The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified,...The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified, to include Newton’s Shell Theorem (NST). By including NST for r, both Schwarzschild singularity at r = 2GM/c2 and at r → 0 singularities are removed from the metric. Near R → 0, the question of maximal density is considered based on Schwarzschild’s modified metric, and compared to the quantum limit of maximal mass density put by Planck’s quantum-based universal units. It is asserted, that General relativity, when combined with Planck’s universal units, inevitably leads to quantization of gravity.展开更多
The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has...The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.展开更多
The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an...The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.展开更多
Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1 ( simplifying as 'g-contraction mapping' ) has a...Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1 ( simplifying as 'g-contraction mapping' ) has a unique fixed point in M . Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.展开更多
The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the...The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.展开更多
Making use of Newton’s classical shell theorem, the Schwarzschild metric is modified. This removes the singularity at r = 0 for a standard object (not a black hole). It is demonstrated how general relativity evidentl...Making use of Newton’s classical shell theorem, the Schwarzschild metric is modified. This removes the singularity at r = 0 for a standard object (not a black hole). It is demonstrated how general relativity evidently leads to quantization of space-time. Both classical and quantum mechanical limits on density give the same result. Based on Planck’s length and the assumption that density must have an upper limit, we conclude that the lower limit of the classical gravitation theory by Einstein is related to the Planck length, which is a quantum phenomenon posed by dimensional analysis of the universal constants. The Ricci tensor is considered under extreme densities (where Kretschmann invariant = 0) and a solution is considered for both outside and inside the object. Therefore, classical relativity and the relationship between the universal constants lead to quantization of space. A gedanken experiment of light passing through an extremely dense object is considered, which will allow for evaluation of the theory.展开更多
A novel decentralized PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output (MIMO)dynamic processes. The first key feature of the design procedure is t...A novel decentralized PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output (MIMO)dynamic processes. The first key feature of the design procedure is that a whole MIMO control system is decomposed into multiple control loops, therefore the sub-controllers can be efficiently flexibly designed in parallel prototype.The second key feature is that the decentralized controller has equivalency to those designed by backstepping approach. As a complementary support to the design procedure, the sufficient condition of the whole closed-loop system stability is analyzed via the small gain theorem and it can be proven that the process tracking performance is improved. The simulation results of the Shell benchmark control problem are provided to verify the effectiveness and practicality of the proposed decentralized PID control.展开更多
文摘The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified, to include Newton’s Shell Theorem (NST). By including NST for r, both Schwarzschild singularity at r = 2GM/c2 and at r → 0 singularities are removed from the metric. Near R → 0, the question of maximal density is considered based on Schwarzschild’s modified metric, and compared to the quantum limit of maximal mass density put by Planck’s quantum-based universal units. It is asserted, that General relativity, when combined with Planck’s universal units, inevitably leads to quantization of gravity.
文摘The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.
文摘The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.
文摘Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1 ( simplifying as 'g-contraction mapping' ) has a unique fixed point in M . Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.
文摘The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.
文摘Making use of Newton’s classical shell theorem, the Schwarzschild metric is modified. This removes the singularity at r = 0 for a standard object (not a black hole). It is demonstrated how general relativity evidently leads to quantization of space-time. Both classical and quantum mechanical limits on density give the same result. Based on Planck’s length and the assumption that density must have an upper limit, we conclude that the lower limit of the classical gravitation theory by Einstein is related to the Planck length, which is a quantum phenomenon posed by dimensional analysis of the universal constants. The Ricci tensor is considered under extreme densities (where Kretschmann invariant = 0) and a solution is considered for both outside and inside the object. Therefore, classical relativity and the relationship between the universal constants lead to quantization of space. A gedanken experiment of light passing through an extremely dense object is considered, which will allow for evaluation of the theory.
文摘A novel decentralized PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output (MIMO)dynamic processes. The first key feature of the design procedure is that a whole MIMO control system is decomposed into multiple control loops, therefore the sub-controllers can be efficiently flexibly designed in parallel prototype.The second key feature is that the decentralized controller has equivalency to those designed by backstepping approach. As a complementary support to the design procedure, the sufficient condition of the whole closed-loop system stability is analyzed via the small gain theorem and it can be proven that the process tracking performance is improved. The simulation results of the Shell benchmark control problem are provided to verify the effectiveness and practicality of the proposed decentralized PID control.
