真诚  勤勉    达观  自然


1 阎坤. 宇宙分维构造及其数学基础[J]. 地球物理学进展,200419(3)709716.
YAN Kun. Fractal dimension structure of Cosmos and its mathematical foundations[J]. Progress in Geophysics (in Chinese with abstract in English)
200419(3)709716. DOI:10.3969/j.issn.1004-2903.2004.03.036.

宇宙分维构造及其数学基础


阎坤

(西安现代非线性科学应用研究所, 西安 710061)


 
探讨了宇宙分维构造的形式,给出了分维微积分及分形测度的数学基础,包括分维导数及分维微积分的表述形式、分维微分方程的规整空间积分解、分形测度的分维微积分定义及自相似分形的测度计算方程。作为诠释,探讨了原子核内中子与质子的趋势关系方程,以及其周期解和原子序数极限值。

关键词宇宙,分维构造,分维微积分,分维微分方程,分形测度,原子序数极限

DOI:10.3969/j.issn.1004-2903.2004.03.036.    中图分类号  P159 O17  文献标识码  A

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

   http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWJ200403036.htm

    http://www.nature.ac.cn/papers/paper-pdf/cosmosandmaths-pdf.pdf

 

2         阎坤. 关于超光速与量子分形的能量交换描述方法[J]. 纺织高校基础科学学报, 2004, 17(3):223227.
YAN Kun. Energy-exchange descriptions on the superluminal velocity and quantum fractal[J]. Basic Science Journal of Textile Universities (in Chinese with abstract in English) , 2004, 17(3):223
227.   DOI:10.3969/j.issn.1006-8341.2004.03.010.

关于超光速与量子分形的能量交换描述方法


阎坤

(西安现代非线性科学应用研究所, 西安 710061)
 

摘要通过对光速守恒及能量交换方程的深入讨论,给出双程光速守恒的机理方程、粒子超光速运动及量子分形的表述形式。结果表明,基于能量交换方程,能够确立既包含超光速运动,同时又融合Einstein狭义相对论及量子理论有关结论的一致性描述方法

关键词超光速,量子分形,能量交换,粒子分形运动

DOI:10.3969/j.issn.1006-8341.2004.03.010.    中图分类号:O412  O413     文献标识码:

Energy-exchange descriptions on the superluminal velocity and quantum fractal

YAN Kun  (yankun@nature.ac.cn)

(Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China)

Abstract  By exploring the constancy of light velocity in the vacuum and the energy-exchange equation of a particle, the expressional forms of mechanical equation of the constancy of two-way velocity of lightsuperluminal velocity, fractal motion of a particle 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.

Keywords  superluminal velocity, quantum fractal, energy exchange, particle fractal motion.

   http://en.cnki.com.cn/Article_en/CJFDTOTAL-FGJK200403010.htm

    http://www.nature.ac.cn/papers/paper-pdf/physics-pdf.pdf

 

3 阎坤. 天体运行的介质层壳与离散轨道引论[J]. 地球物理学进展,200419(4)984995.
 YAN Kun. Introductions on the medium shell and discrete orbits of celestial bodies motion[J]. Progress in Geophysics (in Chinese with abstract in English)200419(4):984995. DOI:10.3969/j.issn.1004-2903.2004.04.046.

天体运行的介质层壳与离散轨道引论


(西安现代非线性科学应用研究所, 西安 710061)
 

  采用介质层壳弯曲的唯象方法,在规整三维空间中给出了能量方程及物体间的能量引力形式表述,其引力方程的二个条件解分别与Newton引力理论及Einstein引力理论的有关结果相近。讨论了目前分维微积分在函数方面的局限性,给出了相似扩展方程,随后通过讨论天体运行轨道的基线扩展特征,给出了天体运行的离散轨道方程,并以太阳系行星及部分卫星为例,给出了这些天体运行离散轨道方程的具体表述形式。

关键词介质层壳弯曲,离散轨道方程,能量方程,分维微积分的局限,相似扩展方程,分维扩展

DOI:10.3969/j.issn.1004-2903.2004.04.046.    中图分类号  P13 O41 O17      文献标识码  A 

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 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 at present are discussed, and the similar expanded equation is given. Subsequentlyby 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.

Keywords medium shell curve, discrete orbital equation of celestial bodies motion, energy equation, localization of fractal dimension calculus, similar expanded equation, fractal dimension expanded

   http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWJ200404046.htm

    http://www.nature.ac.cn/papers/paper-pdf/celestial-pdf.pdf

 

4  阎坤. 天体运行轨道的一般性Binet方程形式[J]. 地球物理学进展,200520(2)534539.

    YAN Kun. The general expression of Binet equation about celestial bodies motion orbits [J]. Progress in Geophysics (in Chinese with abstract in English)200520(2):534539. DOI:10.3969/j.issn.1004-2903.2005.02.052.

 

天体运行轨道的一般性Binet方程形式


(西安现代非线性科学应用研究所  西安 710061)
 

  通过讨论已有质速关系的方程形式,给出质速关系的等效极坐标方程及其Binet方程,进而给出质速关系及质能关系的几个较为具体的方程形式,包括超光速运动形式。随后应用质能关系探讨介质层壳弯曲方法中能量方程解的一般形式,给出天体运行轨道的一般性Binet方程及其在弱场、强场时的近似解表述给出行星近日点进动、光线弯曲的解析分析。

关键词天体运行轨道,质速关系方程, Binet方程,近日点进动,光线弯曲,引力频移

DOI:10.3969/j.issn.1004-2903.2005.02.052.   中图分类号  P13O41   文献标识码  A 

 

The general expression of Binet equation about celestial bodies motion orbits

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, the equivalent polar coordinate equation and its Binet equation of the mass-velocity relation are given, and the expressions of the mass-velocity relation and mass-energy relation are given too, which include the forms of superluminal motion. Subsequently, using the mass-energy relation, the general expression of the solution of the energy-curvature 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 mass-velocity relation, Binet equation, superluminal motion, advance of the perihelion of planets, bending of light, gravitational frequency shift

   http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWJ200502052.htm

    http://www.nature.ac.cn/papers/paper-pdf/celestialBinet-pdf.pdf

 

5  阎坤. 地球空间稳定核素的趋势分析方程与物质的超光速运动规律[J]. 地球物理学进展,200621(1)3847.

    YAN Kun. The tendency analytical equations of stable nuclides and the superluminal velocity motion laws of matter in geospace[J]. Progress in Geophysicsin Chinese with abstract in English),200621(1)3847. DOI:10.3969/j.issn.1004-2903.2006.01.007.

地球空间稳定核素的趋势分析方程与物质的超光速运动规律

(西安现代非线性科学应用研究所  西安 710061)
 

  通过讨论地球空间已有稳定核素内质子数与中子数的分布趋势,介绍了稳定核素的趋势分析方法及其有关周期性分布方程形式,给出了理论方程曲线与地球空间稳定核素实验数据分布点的对比结果,进而给出了稳定核素极限值和元素周期表中化学元素极限,以及其与正负粒子对的可能对应关系方程,包括位于电子中微子层面附近的粒子质量量级初步估计。随后通过建立真空物质能量状态的二个假设,及基于等效Binet方程,给出了与Einstein狭义相对论有关结论相融合的物质粒子以光速及超光速运动的质量及能量方程;作为推论,对这些方程与暗物质及暗能量的可能对应关系予以了初步探讨。

关键词稳定核素,趋势分析方程,周期性规律,化学元素极限,真空物质能量状态,超光速运动方程

DOI:10.3969/j.issn.1004-2903.2006.01.007.   中图分类号  P35O57O41  文献标识码  A 

 

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 positron-particle 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 light-velocity or superluminal-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

   http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWJ200601006.htm

    http://www.nature.ac.cn/papers/paper-pdf/vacuumenergy-pdf.pdf

 

6    阎坤. 天体运行轨道的背景介质理论导引与自相似分形测度计算的分维微积分基础[J]. 地球物理学进展,200722(2)451462.

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)200722(2)451462. DOI:10.3969/j.issn.1004-2903.2007.02.018.
 

天体运行轨道的背景介质理论导引与自相似分形测度计算的分维微积分基础


( 西安现代非线性科学应用研究所, 西安 710061)
 

  : 通过讨论天体运行背景介质理论的连续轨道及离散轨道这二个研究方向的基础假设,介绍了天体运行轨道的具体方程形式及理论框架概要;进一步地通过讨论天体运行轨道Binet方程的一般形式及其行星近日点进动角的解,给出了连续轨道理论与Newton理论及Einstein广义相对论的联系与区别;通过讨论天体运行轨道的分维扩展方程,给出了包括太阳系行星、天王星卫星、地球卫星、绕月航天器等在内的离散轨道(稳定性轨道)方程及其预言数据。特别地,作为对天体在较为广泛区域作用曲线的初步探讨推论,指出仅由天体引力难以形成质量密度趋于无穷大的理想黑洞。通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设,进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式,给出分维导数与分数阶导数的区别,随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式,给出了其与目前Hausdorff测度方法(覆盖方法)的区别,并对包括三分Cantor集合、Koch曲线、Sierpinski垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

关键词天体运行轨道,背景介质理论,连续轨道,离散轨道,自相似分形测度,分维微积分,分维导数

DOI:10.3969/j.issn.1004-2903.2007.02.018.   中图分类号  P13O17O18  文献标识码  A

Introduction on background medium theory about celestial body motion orbit

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 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 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 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 fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension 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 self-similar fractals which include middle-third 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, self-similar fractal measure, fractional-dimension calculus, fractional-dimension derivative

   http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWJ200702017.htm

    http://www.nature.ac.cn/papers/paper-pdf/celestialandmaths-pdf.pdf

 

7       阎坤. 关于对无穷予以虚数形式标记的初步注释[R]. 西安现代非线性科学应用研究所,2009 03 18.

YAN Kun. Primary annotation of symbol basing on imaginary form about infinity[R]. Xi’an Modern Nonlinear Science Applying Institute, 18 March 2009.

关于对无穷予以虚数形式标记的初步注释

( 西安现代非线性科学应用研究所  西安 710061)
 

  给出对无穷予以虚数形式标记的初步讨论注释。
关键词
无穷,0,虚数形式,标记,注释,Euler公式

Primary annotation of symbol basing on imaginary form about infinity

YAN Kun  (yankun@nature.ac.cn)

(Xi’an Modern Nonlinear Science Applying Institute, Xi’an 710061, China)

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

   http://www.nature.ac.cn/papers/paper-pdf/spirit-pdf.pdf

 8  阎坤. 60年来大气中二氧化碳浓度数据的趋势方程研究[J].地球物理学进展,2009,24(5):16651670.

          YAN Kun. Research on tendency equation about the concentration data of carbon dioxide in the atmosphere over the past 60 years[J]. Progress in Geophys. (in Chinese with abstract in English), 2009,24(5):16651670.
DOI:
10.3969/j.issn.
1004-2903.2009.05.016.


60
年来大气中二氧化碳浓度数据的趋势方程研究

( 西安现代非线性科学应用研究所  西安 710061)
 

  通过讨论已有的60年来大气中CO2浓度数据的分布状态,采用趋势分析方法,给出了具体趋势方程形式。与冰芯分析或观测数据对比结果表明,趋势方程曲线与已有数据基本符合,随后初步给出了2010年至2016年间大气中CO2浓度预测值。

关键词二氧化碳浓度,大气,趋势方程,曲线拟合,预测值,数据分析

DOI:10.3969/j.issn.1004-2903.2009.05.016     中图分类号  P351P401    文献标识码  A

 

Research on tendency equation about the concentration data of carbon dioxide

in the atmosphere over the past 60 years

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, the concrete tendency equation forms of the CO2 concentration are presented at first. Further more, the 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, the predictive data of the CO2 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

 

   http://d.wanfangdata.com.cn/Periodical_dqwlxjz200905016.aspx

    http://www.nature.ac.cn/papers/paper-pdf/co2concentration-pdf.pdf

阎坤. 数据曲线间断区域的自适应连接方程研究[J]. 地球物理学进展, 2011,26(1):162171.

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): 162171. DOI:10.3969/j.issn.1004-2903.2011.01.018.

 

数据曲线间断区域的自适应连接方程研究

( 西安现代非线性科学应用研究所  西安 710061 )

  通过讨论非线性动力学方程的近似等效解析解及数据曲线间断区域的性质,给出间断区域的自适应连接方程形式及其参数确定的预置迭代方法,随后给出计算实例。其中对于缓变数据曲线阶跃间断区域,可自动计算生成连接方程形式。文中基于自适应连接方程探讨分析了磁性材料磁滞回线方程、零点能量阶跃方程、平滑平均能量方程(诸如负绝对温度区域平均能量方程)、稳定核素比结合能方程、势能函数曲线方程(诸如双原子分子势能函数曲线方程)、自然饱和过程方程(诸如钢材料断裂韧性方程)及金属或岩石蠕变过程方程。

关键词非线性动力学方程,数据曲线间断区域,自适应连接方程,预置迭代方法,磁滞回线方程,平均能量方程,比结合能方程,势能函数曲线方程,自然饱和过程方程,蠕变过程方程

DOI:10.3969/j.issn.1004-2903.2011.01.018     中图分类号  O174TP301O411     文献标识码  A

Research on adaptive connection equation in discontinuous area of data curve

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 form of adaptive connection equation and the preset iteration method determining parameters in discontinuous area are given. Subsequently, a computing example is given too. For the step discontinuous area of slowly varying data curve, its form of adaptive connection equation can be obtained by automatic calculating. And in this paper, basing on the form of adaptive connection equation, equations of magnetic hysteresis loop for magnetic material, zero-point energy step equation, smooth average energy equation (such as average energy equation at negative absolute temperature, etc), equation of average binding energy per nucleon in stable nuclidecurvilinear 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, preset iteration method, equations of magnetic hysteresis loop, average energy equation, equation of average binding energy per nucleon, curvilinear equation of potential energy function, equation of natural saturation process, equation of creep process

   http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWJ201101020.htm

    http://www.nature.ac.cn/papers/paper-pdf/curveandequation-pdf.pdf

 

10     阎坤. 关于连接方程的简略注释[R]. 西安现代非线性科学应用研究所,2011 03 18.

YAN Kun. Brief annotation of the connection equation[R]. Xi’an Modern Nonlinear Science Applying Institute, 18 March 2011.

关于连接方程的简略注释

( 西安现代非线性科学应用研究所  西安 710061 )

  给出了连接方程若干性质及应用的简略注释。

关键词连接方程,曲线形态,趋势性方程,非线性动力学方程,近似等效解析解,RLCN串联电路非线性微分方程,电存元件,理想饱和过程,年度能源消费总量,人口总数,GDP总值,岩石,单晶高温合金,蠕变过程,半导体分立器件,VA特性曲线,超导材料,R(或ρT曲线,双晶Josephson结,直流IU特性曲线,Shapiro台阶,电流阶跃幅值,方程局限性

Brief annotation of the connection equation

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 the properties and applications of connection equation are given.

Keywords connection equation, shape of curve, tendency equation, nonlinear dynamics equation, approximate equivalent analytical solution, nonlinear differential equation for a RLCN series circuit, nonlinstor, ideal saturation process, total annual energy consumption, annual population, annual GDP, rock, single-crystal superalloy, creep process, discrete semiconductor device, Volt-Ampere characteristic curve, superconducting material, Resistance (or Resistivity)-Temperature curve, bicrystal Josephson junction, direct current I-U characteristic curve, Shapiro steps, current step amplitude, localization of the equation

   http://www.nature.ac.cn/papers/paper-pdf/ConnectionEquation-pdf.pdf

 


节选

Before Initially(Āgama)

   http://www.nature.ac.cn/sky/nature-sky-pdf.pdf

朴本

After Finally(Tathatā)

  http://www.nature.ac.cn/star/nature-star-pdf.pdf

 

doc     pdf


Email: yankun@nature.ac.cn