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The Annals of Probability
Contents:
  1. Journal of Mathematical Cryptology
  2. Recommended for you
  3. Measuring Risk Literacy: The Berlin Numeracy Test

Oosterhoff, Power approximations to multinomial tests of fit, J. A28 , 1— Harpes, G. Kramer and J. Hermelin, J. Cho and K. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions, Vol. Kaliski Jr and M. Mantin and A. Theory 52 , — Murphy, F. Piper, M. Walker and P. Sazonov, On the multi-dimensional central limit theorem, Sankhya A 30 , — Cryptology 21 , — Tardy-Corfdir and H.

3. Probability Theory

Tyurin, An improvement of upper estimates of the constants in the Lyapunov theorem, Russian Math. Surveys 65 , — Walker, A note on the asymptotic distribution of sample quantiles, J. Export Citation. Here you can find all Crossref-listed publications in which this article is cited.

Journal of Mathematical Cryptology

User Account Log in Register Help. Search Close Advanced Search Help. My Content 1 Recently viewed 1 Another look at normal Show Summary Details. More options …. Journal of Mathematical Cryptology. Managing Editor: Magliveras, Spyros S. See all formats and pricing. Online ISSN See all formats and pricing Online. Prices are subject to change without notice. Prices do not include postage and handling if applicable. Distortion maps for supersingular genus two curves by Galbraith, Steven D.

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  • Another look at normal approximations in cryptanalysis : Journal of Mathematical Cryptology.
  • Scattered Skeletons in our Closet.
  • The granularity of weakly occupied bosonic fields beyond the local density approximation?
  • The Gold Apples?

Volume 1 Issue 4 Dec , pp. El Kaabouchi, L. Nivanen and Qiuping A. However, when the fractality arises, the mechanics principles may no more be extended especially because the time and space singularity appears on the boundary and creates curvature. There is no more equilibrium state, but only a horizon which might play a same role as equilibrium but does not close the problem - especially the problem of the invariance of the energy - which requires two complementary factors: a first one related to the closure in the dimensional space, and the second to scan dissymmetry stemming from the default of tiling the space time.

A new discrete time arises from fractality. It leads irreversible thermodynamic properties. Space and time singularities lead to the relation between the above mentioned problematic and the Riemann zeta functions as well as its zeros. The 1-d fermionic case with a quasi-periodic 2-body potential provides a physical framework for understanding the Riemann hypothesis. Roussou, J.

Smyrnakis, M. Magiropoulos, Nikolaos K. Efremidis, G. Kavoulakis, P. Sandin, M. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

Maslov, allowing you to take a fresh look at the statistics of Bose—Einstein and Fermi—Dirac ideal gases. This new point of view allows us to interpret the indicated statistics as particular cases of statistical properties in number theory, on the one hand, and to indicate the limits of phase transitions from Bose to Fermi distributions.

It reduces the Riemann hypothesis to a softer form. Furthermore I proposed a pair of creation-annihilation operators for BEC phenomena. These set of creation-annihilation operators is defined on a complex Hilbert space. They build a set up to interpret this type of BEC as a creation-annihilation phenomena of the virtual hypothetical particle. In this talk a review of earlier work on finite temperature strings was presented. Several topics were covered, including the canonical and microcanonical ensemble of strings, the behavior of strings near the Hagedorn temperature as well as speculations on the possible phases of high temperature strings.

The connection of the string ensemble and, more generally, statistical systems with an exponentially growing density of states with number theory was also discussed. Tran, M. Murthy, R. We show that the same statistical mechanics technique for the density of states of bosons in a power-law spectrum yields the partitioning formula for p s n , the latter being the number of partitions of n into a sum of s -th powers of a set of integers. By making an appropriate modification of the statistical technique, we are also able to obtain d s n for distinct partitions.

We find that the distinct square partitions d 2 n show pronounced oscillations as a function of n about the smooth curve derived by us. The origin of these oscillations from the quantum point of view is discussed. Weiss, S. Page, and M.

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This correspondence is used for characterising the probability distribution which governs the number of factors in a randomly selected factorisation of an asymptotically large N. Asymptotic upper bounds on both the skewness and the excess of this distribution, and on the total number of factorisations, are conjectured. The asymptotic formulas are checked against exact numerical data obtained with the help of recursion relations.

It is also demonstrated that for large numbers which are the product of different primes the probability distribution approaches a Gaussian, while identical prime factors give rise to non-Gaussian statistics. By studying partial sums we show that that the transition amplitude formulation is analogous to neutrino mixing in a low dimensional context. In an alternative harmonic oscillator formalism we discuss the relation to the fermionic description of two dimensional string theory and matrix models.

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Measuring Risk Literacy: The Berlin Numeracy Test

Finally we derive various representations of the Green's function using energy momentum integrals, point particle path integrals, and string propagators. Abdesselam and A. Statistical models associated to such N 2 x N 2 matrices for odd N are studied here. There are N possible states at each site. For order r , N eigenvalues consitute the trace and the remaining N r - N eigenvalues involving the full range of parameters come in zero-sum multiplets formed by the r -th roots of unity, or lower dimensional multiplets corresponding to factors of the order r when r is not a prime number.

For r a prime number an amusing relation of the number of multiplets with a theorem of Fermat is pointed out. Chain Hamiltonians and potentials corresponding to factorizable S matrices are constructed starting from our braid matrices. Perspectives are discussed. By also considering some explicit discrete probability distributions p x for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory.

Sequences of numbers are treated as the size measure of finite sets. In particular, this yields to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers.

A possible relevance to prime numbers is also analyzed.