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

2014
*
arXiv
*
pre-print

Here, for

arXiv:1204.4104v2
fatcat:ip5u7lyuevdojoegq2xxdtpxia
*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

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]

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

2015
*
International Journal of Geometric Methods in Modern Physics (IJGMMP)
*

(and informal) concept

doi:10.1142/s0219887815600154
fatcat:v3aaieytevglnhmwb67cot3suy
*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]

2015
*
arXiv
*
pre-print

It provides

arXiv:1502.03208v1
fatcat:hzbuon5lmjbxnp7uwjbpohatga
*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. ...##
###
The November meeting in Pasadena

1950
*
Bulletin of the American Mathematical Society
*

The music theoretic interpretation is: that K n is the

doi:10.1090/s0002-9904-1950-09343-4
fatcat:jchadiujxvaitcksouoahlz3uq
*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]

2017
*
Quantum Systems in Physics, Chemistry, and Biology
*

The mathematical formulation

doi:10.1007/978-3-319-50255-7_24
fatcat:ufl3ebvtorbzhhcfraaiw4bhsi
*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]

2021
*
bioRxiv
*
pre-print

beyond

doi:10.1101/2021.02.09.430402
fatcat:z6suu5ucwjffpniyej4onfjplu
*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

1953
*
Bulletin of the American Mathematical Society
*

Volodymyr Bohun-Chudyniv: On

doi:10.1090/s0002-9904-1953-09696-3
fatcat:7ukkv6ewzbhwpoot2yh25imsbe
*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]

2008
*
arXiv
*
pre-print

Discussion

arXiv:0805.2859v2
fatcat:awbhg57kmza6nmkoj2nd3yj64q
*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

doi:10.1006/brcg.2000.1285
fatcat:k6c2qcfpubdxzjdkbgzktkigz4
*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]

1997
*
arXiv
*
pre-print

The degree

arXiv:hep-th/9609093v2
fatcat:xm5zcw57yvdurhoxbrhjugyyse
*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 . ...##
###
The summer meeting in Madison

1948
*
Bulletin of the American Mathematical Society
*

The proof however necessitates the

doi:10.1090/s0002-9904-1948-09093-0
fatcat:zmjkl55lgjhvfl5kdcms7yg6cu
*disjunction*between*a*great*number**of*cases. ... Leonard Tornheim :*Construction**of*an integral basis*of*any algebraic*number*field by means*of*valuations.*A**construction*for the valuations*of*an algebraic field has been given by S. ...##
###
Elements of Mathematics
[article]

2022
*
Zenodo
*

The present chapter introduces the fields

doi:10.5281/zenodo.6080488
fatcat:duf7ea2kpbemvj4yfg4ewizlw4
*of*mathematics that will be considered "elementary" in this book. ... But even "elementary" topics have their mysteries and difficulties, which call for explanation from*a*"higher standpoint." ... For the germ*of*the idea that led to this book, credit should go to Vagn Lundsgaard Hansen and Jeremy Gray, who commissioned my article on Klein, and later suggested that I write*a*book*of**a*similar kind ...
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