → 0 in probability if and only if Sn/an → 0 in L1. From this result several known strong laws of large numbers in Banach spaces are easily derived.
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35

Massey, Calvin. "Craig M. Bradley, editor, The Rehnquist Legacy, New York: Cambridge University Press, 2006. Pp. xxi + 392. $80.00 cloth (ISBN 0-521-85919-0); $35.99 paper (ISBN 0-521-68366-1)." Law and History Review 25, no. 3 (2007): 683–84. http://dx.doi.org/10.1017/s0738248000004569.

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36

McCormick, William P. "Weak and strong law results for a function of the spacings." Journal of Applied Probability 22, no. 03 (September 1985): 543–55. http://dx.doi.org/10.1017/s0021900200029314.

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Let be i.i.d. uniform on (0,1) random variables and define Si,n = Ui ,n–1 Ui– 1,n–1, i = 1, · ··, n where the Ui –n–1 are the order statistics from a sample of size n – 1 and U 0,n–1 =0 and Un,n– 1 = 1. The Si,n are called the spacings divided by U 1,· ··,Un– 1. For a fixed integer l, set . Exact and weak limit results are obtained for the Ml,n. Further we show that with probability 1 This extends results of Cheng.
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37

Fuchs, Michael, and Mehri Javanian. "Limit behavior of maxima in geometric words representing set partitions." Applicable Analysis and Discrete Mathematics 9, no. 2 (2015): 313–31. http://dx.doi.org/10.2298/aadm150619013f.

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We consider geometric words ?1....?n with letters satisfying the restricted growth property ?k ? d + max{?0,...,?k-1}, where ?0 := 0 and d ? 1. For d = 1 these words are in 1-to-1 correspondence with set partitions and for this case, we show that the number of left-to-right maxima (suitable centered) does not converge to a fixed limit law as n tends to infinity. This becomes wrong for d ? 2, for which we prove that convergence does occur and the limit law is normal. Moreover, we also consider related quantities such as the value of the maximal letter and the number of maximal letters and show again non-convergence to a fixed limit law.
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38

GUILLERMO, MAURICIO, and ALEXANDRE MIQUEL. "Specifying Peirce's law in classical realizability." Mathematical Structures in Computer Science 26, no. 7 (November 17, 2014): 1269–303. http://dx.doi.org/10.1017/s0960129514000450.

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This paper deals with the specification problem in classical realizability (such as introduced by Krivine (2009 Panoramas et synthéses27)), which is to characterize the universal realizers of a given formula by their computational behaviour. After recalling the framework of classical realizability, we present the problem in the general case and illustrate it with some examples. In the rest of the paper, we focus on Peirce's law, and present two game-theoretic characterizations of its universal realizers. First, we consider the particular case where the language of realizers contains no extra instruction such as ‘quote’ (Krivine 2003 Theoretical Computer Science308 259–276). We present a first game $\mathds{G}$0 and show that the universal realizers of Peirce's law can be characterized as the uniform winning strategies for $\mathds{G}$0, using the technique of interaction constants. Then we show that in the presence of extra instructions such as ‘quote’, winning strategies for the game $\mathds{G}$0 are still adequate but no more complete. For that, we exhibit an example of a wild realizer of Peirce's law, that introduces a purely game-theoretic form of backtrack that is not captured by $\mathds{G}$0. We finally propose a more sophisticated game $\mathds{G}$1, and show that winning strategies for the game $\mathds{G}$1 are both adequate and complete in the general case, without any further assumption about the instruction set used by the language of classical realizers.
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39

Lane, Jan Erik. "Rule of/by Law." Advances in Politics and Economics 4, no. 2 (April 6, 2021): p17. http://dx.doi.org/10.22158/ape.v4n2p17.

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One can go the World Justice Project (WJP) to find a valuable set of data on roughly 130 states, constructed from experts’ ranking. A large number of country and international experts have given scores between 0 and 1 of state performance on a set of aspects or manifest variables much discussed. The WJP measures 8 or 9 state properties, which will be reduced to two latent variables here.
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40

Jeandesboz, Julien. "Review of Basaran’s Security, Law and Borders." Surveillance & Society 9, no. 3 (March 27, 2012): 333–35. http://dx.doi.org/10.24908/ss.v9i3.4279.

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41

Asselah, Amine. "Stability of a front for a nonlocal conservation law." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 2 (1998): 219–34. http://dx.doi.org/10.1017/s0308210500012750.

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We study the stability of a front for the law 2wt − (wx − γ(1 − w2)(K * w)x)x = 0. It was proved by Del Passo and De Mottoni that an increasing stationary solution, u, exists. We show that it is stable in the following sense: there is ε > 0 such that if w(0) = u + v with |v|2 < ε, then there is α(t) differentiable such that w(x, t) = u(α(t) + x) + v(x, t) and supℝ |v(x, t)| converges to 0 as t goes to infinity. Also, if v is initially odd, α(t) ≡ 0.
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42

MUBAYI, DHRUV, and CAROLINE TERRY. "DISCRETE METRIC SPACES: STRUCTURE, ENUMERATION, AND 0-1 LAWS." Journal of Symbolic Logic 84, no. 4 (August 19, 2019): 1293–325. http://dx.doi.org/10.1017/jsl.2019.52.

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AbstractFix an integer $r \ge 3$. We consider metric spaces on n points such that the distance between any two points lies in $\left\{ {1, \ldots ,r} \right\}$. Our main result describes their approximate structure for large n. As a consequence, we show that the number of these metric spaces is $\left\lceil {{{r + 1} \over 2}} \right\rceil ^{\left( {\matrix{ n \cr 2 \cr } } \right) + o\left( {n^2 } \right)} .$Related results in the continuous setting have recently been proved by Kozma, Meyerovitch, Peled, and Samotij [34]. When r is even, our structural characterization is more precise and implies that almost all such metric spaces have all distances at least $r/2$. As an easy consequence, when r is even, we improve the error term above from $o\left( {n^2 } \right)$ to $o\left( 1 \right)$, and also show a labeled first-order 0-1 law in the language ${\cal L}_r $, consisting of r binary relations, one for each element of $[r]$ . In particular, we show the almost sure theory T is the theory of the Fraïssé limit of the class of all finite simple complete edge-colored graphs with edge colors in $\left\{ {r/2, \ldots ,r} \right\}$.Our work can be viewed as an extension of a long line of research in extremal combinatorics to the colored setting, as well as an addition to the collection of known structures that admit logical 0-1 laws.
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43

Maffei, Vincenzo, Emiliano Macaluso, Iole Indovina, Guy Orban, and Francesco Lacquaniti. "Processing of Targets in Smooth or Apparent Motion Along the Vertical in the Human Brain: An fMRI Study." Journal of Neurophysiology 103, no. 1 (January 2010): 360–70. http://dx.doi.org/10.1152/jn.00892.2009.

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Neural substrates for processing constant speed visual motion have been extensively studied. Less is known about the brain activity patterns when the target speed changes continuously, for instance under the influence of gravity. Using functional MRI (fMRI), here we compared brain responses to accelerating/decelerating targets with the responses to constant speed targets. The target could move along the vertical under gravity (1 g), under reversed gravity (−1 g), or at constant speed (0 g). In the first experiment, subjects observed targets moving in smooth motion and responded to a GO signal delivered at a random time after target arrival. As expected, we found that the timing of the motor responses did not depend significantly on the specific motion law. Therefore brain activity in the contrast between different motion laws was not related to motor timing responses. Average BOLD signals were significantly greater for 1 g targets than either 0 g or −1 g targets in a distributed network including bilateral insulae, left lingual gyrus, and brain stem. Moreover, in these regions, the mean activity decreased monotonically from 1 g to 0 g and to −1 g. In the second experiment, subjects intercepted 1 g, 0 g, and −1 g targets either in smooth motion (RM) or in long-range apparent motion (LAM). We found that the sites in the right insula and left lingual gyrus, which were selectively engaged by 1 g targets in the first experiment, were also significantly more active during 1 g trials than during −1 g trials both in RM and LAM. The activity in 0 g trials was again intermediate between that in 1 g trials and that in −1 g trials. Therefore in these regions the global activity modulation with the law of vertical motion appears to hold for both RM and LAM. Instead, a region in the inferior parietal lobule showed a preference for visual gravitational motion only in LAM but not RM.
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44

Pakes, Anthony G. "Critical markov branching process limit theorems allowing infinite variance." Advances in Applied Probability 42, no. 2 (June 2010): 460–88. http://dx.doi.org/10.1239/aap/1275055238.

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This paper gives easy proofs of conditional limit laws for the population size Zt of a critical Markov branching process whose offspring law is attracted to a stable law with index 1 + α, where 0 ≤ α ≤ 1. Conditioning events subsume the usual ones, and more general initial laws are considered. The case α = 0 is related to extreme value theory for the Gumbel law.
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45

Pakes, Anthony G. "Critical markov branching process limit theorems allowing infinite variance." Advances in Applied Probability 42, no. 02 (June 2010): 460–88. http://dx.doi.org/10.1017/s0001867800004158.

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This paper gives easy proofs of conditional limit laws for the population size Z t of a critical Markov branching process whose offspring law is attracted to a stable law with index 1 + α, where 0 ≤ α ≤ 1. Conditioning events subsume the usual ones, and more general initial laws are considered. The case α = 0 is related to extreme value theory for the Gumbel law.
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46

Bernard, Catherin. "A Social Policy for Europe: Politicians 1, Lawyers 0." International Journal of Comparative Labour Law and Industrial Relations 8, Issue 1 (March 1, 1992): 15–31. http://dx.doi.org/10.54648/ijcl1992003.

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47

Rosales-García, J., J. A. Andrade-Lucio, and O. Shulika. "Conformable derivative applied to experimental Newton's law of cooling." Revista Mexicana de Física 66, no. 2 Mar-Apr (March 1, 2020): 224. http://dx.doi.org/10.31349/revmexfis.66.224.

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It has been proved that the integer order dierential equation does notrepresent the real behaviour of nature for the Newton's law of cooling.Then, we solve the Newton's cooling law using the conformable deriva-tive, as result we obtain the Kohlrausch stretched exponential function.Due to the free parameter 0 < 1, we can t this function with thegraph of the experimental data set. It is shown that the experimental datacoincide with those theoretical when = 0:77269 and k = 0:018765.
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48

Allan, T. R. S. "Civil Liberties and Human Rights in England and Wales. By David Feldman [Oxford: Clarendon Press. 1993. lix 914 and (Index) 13pp. Hardback. £48.00, Paperback £22:50 net. ISBN 0–19–876232–1. (hb), 0–19–876229–1 (pb).]." Cambridge Law Journal 53, no. 3 (November 1994): 610–12. http://dx.doi.org/10.1017/s0008197300081046.

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49

Pacholski, Leszek, and WiesŁaw Szwast. "Asymptotic probabilities of existential second-order Gödel sentences." Journal of Symbolic Logic 56, no. 2 (June 1991): 427–38. http://dx.doi.org/10.2307/2274691.

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In [9] and [10] P. Kolaitis and M. Vardi proved that the 0-1 law holds for the second-order existential sentences whose first-order parts are formulas of Bernays-Schonfinkel or Ackermann prefix classes. They also provided several examples of second-order formulas for which the 0-1 law does not hold, and noticed that the classification of second-order sentences for which the 0-1 law holds resembles the classification of decidable cases of first-order prenex sentences. The only cases they have not settled are the cases of Gödel classes with and without equality.In this paper we confirm the conjecture of Kolaitis and Vardi that the 0-1 law does not hold for the existential second-order sentences whose first-order part is in Gödel prenex form with equality. The proof we give is based on a modification of the example employed by W. Goldfarb [5] in his proof that, contrary to the Gödel claim [6], the class of Gödel prenex formulas with equality is undecidable.
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50

Shi, Long. "Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk." Advances in Mathematical Physics 2019 (June 2, 2019): 1–5. http://dx.doi.org/10.1155/2019/3479715.

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In this work, a generalization of continuous time random walk is considered, where the waiting times among the subsequent jumps are power-law correlated with kernel function M(t)=tρ(ρ>-1). In a continuum limit, the correlated continuous time random walk converges in distribution a subordinated process. The mean square displacement of the proposed process is computed, which is of the form 〈x2(t)〉∝tH=t1/(1+ρ+1/α). The anomy exponent H varies from α to α/(1+α) when -1<ρ<0 and from α/(1+α) to 0 when ρ>0. The generalized diffusion equation of the process is also derived, which has a unified form for the above two cases.
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