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真诚 勤勉 达观 自然 |
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真诚 勤勉 达观 自然 |
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Fractal dimension structure of Cosmos and its mathematical foundations YAN Kun (yankun@nature.ac.cn) (Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China) Abstract Fractal dimension structure of the Cosmos are explored, and the mathematical foundation, which include the expressions of fractal dimension differential and calculus, regular space integral solutions of fractal dimension differential equations, the fractal calculus definitions of fractal measure as well as the measure computational equation of self-similar fractal, fractal dimension calculus and fractal measure are given. As annotation, an equation of the relation between neutrons and protons in nuclei and its periodical solutions as well as atomic number limit are discussed. Keywords Cosmos, fractal dimension structure, fractal dimension calculus, fractal differential equation, fractal measure, atomic number limit
Yan Kun. Fractal
dimension structure of Cosmos and its mathematical foundations[J].
Progress in Geophysics(in Chinese), 2004, 19(3): 709～716.
DOI:10.3969/j.issn.1004-2903.2004.03.036.
YAN Kun
(yankun@nature.ac.cn)
Abstract
In this paper,
consider taking the vacuum as a form of medium, which preliminary shows
that the vacuum has the backgrounds at the several levels interaction
each other, and it can block or quickly transfer the specific mechanical
vibration, and the vacuum has the natural frequency oscillation (or the
vacuum ripple), by exploring the constancy of light velocity in the
vacuum, energy-exchange equation and vortex shedding wavelength equation
in Karman vortex-street, expressional forms of
equation of the one-way
velocity of light (also equation of the
one-way
speed of light, or equation of
one-way
variable speed of light)
for the constancy of the two-way velocity of light (or constancy of the
two-way speed of light),
experimental
criterion equation for the closed strings model of the photon (general
refraction equation of the photon with one same rotation plane),
superluminal (also
faster-than-light or FTL) velocity, medium action
equation of particle fractal motion for the wave-particle
duality, and quantum fractal are studied deeply. As a result, it shows
that a tentative theoretical frame which includes not only the
superluminal-velocity motion but consists with Einstein special
relativity and quantum theory can be established.
Yan Kun. Energy-exchange
descriptions on the superluminal velocity and quantum fractal[J]. Basic
Science Journal of Textile Universities(in Chinese), 2004, 17(3):223～227.
DOI:10.3969/j.issn.1006-8341.2004.03.010.
Introductions on the medium shell and discrete orbits of celestial
bodies motion YAN Kun (yankun@nature.ac.cn)
(Xi’an Modern Nonlinear
Science Applying Institute, Xi’an 710061, China)
Abstract
By
using phenomenological method for the medium shell curve, an energy
equation on three dimensions regular space and an energy-gravitation
form about gravitational interaction between bodies are given. Further
more, two condition solutions of the gravitational expression is close
by with the results of Newton’s gravitational theory and Einstein’s
general relativity respectively. The localizations in the functions of
the fractal dimension calculus compared with the fractional-order
calculus at present are discussed, and similar expanded equation is
given. Subsequently，by
discussing the expanded baseline property on the celestial motion orbit,
discrete orbital equations of the celestial bodies motion are given. And
referring to the related orbital data of planets and some satellites in
the Solar System, the concrete expression on the discrete orbit of the
celestial bodies motion are given too.
YAN Kun (yankun@nature.ac.cn) (Xi’an Modern Nonlinear Science Applying Institute，Xi’an 710061，China)
Abstract
By
discussing the existent equations of mass-velocity relation, an
equivalent polar coordinate equation and its Binet equation of the
mass-velocity relation are given, and expressions of the mass-velocity
relation and mass-energy relation are given too, which include forms of
superluminal (also
faster-than-light or FTL) motion. Subsequently, using the
mass-energy relation, the general expression of the solution of the
energy equation on the medium shell curve method is discussed, and
general expression of Binet equation and its approximate solutions about
orbits of the celestial bodies motion in weak and strong gravitational
field are given. Further more, analysis solutions of the
advance of the perihelion of planets
and bending of light for the gravitational
force are given.
Keywords
orbit of the
celestial bodies motion, equations of mass-velocity relation, Binet
equation, superluminal motion, advance of the
perihelion of planets, bending of light, gravitational frequency
shift
Yan
Kun. The general expression of Binet equation about celestial bodies
motion orbits[J]. Progress in Geophysics(in Chinese with abstract in
English), 2005, 20(2): 534～539.
DOI:10.3969/j.issn.1004-2903.2005.02.052. The tendency analytical equations of stable nuclides and the superluminal velocity motion laws of matter in geospace YAN Kun (yankun@nature.ac.cn) (Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China)
Abstract
In this paper,
by discussing the existent distribution trend of relation for the proton
number and the neutron number to be included by the stable nuclides in
geospace, tendency analytical method and it’s periodic distribution
equation forms of the stable nuclides are expressed at first. Then a
comparison result between the curve of the theoretical equation analysis
and the points of the experimental distribution data of the stable
nuclides in geospace are given. Further more, stable nuclide limit and
chemical element limit for the chemical element periodic table are
given, and possible corresponding relation equation with the
positron-particle annihilation is expressed, which includes estimation
of order of the static mass to be situated nearby at the electron
neutrino structural dimension
and a tendency distribution equation (with the characteristics of dense
distribution in the partial closed intervals and sparse distribution in
the few open intervals) of the particles mass.
Subsequently, by forming two hypotheses about energy state of vacuum
matter, and basing on an equivalent Binet’s equation, mass equations and
energy equations of the partial moving with light-velocity or
superluminal (also
faster-than-light or FTL) velocity motion fusing with the results
of Einstein special relativity are expressed. As inference, possible
corresponding relations between the mass equations and energy equations
with the dark matter and dark energy are discussed tentatively.
Keywords
stable nuclide, tendency analytical equation, periodic law, chemical
element limit, tendency distribution of the
particles mass, energy state of vacuum matter, equations of
superluminal velocity motion
and foundation of fractional-dimension calculus about self-similar fractal measure calculation YAN Kun (yankun@nature.ac.cn) (Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China)
Abstract
In this paper,
by discussing the basic hypotheses about the continuous orbit and
discrete orbit in two research directions of background medium theory
for celestial body motion, concrete equation forms and their summary of
the theoretic frame of celestial body motion are introduced. Future
more, by discussing the general form of Binet’s equation of celestial
body motion orbit and it’s solution of the
advance of the
perihelion of
planets, some relations and differences between the continuous orbit
theory and Newton’s gravitational theory and Einstein’s general
relativity are given. And by discussing fractional-dimension expanded
equation for the celestial body motion orbits, the concrete equations
and the prophesy data of discrete orbit or stable orbits of celestial
bodies which included the planets in the Solar System, satellites in the Uranian
System, satellites in the Earth System and satellites obtaining
the Moon obtaining from discrete orbit theory are given too. Especially,
as preliminary exploration and inference to the gravitational curve of
celestial bodies in broadly range, the concept for the ideal black hole
with trend to infinite in mass density difficult to be formed by
gravitation only is explored. By discussing the position hypothesis of
fractional-dimension derivative about function and formula form the
hypothesis of fractional-dimension derivative about power function,
concrete equation formulas of fractional-dimension derivative,
differential and integral are described distinctly further, and
difference between the fractional-dimension derivative and the
fractional-order derivative are given too. The difference equations
description of the self-similar fractal extension and
fractional-dimension extension are discussed. Subsequently, the concrete
forms of measure tendency calculus equations of self-similar fractal
obtaining by based on the definition of form in non-integral order
calculus about general fractal measure are discussed again, and
differences with Hausdorff measure method or the covering method at
present are given. By applying the measure calculation equations,
measure of self-similar fractals which include middle-third Cantor set,
Koch curve, Sierpinski gasket and orthogonal cross star are calculated
and analyzed. At the end, the calculating equations of dimension and
measure of an ideal points set are explored.
Keywords
orbit
of celestial body motion, background medium theory, continuous orbit,
discrete orbit, self-similar fractal measure, non-integral order
calculus, fractional-order calculus, fractional-dimension calculus
YAN Kun. Introduction on
background medium theory about celestial body motion orbit and
foundation of fractional-dimension calculus about self-similar fractal
measure calculation[J]. Progress in Geophysics(in Chinese with abstract
in English), 2007, 22(2): 451～462.
DOI:10.3969/j.issn.1004-2903.2007.02.018.
Primary annotation of symbol basing on imaginary form about infinity
YAN Kun
(yankun@nature.ac.cn) Abstract In this paper, primary annotation of symbol basing on imaginary form about infinity is given.
Keywords
infinity,
zero, imaginary form, symbol, annotation, Euler’s formula
YAN Kun (yankun@nature.ac.cn) ( Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China )
Abstract
In
this paper, by discussing the existing distribution of the CO2
concentration data in the atmosphere over the
past 60 years, and adopting the tendency analytical method, concrete
tendency equation forms of the CO2 concentration are
presented at first. Further more, comparison result between the curve of
the theoretical equation and the data curve of CO2
concentration from the ice cores analysis or the observation
is given.
The result shows that the tendency equation curve agree well with the
existing data. Subsequently, predictive data of the CO2
concentration in the atmosphere during the year from 2010 to 2016 are
suggested tentatively, and the coupling model of the relationship among
the rotation, rotation and the global plate motion of the earth is
briefly discussed.
Keywords
concentration of carbon dioxide, atmosphere, tendency equation, curve
fitting, predictive data, data analysis, coupling model
YAN Kun (yankun@nature.ac.cn) ( Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China )
Abstract
In
this paper, by discussing approximate equivalent analytical solution of
nonlinear dynamics equation and some properties in discontinuous area of
data curve, a general
constructing form of adaptive connection equation and preset iteration
method determining parameters in discontinuous area are given. And then,
a connecting method of the mapping equations for the discontinuous areas
of general curves is also given. Subsequently, computing examples which
included the discontinuous areas with dislocation and turn-back are
given too. This adaptive connection equation can be applied as a general
form of expansion (extended hyperbolic tangent function) of the
classical S-curve (sigmoid curve) equation or Logistic function, and for
step discontinuous area of slowly varying data curve, its form of the
adaptive connection equation can be obtained by automatic calculating.
In this paper, compatibility of the nonlinear equation in classical
Newton dynamic equation and the charge equation of the RLC series
circuit is analyzed. Basing on the form of the adaptive connection
equation, an approximate expression of extended hyperbolic tangent
series for the
characteristic function of the series phases transition of the
evolution of phenomena, equations of magnetic hysteresis
loop for magnetic material, extended form of average energy equation (or
Einstein-Stern
equation) and tendency
differential equation of the average particle number for the statistical
distributions of the particles,
equation
of average binding energy per nucleon (or
specific binding
energy) of stable nuclide, a theoretical maximum of the
nuclear binding energy and its
corresponding proton number, abundances equation of elements in the
Solar System, curvilinear equation of potential energy function (such as
curvilinear equation of potential energy function of diatomic molecule,
etc), equation of natural saturation process (such as tree growth and
physical reaction or chemical reaction process, equation of fracture
toughness for steel material, etc) and equation of typical creep process
for metal or rock material are explored and analyzed tentatively. Keywords nonlinear dynamics equation, discontinuous area of data curve, adaptive connection equation, connecting method of the mapping equations, equations of magnetic hysteresis loop, equation of statistical distributions of the particles, equation of average binding energy per nucleon, abundances equation of elements in Solar System, curvilinear equation of potential energy function, equation of natural saturation process, equation of creep process
YAN Kun. Research
on adaptive connection equation in discontinuous area of data curve[J].
Progress in Geophys(in Chinese with abstract in English), 2011,26(1):
162～171.
DOI:10.3969/j.issn.1004-2903.2011.01.018.
YAN Kun (yankun@nature.ac.cn) ( Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China )
Abstract
In this paper, brief annotation of a constructing procedure and the
applications of connection equation are given. An
analytical method
of the connection equation as an approximate equivalent analytical
solution of nonlinear dynamics equations is discussed. The expressions
of the basic analytical solution of a class of simple nonlinear
differential equations are analyzed. Research direction of Jiansics or
Dimennics about spectrum(spectrum array) formed by series of laws and
their connections in evolution processes of natural phenomena are
explored, an equation of the transformation of the phenomena between the
states in evolutionary process is presented, that it follows a natural
optimum principle or a natural conciseness principle in general, which
having an equation form of the smooth curve with the optimal path or the
most concise path, simple constructing forms of forward
partial-symmetrical equation(or weak-symmetrical equation) and backward
partial-symmetrical equation are given, an approximate expression of
extended hyperbolic tangent series for
the characteristic
function of the series phases transition of the evolution of phenomena
is
constructed,
then natural
evolution-balance rule is presented, and tendency equation
of biological growth process is given too. According to approximate form
of the nonlinear dynamics equation of the connection equation, two new
electronic circuit elements(nonlinstor and geomsentor) with deepening
charge-controlled capacitor properties based on form of the nonlinear
differential equation is predicted, and the nonlinear differential
equation for a RLCNG series circuit is also analyzed, extended direction
of the general distribution function and the general distribution
density function, tendency equation and its conditional solutions of the
statistical distributions of the particles are given, properties of the
frequency interval of Planck’s quantum equation are explored, nonlinear
differential equation expressions with solution of approximate linear
frequency conversion and their characteristics of curve shapes of
frequency conversion wave equations at negative frequency are discussed,
a concise model of database theoretical
framework (this framework to be
made up of
foundation database,
tendency equation, and analytic
database) is explored, an equation of relationship between the
total annual energy consumption with the
annual GDP in the United States, and an equation of relationship
between the annual population with the
annual GDP in the United Kingdom are established, and
limit values of the total annual energy
consumption in the United States and the
annual
population in the United Kingdom are
calculated and predicted. Subsequently, tendency fitting
equations of curves are explored, which included the creep process curve
of the rock and the single-crystal superalloy, the Volt-Ampere
characteristic curve of the discrete semiconductor device, the
resistance (or resistivity )-absolute temperature curve of the
superconducting material, the direct current I-U
characteristic curve of the bicrystal Josephson junction, and the
current step amplitude of Shapiro steps, the
friction-speed characteristic curve (that included the
stages of
Coulomb friction, Stribeck friction,
viscous friction, friction hysteresis, and anomalous
friction
hysteresis effect)
in mechanical system or servo system, an
expanded equation form of the
Newton's law of cooling, the
shear stress-shear rate in the
flow curve (that included the
sections
of first Newtonian fluid-flow,
pseudoplastic flow, second Newtonian
fluid-flow, dilatant flow, turbulent flow, and
anomalous
shearing effect) of the polymer melts, etc. On
phenomenological and tendency levels, research directions of similar
property of creep curves of materials with the flow curves of polymer
melt, and similarity in the fractal measure of the evolutions of
fracture cracks growth structure and fluid turbulent eddies nested
structure are pointed out. At the end, limitations of the connection
equation in data fitting and long-range forecasting are discussed.
Analysis method of PSSIR model equations and its tendency prediction for the infection data of the novel coronavirus pneumonia(NCP) in China YAN Kun (yankun@nature.ac.cn) ( Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China ) Abstract In this paper, by discussing the cumulative number of people of confirmed SARS(severe acute respiratory syndrome) virus infection in Beijing and Hongkong in 2003, and basing on the data of the number of novel coronavirus pneumonia(called NCP or 2019-nCOV(2019-new coronavirus)) confirmed infection in China between 11 January and 21 February 2020, using the simple analysis method of the general saturation process, corresponding partial-symmetrical equations(or weak-symmetrical equations) are given. Then by using the partial-symmetrical equations, the SIR model equations with the small sample data volume are discussed, PSSIR model equations and its approximate solutions are given preliminarily, and the accumulated data of the novel coronavirus pneumonia infection in China and in China except for Hubei Province are analyzed and calculated tentatively. At the same time, corresponding inflection point position and stage limit value of tendency prediction are given too. The results of this paper provide a reference for the description of multivariable nonlinear dynamic equations in the development of viral infection.
Keywords
novel coronavirus
pneumonia,
SARS
virus, infection data, partial-symmetrical equations, PSSIR model
equations, approximate solutions, tendency prediction YAN Kun. Analysis method of PSSIR model equations and its tendency prediction for the infection data of the novel coronavirus pneumonia(NCP) in China[Report]. Xi’an Modern Nonlinear Science Applying Institute, 22 February 2020. http://www.nature.ac.cn/papers/paper-pdf/ModelEquations-pdf.pdf Before Initially (Āgama) http://www.nature.ac.cn/sky/nature-sky-pdf.pdf After Finally(Tathatā) http://www.nature.ac.cn/star/nature-star-pdf.pdf
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Email: yankun@nature.ac.cn |
