A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic...A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic one, but is connected with the inverse of Sommerfeld’s fine-structure constant and this way again connected with the electron. From number-theoretical realities, including the reciprocity relation of the golden ratio as effective pre-calculator of nature’s creativeness, a proposed closeness to the icosahedron may point towards the structure of the electron, thought off as a single-strand compacted helically self-confined charged elemantary particle of less spherical but assumed blunted icosahedral shape generated from a high energy double-helix photon. We constructed a chiral Moebius “ball” from a 13 times 180˚twisted double helix strand, where the turning points of 12 generated slings were arranged towards the vertices of a regular icosahedron, belonging to the non-centrosymmetric rotation group I532. Mathematically put, we convert the helical motion of an energy quantum into a stationary motion on a Moebius stripe structure. The radius of the ball is about the Compton radius. This chiral closed circuit Moebius ball motion profile can be tentatively thought off as the dominant quantum vortex structure of the electron, and the model may be named CEWMB (Charged Electromagnetic Wave Moebius Ball). Also the gyromagnetic factor of the electron (g<sub>e</sub> = 2.002319) can be traced back to this special structure. However, nature’s energy infinity principle would suggest a superposition with additional less dominant (secondary) structures, governed also by the golden mean. A suggestion about the possible structure of delocalized hole carriers in the superconducting state is given.展开更多
By combination of finite number theory and quantum information, the complete quantum information in the <em>DNA</em> genetic code has been made likely by <em>Planat et al</em>. (2020). In the p...By combination of finite number theory and quantum information, the complete quantum information in the <em>DNA</em> genetic code has been made likely by <em>Planat et al</em>. (2020). In the present contribution a varied quartic polynomial contrasting the polynomial used by <em>Planat et al</em>. is proposed that considered apart from the golden mean also the fifth power of this dominant number of nature to adapt the code information. The suggested polynomial is denoted as <em>g</em>(<em>x</em>) = <em>x</em><sup>4</sup> - <em>x</em><sup>3</sup> - (4 - <em><i style="white-space:normal;">ϕ</i></em><sup>2</sup> )<em>x</em><sup>2</sup> + (4 – <i>ϕ</i><sup>2</sup>)x + 1, where <img src="Edit_40efe764-d690-499f-8424-129f9ca46f78.bmp" alt="" /> is the golden mean. Its roots are changed to more golden mean based ones in comparison to the <em>Planat</em> polynomial. The new coefficients 4 – <em>ϕ</em><sup>2</sup> instead of 4 would implement the fifth power of the golden mean indirectly applying <img src="Edit_5b44b644-3f59-4fad-a586-ec5345ba6be4.bmp" alt="" />. As an outlook, it should be emphesized that the connection between genetic code and resonance code of the <em>DNA</em> may lead us to a full understanding of how nature stores and processes compacted information and what indeed is consciousness linking everything with each other suggestedly mediated by all-pervasive dark constituents of matter respectively energy. The number-theoretical approach to <em>DNA</em> coding leads to the question about the helical structure of the electron.展开更多
In the structure of quasicrystal, the coordination icosahedron has long ordering but no translation ordering. The author dealt with the building principle ofquasicrystal and thought that two principles played a certai...In the structure of quasicrystal, the coordination icosahedron has long ordering but no translation ordering. The author dealt with the building principle ofquasicrystal and thought that two principles played a certain role in the quasicrystal structure, i.e. the icosahedron principle and the golden mean principle. We obtained the most simple.structure model of quasicrystals, and could explain all details of the high-resolution electron microscopic image of the A1-Mn quasicrystal based on the two principles. The author’s model has the characteristic of fractal structure, therefore, we call it the particle fractal structure madeh The author has made a systematic deduction of quasicrystal point group, forms, possible type of quasicrystal lattice.展开更多
Five-fold symmetric diamond crystals（FSDCs） were synthesized by hot filament chemical vapour deposition（HFCVD） methods. Their surface morphologies and defects were characterised by scanning electron microscopy（SE...Five-fold symmetric diamond crystals（FSDCs） were synthesized by hot filament chemical vapour deposition（HFCVD） methods. Their surface morphologies and defects were characterised by scanning electron microscopy（SEM）. From the perspective of nucleation-growth, a growth mechanism for icosahedral and other five-fold symmetric diamond crystals was discussed. Computer modelling was also carried out. The results show that the dodecahedrane（C20H20） molecule is proposed as a nucleus for the growth of icosahedral diamond crystals（IDCs）, wherein the 20 {111} surface planes develop orthogonal to the direction of the original 20 C—H bonds by sequential H abstraction and CH3 addition reactions. IDC can be pictured as an assembly of isosceles tetrahedra, with each tetrahedron contributing a {111} plane to the surface of the IDC and the remainder of the tetrahedral surfaces forming twin planes with neighbouring tetrahedra. The small mismatch（1.44°） between the {111} surface dihedral angle of a perfect icosahedron and that of a twinned icosahedron reveals itself via twin planes in the IDC grain. The modelling suggests how the relief of strain induced by this distortion could lead to the formation of defects such as concave pentagonal cavities at vertices and grooves along the grain edges that accord well with those observed experimentally. Similar arguments based on growth from the hexacyclo pentadecane（C15H20） nucleus can also account for the observed formation of star and rod shaped FSDCs, and some of their more obvious morphological defects.展开更多
文摘A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic one, but is connected with the inverse of Sommerfeld’s fine-structure constant and this way again connected with the electron. From number-theoretical realities, including the reciprocity relation of the golden ratio as effective pre-calculator of nature’s creativeness, a proposed closeness to the icosahedron may point towards the structure of the electron, thought off as a single-strand compacted helically self-confined charged elemantary particle of less spherical but assumed blunted icosahedral shape generated from a high energy double-helix photon. We constructed a chiral Moebius “ball” from a 13 times 180˚twisted double helix strand, where the turning points of 12 generated slings were arranged towards the vertices of a regular icosahedron, belonging to the non-centrosymmetric rotation group I532. Mathematically put, we convert the helical motion of an energy quantum into a stationary motion on a Moebius stripe structure. The radius of the ball is about the Compton radius. This chiral closed circuit Moebius ball motion profile can be tentatively thought off as the dominant quantum vortex structure of the electron, and the model may be named CEWMB (Charged Electromagnetic Wave Moebius Ball). Also the gyromagnetic factor of the electron (g<sub>e</sub> = 2.002319) can be traced back to this special structure. However, nature’s energy infinity principle would suggest a superposition with additional less dominant (secondary) structures, governed also by the golden mean. A suggestion about the possible structure of delocalized hole carriers in the superconducting state is given.
文摘By combination of finite number theory and quantum information, the complete quantum information in the <em>DNA</em> genetic code has been made likely by <em>Planat et al</em>. (2020). In the present contribution a varied quartic polynomial contrasting the polynomial used by <em>Planat et al</em>. is proposed that considered apart from the golden mean also the fifth power of this dominant number of nature to adapt the code information. The suggested polynomial is denoted as <em>g</em>(<em>x</em>) = <em>x</em><sup>4</sup> - <em>x</em><sup>3</sup> - (4 - <em><i style="white-space:normal;">ϕ</i></em><sup>2</sup> )<em>x</em><sup>2</sup> + (4 – <i>ϕ</i><sup>2</sup>)x + 1, where <img src="Edit_40efe764-d690-499f-8424-129f9ca46f78.bmp" alt="" /> is the golden mean. Its roots are changed to more golden mean based ones in comparison to the <em>Planat</em> polynomial. The new coefficients 4 – <em>ϕ</em><sup>2</sup> instead of 4 would implement the fifth power of the golden mean indirectly applying <img src="Edit_5b44b644-3f59-4fad-a586-ec5345ba6be4.bmp" alt="" />. As an outlook, it should be emphesized that the connection between genetic code and resonance code of the <em>DNA</em> may lead us to a full understanding of how nature stores and processes compacted information and what indeed is consciousness linking everything with each other suggestedly mediated by all-pervasive dark constituents of matter respectively energy. The number-theoretical approach to <em>DNA</em> coding leads to the question about the helical structure of the electron.
文摘In the structure of quasicrystal, the coordination icosahedron has long ordering but no translation ordering. The author dealt with the building principle ofquasicrystal and thought that two principles played a certain role in the quasicrystal structure, i.e. the icosahedron principle and the golden mean principle. We obtained the most simple.structure model of quasicrystals, and could explain all details of the high-resolution electron microscopic image of the A1-Mn quasicrystal based on the two principles. The author’s model has the characteristic of fractal structure, therefore, we call it the particle fractal structure madeh The author has made a systematic deduction of quasicrystal point group, forms, possible type of quasicrystal lattice.
基金Projects(51301211,21271188)supported by the National Natural Science Foundation of ChinaProject(2012M521540)supported by the China Postdoctoral Science Foundation+2 种基金Project(2013RS4027)supported by the Postdoctoral Science Foundation of Hunan Province,ChinaProject(20110933K)supported by the Open Foundation of the State Key Laboratory of Powder Metallurgy,ChinaProject supported by the Open-End Fund for Valuable and Precision Instruments of Central South University,China
文摘Five-fold symmetric diamond crystals（FSDCs） were synthesized by hot filament chemical vapour deposition（HFCVD） methods. Their surface morphologies and defects were characterised by scanning electron microscopy（SEM）. From the perspective of nucleation-growth, a growth mechanism for icosahedral and other five-fold symmetric diamond crystals was discussed. Computer modelling was also carried out. The results show that the dodecahedrane（C20H20） molecule is proposed as a nucleus for the growth of icosahedral diamond crystals（IDCs）, wherein the 20 {111} surface planes develop orthogonal to the direction of the original 20 C—H bonds by sequential H abstraction and CH3 addition reactions. IDC can be pictured as an assembly of isosceles tetrahedra, with each tetrahedron contributing a {111} plane to the surface of the IDC and the remainder of the tetrahedral surfaces forming twin planes with neighbouring tetrahedra. The small mismatch（1.44°） between the {111} surface dihedral angle of a perfect icosahedron and that of a twinned icosahedron reveals itself via twin planes in the IDC grain. The modelling suggests how the relief of strain induced by this distortion could lead to the formation of defects such as concave pentagonal cavities at vertices and grooves along the grain edges that accord well with those observed experimentally. Similar arguments based on growth from the hexacyclo pentadecane（C15H20） nucleus can also account for the observed formation of star and rod shaped FSDCs, and some of their more obvious morphological defects.
