This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and order...This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.展开更多
Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for ...Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,展开更多
By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing...By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.展开更多
In this work, the author applied the universal gauge field theory and Noether theorem to prove that universality exists for the Lorentz and Levi-Civita law of conservation of energy momentum tensor density. We also fo...In this work, the author applied the universal gauge field theory and Noether theorem to prove that universality exists for the Lorentz and Levi-Civita law of conservation of energy momentum tensor density. We also found that this conservation law has profound implications in physics. For example, based on this law, one can explore the origin of the matter field, and propose a new view about what is “dark energy” and what is “dark matter”.展开更多
This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having...This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having a long wavelength, being longitudinal and extraordinarily penetrating. In accordance with the principle of least action, the Lagrangian of the electroscalar field and the tensor of energy-moment are determined using the variation the potential and coordinates. The equation of motion the charged particle in electroscalar field is determined and the energy of particle has the negative sign with respect to the mechanical energy of particle and the energy of electromagnetic field. So, this is decreasing the electrical potential of particle during the propagation. The electroscalar energy of charged particle and field’s force acting on the particle during their motion change the particle’s electrical status which, in its turn, may trigger the transition of the particle into a compound state during interaction with any object. Due to the continuity this process can lead the particle to the state which enters into a compound state with a negative energy for a different particle’s velocity. This state is the physical vacuum’s state. Analysis of the solar spectrum demonstrates that scattering and absorption of electroscalar wave go on the cavities of solids. The spreading out of electroscalar field obeys to the law of plane wave and the transfer the energy and information can occur in vacuum and any medium.展开更多
A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator p（...A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator p（t） is derived and the solution of f for the damping and gaining processes are studied separately. Our approach is direct and the result is concise since it is not necessary for us to know the Kraus operators in advance.展开更多
One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free...One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and gravimagnetic charges and currents and generated by them EGM-field. By using generalized functions theory the fundamental and regular solutions of this system are determined and some of them are considered (spinors, plane waves, shock EGM-waves and others). The properties of these solutions are investigated.展开更多
Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether＇s theorem, a unified master balance law and six physically possible balance equations for micropolar co...Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether＇s theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energymomentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally, some existing results are reduced immediately as special cases.展开更多
The paper deals with magnetic field mapping outside a finite length solenoid electromagnet, by an in-house designed and calibrated inductive pick-up or search coil. The search coil is calibrated in a unique methodolog...The paper deals with magnetic field mapping outside a finite length solenoid electromagnet, by an in-house designed and calibrated inductive pick-up or search coil. The search coil is calibrated in a unique methodology based on the azimuthal magnetic field component generated by a straight wire. This unique calibration technique helps us to avoid additional circuitry to integrate the signal obtained from search coil. The methodology proves advantageous in diffusion, implosion studies where the signal frequency changes with dimension and material of experimental job-piece (hollow metal tube). Remedial measures have been taken to avoid electrostatic capacitive pick-up (which eventually exacerbates with integration) keeping measurement simple and accurate. The experimentally measured field values have also been compared with electromagnetic field results obtained from mathematical calculations and finite element based simulations. Two different mathematical approaches have been demonstrated for field computation based on Biot-Savart Law. Both the methods have taken into account the exact geometry of the solenoid, including the inter-turn gaps. The methods use appropriate combination of closed-form mathematical expression and numerical integration techniques and are capable of determining all the vector components of magnetic field anywhere around the finite length solenoid. The mathematical computations are equally significant contributions in the paper especially because exact determination of magnetic fields outside finite length solenoids has not been discussed in sufficient specific details in already existing literature. The mathematical computations, finite element simulations and experimental verification together provide a holistic solution to magnetic field determination problems in pulse power applications that have not been discussed in available literature or books in specific details.展开更多
The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the for...The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.展开更多
This article originates from the observation that field lines are drawn using distinctive rules in magnetic field and electrostatic fields. It aims at reconciliating the definitions of these fields and thus reaching a...This article originates from the observation that field lines are drawn using distinctive rules in magnetic field and electrostatic fields. It aims at reconciliating the definitions of these fields and thus reaching a consensus on the interpretation of field lines. Our unified field definition combines three orthogonal vectors and a unique scalar value. Field lines are then defined as isovalue lines of the scalar value, rendering it simpler to interpret in both field types. Specific to our field definition is the use of square root of vector’s cross product so that all vectors have the same physical unit. This enhanced field definition also enables a more efficient calculation of Biot-Savart law. This article is the first of a series allowing the drawing of isovalue contour lines.展开更多
We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also ...We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also show that the density operator of SCF can be viewed as a generating field of the squeezed number state.展开更多
In “<i>A Self-linking Field Formalism</i>” I establish a self-dual field structure with higher order self-induced symmetries that reinforce the first-order dynamics. The structure was derived from Gauss-...In “<i>A Self-linking Field Formalism</i>” I establish a self-dual field structure with higher order self-induced symmetries that reinforce the first-order dynamics. The structure was derived from Gauss-linking integrals in R<sup>3</sup> based on the Biot-Savart law and Ampere’s law applied to Heaviside’s equations, derived in strength-independent fashion in “<i>Primordial Principle of Self-Interaction</i>”. The derivation involves Geometric Calculus, topology, and field equations. My goal in this paper is to derive the simplest solution of a self-stabilized solitonic structure and discuss this model of a neutrino.展开更多
文摘This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.
基金Supported by National Basic Research Program of China(973 Program No.2007CBS14903)National Science Foundation of China(70671069)
文摘Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,
基金National Natural Science Foundation of China! (No. 19701O11) Foundation of "151 talent project" of Zhejiang provience.
文摘By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.
文摘In this work, the author applied the universal gauge field theory and Noether theorem to prove that universality exists for the Lorentz and Levi-Civita law of conservation of energy momentum tensor density. We also found that this conservation law has profound implications in physics. For example, based on this law, one can explore the origin of the matter field, and propose a new view about what is “dark energy” and what is “dark matter”.
文摘This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having a long wavelength, being longitudinal and extraordinarily penetrating. In accordance with the principle of least action, the Lagrangian of the electroscalar field and the tensor of energy-moment are determined using the variation the potential and coordinates. The equation of motion the charged particle in electroscalar field is determined and the energy of particle has the negative sign with respect to the mechanical energy of particle and the energy of electromagnetic field. So, this is decreasing the electrical potential of particle during the propagation. The electroscalar energy of charged particle and field’s force acting on the particle during their motion change the particle’s electrical status which, in its turn, may trigger the transition of the particle into a compound state during interaction with any object. Due to the continuity this process can lead the particle to the state which enters into a compound state with a negative energy for a different particle’s velocity. This state is the physical vacuum’s state. Analysis of the solar spectrum demonstrates that scattering and absorption of electroscalar wave go on the cavities of solids. The spreading out of electroscalar field obeys to the law of plane wave and the transfer the energy and information can occur in vacuum and any medium.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61141007,11047133,and 11175113)the Natural Science Foundation of Jiangxi Province of China (Grant Nos. 2010GQS0080 and 2010GQW0027)+1 种基金the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ11339)the Sponsored Program for Cultivating Youths of Outstanding Ability in Jiangxi Normal University
文摘A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator p（t） is derived and the solution of f for the damping and gaining processes are studied separately. Our approach is direct and the result is concise since it is not necessary for us to know the Kraus operators in advance.
文摘One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and gravimagnetic charges and currents and generated by them EGM-field. By using generalized functions theory the fundamental and regular solutions of this system are determined and some of them are considered (spinors, plane waves, shock EGM-waves and others). The properties of these solutions are investigated.
基金Project supported by the National Natural Science Foundation of China (Nos.10072024 and 10472041)
文摘Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether＇s theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energymomentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally, some existing results are reduced immediately as special cases.
文摘The paper deals with magnetic field mapping outside a finite length solenoid electromagnet, by an in-house designed and calibrated inductive pick-up or search coil. The search coil is calibrated in a unique methodology based on the azimuthal magnetic field component generated by a straight wire. This unique calibration technique helps us to avoid additional circuitry to integrate the signal obtained from search coil. The methodology proves advantageous in diffusion, implosion studies where the signal frequency changes with dimension and material of experimental job-piece (hollow metal tube). Remedial measures have been taken to avoid electrostatic capacitive pick-up (which eventually exacerbates with integration) keeping measurement simple and accurate. The experimentally measured field values have also been compared with electromagnetic field results obtained from mathematical calculations and finite element based simulations. Two different mathematical approaches have been demonstrated for field computation based on Biot-Savart Law. Both the methods have taken into account the exact geometry of the solenoid, including the inter-turn gaps. The methods use appropriate combination of closed-form mathematical expression and numerical integration techniques and are capable of determining all the vector components of magnetic field anywhere around the finite length solenoid. The mathematical computations are equally significant contributions in the paper especially because exact determination of magnetic fields outside finite length solenoids has not been discussed in sufficient specific details in already existing literature. The mathematical computations, finite element simulations and experimental verification together provide a holistic solution to magnetic field determination problems in pulse power applications that have not been discussed in available literature or books in specific details.
文摘The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.
文摘This article originates from the observation that field lines are drawn using distinctive rules in magnetic field and electrostatic fields. It aims at reconciliating the definitions of these fields and thus reaching a consensus on the interpretation of field lines. Our unified field definition combines three orthogonal vectors and a unique scalar value. Field lines are then defined as isovalue lines of the scalar value, rendering it simpler to interpret in both field types. Specific to our field definition is the use of square root of vector’s cross product so that all vectors have the same physical unit. This enhanced field definition also enables a more efficient calculation of Biot-Savart law. This article is the first of a series allowing the drawing of isovalue contour lines.
基金Project supported by the National Natural Science Foundation of China(Grant No.10574647)the Natural Science Foundation of Shandong Province,China(Grant No.Y2008A16)the University Experimental Technology Foundation of Shandong Province of China(Grant No.S04W138)
文摘We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also show that the density operator of SCF can be viewed as a generating field of the squeezed number state.
文摘In “<i>A Self-linking Field Formalism</i>” I establish a self-dual field structure with higher order self-induced symmetries that reinforce the first-order dynamics. The structure was derived from Gauss-linking integrals in R<sup>3</sup> based on the Biot-Savart law and Ampere’s law applied to Heaviside’s equations, derived in strength-independent fashion in “<i>Primordial Principle of Self-Interaction</i>”. The derivation involves Geometric Calculus, topology, and field equations. My goal in this paper is to derive the simplest solution of a self-stabilized solitonic structure and discuss this model of a neutrino.
