Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calc...Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.展开更多
<p align="justify"> <span style="font-family:Verdana;">It is often claimed that Maxwell’s electromagnetic equations were originally written in terms of quaternions. Once returned to th...<p align="justify"> <span style="font-family:Verdana;">It is often claimed that Maxwell’s electromagnetic equations were originally written in terms of quaternions. Once returned to that form and treated with left and right hand operators as in the mathematics of P. M. Jack, a new seventh scalar electromagnetic field component emerges with possible relations to clean energy extraction and gravitation. It is the purpose here to examine this approach afresh and see how it might link up with other fairly recent, but little known, work in the field. Again, as with the usual form of Maxwell’s equations, a new scalar wave equation is derived but, on this occasion, due to the presence of the scalar component of the quaternion, that equation exhibits a wave speed greater than the speed of light. Historical and present uses within military and humanitarian contexts are considered briefly.</span> </p>展开更多
Based on 'the matrix theory for the propagation of a scalar light wave in a system consisting of plane screens (cylindrical coordinates)' proposed by one of the authors (1981), the propagation of the self-cons...Based on 'the matrix theory for the propagation of a scalar light wave in a system consisting of plane screens (cylindrical coordinates)' proposed by one of the authors (1981), the propagation of the self-consistent field in PCR is analyzed, and a matrix eigen-equation of the self-consistent field is presented. By solving the eigen-equation, the axisymmetrical PCR with finite aperture is calculated, and the diffraction losses, phase shifts, relative amplitude and phase distributions on each mirror surface of various order transverse modes (including high-order modes, whose l≥2, p≥1) are introduced.A quasi-equivalence relation of PCR is also given. According to this relation, some characteristics (as the diffraction loss, the field distribution on the surface of spherical mirror) of all transverse modes in a PCR are just the same as those in some of the other PCR with different g_1.Some examples of calculation results are also given. They show that (ⅰ) the convengence of the above-mentioned equation is very good, (ⅱ) the calculation results with very high precision can be obtained practically, and the characteristics of TEM with very small or large losses can also be calculated precisly and (ⅲ) the choice of the reference light field does not affect correctness of the theory but affects the amount of calculation.Only the PCR with only one PCM being one of the two endreflectors of resonators is discussed, and the effect of response time of the PCM is ignored in this paper.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Using the Hartle-Hawking method, we discuss the quantum Cosmology with O_(8N+1)^-symmetric coupling scalar field. The corresponding Wheeler-De Witt equation has been derived, and the wave function of the universe calculated. We got the material solution of the cosmic wave function in harmonic eigenstate, and the solution of space is the product of the Gauss factor and one polynomial. After analysing the wave function of the universe under the quantum effect, we found that the probability density of the universe appearing at a=0 is zero, and that the minimal radius of the ground state of the universe is on the Planck scale. The analysis of the wave function of the universe, also reveals that at the very early stage of the universe the probability density of the multl-scalar field is smaller than that of the onescalar field.
文摘<p align="justify"> <span style="font-family:Verdana;">It is often claimed that Maxwell’s electromagnetic equations were originally written in terms of quaternions. Once returned to that form and treated with left and right hand operators as in the mathematics of P. M. Jack, a new seventh scalar electromagnetic field component emerges with possible relations to clean energy extraction and gravitation. It is the purpose here to examine this approach afresh and see how it might link up with other fairly recent, but little known, work in the field. Again, as with the usual form of Maxwell’s equations, a new scalar wave equation is derived but, on this occasion, due to the presence of the scalar component of the quaternion, that equation exhibits a wave speed greater than the speed of light. Historical and present uses within military and humanitarian contexts are considered briefly.</span> </p>
文摘Based on 'the matrix theory for the propagation of a scalar light wave in a system consisting of plane screens (cylindrical coordinates)' proposed by one of the authors (1981), the propagation of the self-consistent field in PCR is analyzed, and a matrix eigen-equation of the self-consistent field is presented. By solving the eigen-equation, the axisymmetrical PCR with finite aperture is calculated, and the diffraction losses, phase shifts, relative amplitude and phase distributions on each mirror surface of various order transverse modes (including high-order modes, whose l≥2, p≥1) are introduced.A quasi-equivalence relation of PCR is also given. According to this relation, some characteristics (as the diffraction loss, the field distribution on the surface of spherical mirror) of all transverse modes in a PCR are just the same as those in some of the other PCR with different g_1.Some examples of calculation results are also given. They show that (ⅰ) the convengence of the above-mentioned equation is very good, (ⅱ) the calculation results with very high precision can be obtained practically, and the characteristics of TEM with very small or large losses can also be calculated precisly and (ⅲ) the choice of the reference light field does not affect correctness of the theory but affects the amount of calculation.Only the PCR with only one PCM being one of the two endreflectors of resonators is discussed, and the effect of response time of the PCM is ignored in this paper.
