Series of exponential equations in the form of were solved graphically, numerically and analytically. The analytical solution was derived in terms of Lambert-W function. A general numerical solution for any y is found...Series of exponential equations in the form of were solved graphically, numerically and analytically. The analytical solution was derived in terms of Lambert-W function. A general numerical solution for any y is found in terms of n or in base y. A solution is close to the fine structure constant. The equation which provided the solution as the fine structure constant was derived in terms of the fundamental constants.展开更多
In this paper, we study the equation of the form of which can also be written as . Apart from the trivial solution x = y, a non-trivial solution can be expressed in terms of Lambert W function as . For y > e, the s...In this paper, we study the equation of the form of which can also be written as . Apart from the trivial solution x = y, a non-trivial solution can be expressed in terms of Lambert W function as . For y > e, the solutions of x are in-between 1 and e. For integer y values between 4 and 12, the solutions of x written in base y are in-between 1.333 and 1.389. The non-trivial solutions of the equations and written in base y are exactly one and two orders higher respectively than the solutions of the equation . If y = 10, the rounded nontrivial solutions for the three equations are 1.3713, 13.713 and 137.13, i.e. 100.13713 = 1.3713. Further, ln(1.3713)/1.3713 = 0.2302 and W(-0.2302) = -2.302. The value 137.13 is very close to the fine structure constant value of 137.04 within 0.1%.展开更多
The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants including particles and bosons are associated with specific quantum integers, n. These integers define partial har...The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants including particles and bosons are associated with specific quantum integers, n. These integers define partial harmonic fractional exponents, 1 ± (1/n), of a fundamental frequency, Vf. The goal is to evaluate the prime and composite factors associated with the neutron n0, the quarks, the kinetic energy of neutron beta decay, the Rydberg constant, R, e, a0, H0, h, α, W, Z, the muon, and the neutron gluon. Their pure number characteristics correspond and explain the hierarchy of the particles and bosons. The elements and black body radiation represent consecutive integer series. The relative scale of the constants cluster in a partial harmonic fraction pattern around the neutron. The global numerical organization is related to the only possible prime factor partial fractions of 2/3, or 3/2, as pairs of 3 physical entities with a total of 6 in each group. Many other progressively resonant prime number factor patterns are identified with increasing numbers of smaller factors, higher primes, or larger partial fractions associated with higher order particles or bosons.展开更多
Using the one atom theory, the electronic structures of pure Cr, Mo and W with bcc structure were determined respectively as: [Ar] (3d c) 3.32 (3d n) 2.26 (4s c) 0.25 (4s f) 0.17 , [Kr] (4d c) 4.23 (4d n) 1.48 (5s c) ...Using the one atom theory, the electronic structures of pure Cr, Mo and W with bcc structure were determined respectively as: [Ar] (3d c) 3.32 (3d n) 2.26 (4s c) 0.25 (4s f) 0.17 , [Kr] (4d c) 4.23 (4d n) 1.48 (5s c) 0.02 (5s f) 0.27 and [Xe](5d c) 5.16 (6s c) 0.25 (6s f) 0.59 .The electronic structures of these metals with hcp and fcc structures and liquid state were also studied. According to their electronic structures, the relationship between the electronic structure and crystalline structure was explained qualitatively and the relationship between the difference of mechanical properties and transport properties of pure Cr, Mo and W with bcc structure and their electronic structures was also explained qualitatively; the lattice constants, binding energy, potential curves, elasticities and the temperature dependence of the linear thermal expansion coefficient of bcc Cr, bcc Mo and bcc W were calculated quantitatively.展开更多
文摘Series of exponential equations in the form of were solved graphically, numerically and analytically. The analytical solution was derived in terms of Lambert-W function. A general numerical solution for any y is found in terms of n or in base y. A solution is close to the fine structure constant. The equation which provided the solution as the fine structure constant was derived in terms of the fundamental constants.
文摘In this paper, we study the equation of the form of which can also be written as . Apart from the trivial solution x = y, a non-trivial solution can be expressed in terms of Lambert W function as . For y > e, the solutions of x are in-between 1 and e. For integer y values between 4 and 12, the solutions of x written in base y are in-between 1.333 and 1.389. The non-trivial solutions of the equations and written in base y are exactly one and two orders higher respectively than the solutions of the equation . If y = 10, the rounded nontrivial solutions for the three equations are 1.3713, 13.713 and 137.13, i.e. 100.13713 = 1.3713. Further, ln(1.3713)/1.3713 = 0.2302 and W(-0.2302) = -2.302. The value 137.13 is very close to the fine structure constant value of 137.04 within 0.1%.
文摘The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants including particles and bosons are associated with specific quantum integers, n. These integers define partial harmonic fractional exponents, 1 ± (1/n), of a fundamental frequency, Vf. The goal is to evaluate the prime and composite factors associated with the neutron n0, the quarks, the kinetic energy of neutron beta decay, the Rydberg constant, R, e, a0, H0, h, α, W, Z, the muon, and the neutron gluon. Their pure number characteristics correspond and explain the hierarchy of the particles and bosons. The elements and black body radiation represent consecutive integer series. The relative scale of the constants cluster in a partial harmonic fraction pattern around the neutron. The global numerical organization is related to the only possible prime factor partial fractions of 2/3, or 3/2, as pairs of 3 physical entities with a total of 6 in each group. Many other progressively resonant prime number factor patterns are identified with increasing numbers of smaller factors, higher primes, or larger partial fractions associated with higher order particles or bosons.
文摘Using the one atom theory, the electronic structures of pure Cr, Mo and W with bcc structure were determined respectively as: [Ar] (3d c) 3.32 (3d n) 2.26 (4s c) 0.25 (4s f) 0.17 , [Kr] (4d c) 4.23 (4d n) 1.48 (5s c) 0.02 (5s f) 0.27 and [Xe](5d c) 5.16 (6s c) 0.25 (6s f) 0.59 .The electronic structures of these metals with hcp and fcc structures and liquid state were also studied. According to their electronic structures, the relationship between the electronic structure and crystalline structure was explained qualitatively and the relationship between the difference of mechanical properties and transport properties of pure Cr, Mo and W with bcc structure and their electronic structures was also explained qualitatively; the lattice constants, binding energy, potential curves, elasticities and the temperature dependence of the linear thermal expansion coefficient of bcc Cr, bcc Mo and bcc W were calculated quantitatively.
