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Normality and Finite-state Dimension of Liouville numbers [article]

2014 arXiv   pre-print
Here, for a given base k >= 2, we give two simple constructions of a Liouville number which is normal to the base k. The first construction is combinatorial, and is based on de Bruijn sequences.  ...  In the second number-theoretic construction, we use an arithmetic property of numbers - the existence of primitive roots - to construct Liouville numbers normal in finitely many bases, assuming a Generalized  ...  Acknowledgements The first author would like to gratefully acknowledge the help of David Kandathil and Sujith Vijay, for their suggestions during early versions of this work and Mrinal Ghosh, Aurko Roy  ...

Page 1041 of Mathematical Reviews Vol. 55, Issue 4 [page]

1978 Mathematical Reviews
Tkalié, Construction of the solution of the Liouville equation on the basis of the complete integral of the Hamilton-Jacobi equation (pp. 308-313); A. I.  ...  Pahomov, A proof of noncoincidence of classes of simple primitively recursive functions (pp. 115-122); A. O.  ...

The theory of Liouville functions

Pascal Koiran
2003 Journal of Symbolic Logic (JSL)
A Liouville function is an analytic function H: ℂ → ℂ with a Taylor series such the a n 's form a "very fast growing" sequence of integers.  ...  In this paper we exhibit the complete first-order theory of the complex field expanded with H.  ...  Existence for Modified Partial Sums The only property of the coefficients of Liouville functions that will be used in the next proposition is that they are rational numbers.  ...

The theory of Liouville functions [article]

Pascal Koiran
2002 arXiv   pre-print
A Liouville function is a complex analytic function H with a Taylor series ∑_n=1^∞ x^n/a_n such the a_n's form a "very fast growing" sequence of integers.  ...  In this paper we exhibit the complete first-order theory of the complex field expanded with H.  ...  Let h ≥ 2 be an upper bound on their absolute values. Let d ≥ 2 be an upper bound on the degrees of these polynomials, and let m be the number of occurrences of quantifiers in F .  ...

Geometric Hamiltonian formulation of quantum mechanics in complex projective spaces

Davide Pastorello
2015 International Journal of Geometric Methods in Modern Physics (IJGMMP)
(and informal) concept of quantum system through a simple example.  ...  The observables of a quantum system generate a non-abelian C * -algebra which is an absolutely abstract object.  ...  In case of quantum states, the partial integral can be interpreted as the integration of a Liouville density describing a state of a composite system w.r.t. to a marginal measure obtaining a marginal probability  ...

The Unfinished Search for Wave-Particle and Classical-Quantum Harmony [article]

Partha Ghose
2015 arXiv   pre-print
It provides a clear and beautiful harmony of classical waves and particles.  ...  The main purpose of this paper is to review the progress that has taken place so far in the search for a single unifying principle that harmonizes (i) the wave and particle natures of matter and radiation  ...  This is a construction that embeds classical mechanics in a quantum theory with hidden variables.  ...

J. W. Green
1950 Bulletin of the American Mathematical Society
The music theoretic interpretation is: that K n is the number of cadences of n notes (melodies according to distinction of relative and not absolute pitch); while L n is the number of planar cadences (  ...  If the matrix of T' is a disjunction of inequalities, then T is true of I\-for some *£ J if and only if it is true of V.  ...  For example, in a locally orientable w-gm concurrent orientations of the local n-gms may be introduced so as to define orientability of an n-gm by means of an indicatrix and chains of n-gms  ...

The Origin and Evolution of Complex Enough Systems in Biology [chapter]

Erkki Brändas
2017 Quantum Systems in Physics, Chemistry, and Biology
The mathematical formulation of this process derives from a correlated dissipative ensemble, which has a network topology of a quantum nature as well as exhibiting a  ...  A related query, viz., the ontological thesis, that everything is physical, confronts a crucial test on the validity of reductionism as a fundamental approach to science.  ...  Acknowledgements I am grateful to the local organisers of QSCP XX, Prof. Alia Tadjer and Prof. Rossen Pavlov, Sophia, Bulgaria, for generous hospitality and for running an excellent symposium.  ...

Beyond fitness: selection and information flow through the constructive steps in lifecycles [article]

Eric Smith
2021 bioRxiv   pre-print
beyond simple copying.  ...  of fitness to a class of summary statistics that appear as regression coefficients against the autocatalytic flows associated with reproduction, including replication but also including constructive operations  ...  equation ∂ ∂t Ψ(z) = −L z, ∂ ∂z Ψ(z) , (64) in which the Liouville operator L is constructed from the elements of the transition matrix T.  ...

The February meeting in New York

L. W. Cohen
1953 Bulletin of the American Mathematical Society
Volodymyr Bohun-Chudyniv: On a method of determining orthogonal square matrices of (2 1+x -l)2*(Xèl, K^l; \ = 0, K>2) order, composed of differing integers.  ...  It is proved that on a Hodge manifold (in particular, on a nonsingular algebraic variety), the number of simple differentials of second kind that are linearly independent modulo exact differentials is  ...  Robertson: Schlicht solutions of the Sturm-Liouville differential equation. Preliminary report.  ...

Constructive physics [article]

Yuri Ozhigov
2008 arXiv   pre-print
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.  ...  number of more simple compounds, etc.  ...  Briefly, a constructive real number is such a real number, which is the limit of a sequence of rational numbers r 1 , r 2 , . . ., generated by some algorithm.  ...

Abstracts of Presentations

2001 Brain and Cognition
PREFACE This volume contains abstracts of the talks presented at the eleventh conference on Applications of Computer Algebra, held at Nara Women's University, Nara, Japan.  ...  Furthermore, we gave a lecture about RSA cryptography at a junior high school using AsirPad. In our talk, we will explain the details of AsirPad, and report the results of the lecture.  ...  Acknowledgment Abstract Infty Editor [1, 2] is a editor with on-line recognition of handwritten mathematical expressions, which was developed by our research group.  ...

Quantum Chrono-Topology of Nuclear and Sub-Nuclear Reactions [article]

C. Syros, C. Schulz-Mirbach (TU Hamburg-Harburg)
1997 arXiv   pre-print
The degree of disconnectedness of the time-space is a decreasing function of the number of simultaneous or almost simultaneous fundamental interactions.  ...  From an elementary solution of the Liouville equation the quantization of the time follows and the Planck constant has been calculated.  ...  B = {β} is the set of the numbers of interacting particle pairs with disjunct IPN projections in IR 1 .  ...