真诚 勤勉 达观 自然 

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 selfsimilar 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.10042903.2004.03.036.
YAN Kun
(yankun@nature.ac.cn)
Abstract
In this paper,
consider taking the vacuum as a form of medium, by exploring the
constancy of light velocity in the vacuum, the energyexchange equation
and the vortex shedding wavelength equation in Karman vortexstreet, the
expressional forms of
equation of the oneway velocity of light (also equation of the
oneway
speed of light, or equation of
oneway
variable speed of light)
for the constancy of the twoway velocity of light (or constancy of the
twoway speed of light),
the experimental
criterion equation for the closed strings mode of the photon (the
general refraction equation of the photon with a same rotation plane),
superluminal (also
fasterthanlight or FTL) velocity, medium action
equation of particle fractal motion for the waveparticle
duality, and quantum fractal are studied deeply. As a result, it shows
that a tentative theoretical frame which includes not only the
superluminalvelocity motion but consists with Einstein special
relativity and quantum theory can be established.
Yan Kun. Energyexchange
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.10068341.2004.03.010.
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 the energygravitation
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 at present are discussed, and the similar
expanded equation is given. Subsequently，by
discussing the expanded baseline property on the celestial motion orbit,
the discrete orbital equation 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.
YAN Kun (yankun@nature.ac.cn) (Xi’an Modern Nonlinear Science Applying Institute，Xi’an 710061，China)
Abstract
By
discussing the existent equations of massvelocity relation, the
equivalent polar coordinate equation and its Binet equation of the
massvelocity relation are given, and the expressions of the
massvelocity relation and massenergy relation are given too, which
include the forms of superluminal (also
fasterthanlight or FTL) motion. Subsequently, using the
massenergy relation, the general expression of the solution of the
energy equation on the medium shell curve method is discussed, and the
general expression of Binet equation and its approximate solutions about
orbits of the celestial bodies motion in the weak and strong
gravitational field are given. Further more, the analysis solutions of
the advance of the perihelion of
planets and bending of light for the
gravitational force are given too.
Keywords
orbit of the
celestial bodies motion, equations of massvelocity 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.10042903.2005.02.052. 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, the tendency analytical method and it’s periodic distribution
equation forms of the stable nuclides are expressed at first. Then the
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, the stable nuclide limit
and the chemical element limit for the chemical element periodic table
are given, and the possible corresponding relation equation with the
positronparticle annihilation is expressed, which includes the
estimation of the order of the static mass to be situated nearby at the
electron neutrino structural dimension. Subsequently, by forming two
hypotheses about the energy state of vacuum matter, and basing on the
equivalent Binet’s equation, the mass equations and the energy equations
of the partial moving with lightvelocity or superluminal (also
fasterthanlight or FTL) velocity motion fusing with the results
of Einstein special relativity are expressed. As inference, the 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, energy state of vacuum matter, equations of superluminal velocity
motion
and foundation of fractionaldimension calculus about selfsimilar 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 the background medium
theory for celestial body motion, the 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, the relations and differences between the continuous orbit
theory and Newton’s gravitational theory and Einstein’s general
relativity are given. And by discussing the fractionaldimension
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 the 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 fractionaldimension derivative about
function and the formula form the hypothesis of fractionaldimension
derivative about power function, the concrete equation formulas of
fractionaldimension derivative, differential and integral are described
distinctly further, and the difference between the fractionaldimension
derivative and the fractionalorder derivative are given too.
Subsequently, the concrete forms of measure tendency calculus equations
of selfsimilar fractal obtaining by based on the definition of form in
nonintegral order calculus about general fractal measure are discussed
again, and the differences with Hausdorff measure method or the covering
method at present are given. By applying the measure calculation
equations, the measure of selfsimilar fractals which include
middlethird Cantor set, Koch curve, Sierpinski gasket and orthogonal
cross star are calculated and analyzed.
Keywords
orbit
of celestial body motion, background medium theory, continuous orbit,
discrete orbit, selfsimilar fractal measure, nonintegral order
calculus, fractionalorder calculus, fractionaldimension calculus
YAN Kun. Introduction on
background medium theory about celestial body motion orbit and
foundation of fractionaldimension calculus about selfsimilar fractal
measure calculation[J]. Progress in Geophysics(in Chinese with abstract
in English), 2007, 22(2): 451～462.
DOI:10.3969/j.issn.10042903.2007.02.018.
Primary annotation of symbol basing on imaginary form about infinity
YAN Kun
(yankun@nature.ac.cn) Abstract In this paper, the 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 CO_{2}
concentration data in the atmosphere over the
past 60 years, and adopting the tendency analytical method, the concrete
tendency equation forms of the CO_{2} concentration are
presented at first. Further more, the comparison result between the
curve of the theoretical equation and the data curve of CO_{2}
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, the predictive data of the CO_{2}
concentration in the atmosphere during the year from 2010 to 2016 are
suggested tentatively.
Keywords
concentration
of carbon dioxide, atmosphere, tendency equation, curve fitting,
predictive data, data analysis
YAN Kun (yankun@nature.ac.cn) ( Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China )
Abstract
In
this paper, by discussing the approximate equivalent analytical solution
of the nonlinear dynamics equation and the properties in discontinuous
area of data curve, a
general constructing form of
adaptive connection equation and the preset iteration method determining
parameters in the discontinuous area are given.
And then, the connecting method of the mapping equations for the
discontinuous areas of general curves is also given. Subsequently, the
computing examples which included the discontinuous areas with the
dislocation and the turnback are given too. This adaptive connection
equation can be applied as a general form of expansion (extended
hyperbolic tangent function) of the classical Scurve (sigmoid curve)
equation or Logistic function, and for the step discontinuous area of
slowly varying data curve, its form of the adaptive connection equation
can be obtained by automatic calculating. In this paper, the
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 data curve or
the partial continuous functions,
the equations of magnetic hysteresis loop for magnetic material, the
extended form of average energy equation and the
tendency differential equation of the
average particle number for the statistical distributions of the
particles,
the
equation of average binding energy per nucleon in stable nuclide，the
curvilinear equation of potential energy function (such as curvilinear
equation of potential energy function of diatomic molecule, etc), the
equation of natural saturation process (such as tree growth and physical
reaction or chemical reaction process, the equation of fracture
toughness for steel material, etc) and the 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, 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.10042903.2011.01.018.
YAN Kun (yankun@nature.ac.cn) ( Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China )
Abstract
In this paper,
the brief annotation of a constructing procedure and the applications of
the connection equation are given. An
analytical method
of the connection equation as an approximate equivalent analytical
solution of the nonlinear dynamics equations is discussed, the 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. An approximate expression of extended hyperbolic tangent
series for the data curve or the partial
continuous functions is
constructed.
According to the approximate form of the nonlinear dynamics
equation of the connection equation, two new electronic circuit elements
(nonlinstor and geomsentor) with the deepening chargecontrolled
capacitor properties based on the form of the nonlinear differential
equation is predicted, and the nonlinear differential equation for a
RLCNG series circuit is also analyzed, the tendency equation and its
conditional solutions of the statistical distributions of the particles
are given, the
nonlinear differential equation expressions with the solution of
approximate linear frequency conversion and the characteristics of the
curve shapes of frequency conversion wave equations at the negative
frequency are discussed, a concise model of the database theoretical
framework (this framework to be
made up of the
foundation database,
the tendency equation, and the analytic
database) is explored, the equation of relationship between the
total annual energy consumption with the
annual GDP in the United States, and the equation of relationship
between the annual population with the
annual GDP in the United Kingdom are established, and the
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, the tendency fitting
equations of the curves are explored, which included the creep process
curve of the rock and the singlecrystal superalloy, the VoltAmpere
characteristic curve of the discrete semiconductor device, the
resistance (or resistivity )absolute temperature curve of the
superconducting material, the direct current IU
characteristic curve of the bicrystal Josephson junction, and the
current step amplitude of Shapiro steps, the
frictionspeed 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,
the expanded equation form of the
Newton's law of cooling, the
shear stressshear rate in the
flow curve (that included the
sections
of first Newtonian fluidflow,
pseudoplastic flow, second Newtonian
fluidflow, dilatant flow, turbulent flow, and
anomalous
shearing effect) of the polymer melts, etc. On the
phenomenological and tendency levels, the research directions of similar
property of creep curves of materials with the flow curves of polymer
melt, and the 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, the limitations of the connection
equation in the data fitting and longrange forecasting are discussed. Before Initially (Āgama) http://www.nature.ac.cn/sky/natureskypdf.pdf After Finally(Tathatā) http://www.nature.ac.cn/star/naturestarpdf.pdf


Email: yankun@nature.ac.cn 