The Poynting vector includes time-independent contributions which, since they represent photons of zero frequency, need to be absent;this removal resolves several paradoxes that arise when they are left in place;furth...The Poynting vector includes time-independent contributions which, since they represent photons of zero frequency, need to be absent;this removal resolves several paradoxes that arise when they are left in place;furthermore, magnetic monopoles, if they existed, would be accompanied by a Lenz’s law that defies conservation of energy suggesting that magnetic charges might not be found in Nature.展开更多
We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using the...We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using these inequalities and laws of large numbers for two parameter vector valued martingales.展开更多
Harmonic analysis, the traditional tidal forecasting method, cannot take into account the impact of noncyclical factors, and is also based on the BP neural network tidal prediction model which is easily limited by the...Harmonic analysis, the traditional tidal forecasting method, cannot take into account the impact of noncyclical factors, and is also based on the BP neural network tidal prediction model which is easily limited by the amount of data. According to the movement of celestial bodies, and considering the insufficient tidal characteristics of historical data which are impacted by the nonperiodic weather, a tidal prediction method is designed based on support vector machine （SVM） to carry out the simulation experiment by using tidal data from Xiamen Tide Gauge, Luchaogang Tide Gauge and Weifang Tide Gauge individually. And the results show that the model satisfactorily carries out the tide prediction which is influenced by noncyclical factors. At the same time, it also proves that the proposed prediction method, which when compared with harmonic analysis method and the BP neural network method, has faster modeling speed, higher prediction precision and stronger generalization ability.展开更多
The current approach of a system of two bodies that interact through a gravitational force goes beyond the familiar expositions [1-3] and derives some interesting features and laws that are overlooked. A new expressio...The current approach of a system of two bodies that interact through a gravitational force goes beyond the familiar expositions [1-3] and derives some interesting features and laws that are overlooked. A new expression for the angular momentum of a system in terms of the angular momenta of its parts is deduced. It is shown that the characteristics of the relative motion depend on the system’s total mass, whereas the characteristics of the individual motions depend on the masses of the two bodies. The reduced energy and angular momentum densities are constants of motion that do not depend on the distribution of the total mass between the two bodies;whereas the energy may vary in absolute value from an infinitesimal to a maximum value which occurs when the two bodies are of equal masses. In correspondence with infinite possible ways to describe the absolute rotational positioning of a two body system, an infinite set of Laplace-Runge-Lenz vectors (LRL) are constructed, all fixing a unique orientation of the orbit relative to the fixed stars. The common expression of LRV vector is an approximation of the actual one. The conditions for nested and intersecting individual orbits of the two bodies are specified. As far as we know, and apart from the law of periods, the laws of equivalent orbits concerning their associated periods, areal velocities, angular velocities, velocities, energies, as well as, the law of total angular momentum, were never considered before.展开更多
We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characteriza...We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characterizations. The latter is employed to obtain the laws of equivalent orbits, which by definition have the same eccentricity and orbit’s parameter [1]. These laws relate the values of the same physical observables on two equivalent orbits to the corresponding total mass;they include the laws of velocity, angular velocity, radial velocity, areal velocity, acceleration, period, energy and angular momentum. Regardless of the share of the two bodies of a fixed total mass, the same relative orbit occurs for the same initial conditions. Moreover, the same orbit can be traced by different total masses but with different relative velocities. The concept of a gravitational field generated by a set of masses is shown to be meaningful only when the center of mass is not changed by the test mass. The associated concept of the “nothing”, which is an infinitesimal mass that allows for the property just mentioned to be fulfilled, is introduced and its orbits are determined. The perturbation of the nothing orbits due to its replacement by a finite mass is determined. It is proved that such a replacement can have a qualitative effect resulting in a “phase transition” of an orbit from unbound to bound, and that the nothing’s circular orbits cannot be occupied by any material body. The Galileo law of free fall, on which the equivalence principle hinges and which is exact only for “nothing-like” falling objects, is revised to determine the duration of free fall of a body of an arbitrary mass. The wholeness of Newton’s laws and the associated concept of force as an interaction are highlighted, and some contradictions between the Newtonian laws of equivalent Kepler’s orbits and the general relativistic predictions are discussed. It is demonstrated that Newton’s law of gravitation is not an approximation of Einstein field Equations even in the case of a static weak field. However, both theories have a common limit corresponding to the case in which the alien concept of a field can be incorporated in the Newtonian theory. We also show that the relative velocity’s hodograph [2-4], the alternative Laplace-Runge-Lenz (LRL) vector derived by Hamilton [4-6], as well as an infinite set of LRL vectors, result all from one vector. The hodograph is a proper circular arc for hyperbolic motion, a circle less a point for parabolic motion, and a full circle for bound motion.展开更多
Let {X, X_n, n ≥ 1} be a sequence of i.i.d. random vectors with EX =（0,..., 0）_（m×1） and Cov（X, X） = σ~2 Ⅰ_m, and set S_n =∑_（i=1）~n X_i, n ≥ 1. For every d 〉 0 and a_n =o（（log log n）^（-d））, t...Let {X, X_n, n ≥ 1} be a sequence of i.i.d. random vectors with EX =（0,..., 0）_（m×1） and Cov（X, X） = σ~2 Ⅰ_m, and set S_n =∑_（i=1）~n X_i, n ≥ 1. For every d 〉 0 and a_n =o（（log log n）^（-d））, the article deals with the precise rates in the genenralized law of the iterated logarithm for a kind of weighted infinite series of P（｜S_n｜ ≥（ε ＋ a_n）σn^（1/2）（log log n）~d）.展开更多
文摘The Poynting vector includes time-independent contributions which, since they represent photons of zero frequency, need to be absent;this removal resolves several paradoxes that arise when they are left in place;furthermore, magnetic monopoles, if they existed, would be accompanied by a Lenz’s law that defies conservation of energy suggesting that magnetic charges might not be found in Nature.
文摘We obtained a number of inequalities and laws of large numbers for two parameter vector valued martingales.In the other direction we characterized p smoothness and q convexity of Banach spaces by using these inequalities and laws of large numbers for two parameter vector valued martingales.
基金The Shanghai Committee of Science and Technology of China under contract No. 10510502800the Graduate Student Education Innovation Program Foundation of Shanghai Municipal Education Commission of Chinathe National Key Science Foundation Research "973" Project of the Ministry of Science and Technology of China under contract No. 2012CB316200
文摘Harmonic analysis, the traditional tidal forecasting method, cannot take into account the impact of noncyclical factors, and is also based on the BP neural network tidal prediction model which is easily limited by the amount of data. According to the movement of celestial bodies, and considering the insufficient tidal characteristics of historical data which are impacted by the nonperiodic weather, a tidal prediction method is designed based on support vector machine （SVM） to carry out the simulation experiment by using tidal data from Xiamen Tide Gauge, Luchaogang Tide Gauge and Weifang Tide Gauge individually. And the results show that the model satisfactorily carries out the tide prediction which is influenced by noncyclical factors. At the same time, it also proves that the proposed prediction method, which when compared with harmonic analysis method and the BP neural network method, has faster modeling speed, higher prediction precision and stronger generalization ability.
文摘The current approach of a system of two bodies that interact through a gravitational force goes beyond the familiar expositions [1-3] and derives some interesting features and laws that are overlooked. A new expression for the angular momentum of a system in terms of the angular momenta of its parts is deduced. It is shown that the characteristics of the relative motion depend on the system’s total mass, whereas the characteristics of the individual motions depend on the masses of the two bodies. The reduced energy and angular momentum densities are constants of motion that do not depend on the distribution of the total mass between the two bodies;whereas the energy may vary in absolute value from an infinitesimal to a maximum value which occurs when the two bodies are of equal masses. In correspondence with infinite possible ways to describe the absolute rotational positioning of a two body system, an infinite set of Laplace-Runge-Lenz vectors (LRL) are constructed, all fixing a unique orientation of the orbit relative to the fixed stars. The common expression of LRV vector is an approximation of the actual one. The conditions for nested and intersecting individual orbits of the two bodies are specified. As far as we know, and apart from the law of periods, the laws of equivalent orbits concerning their associated periods, areal velocities, angular velocities, velocities, energies, as well as, the law of total angular momentum, were never considered before.
文摘We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characterizations. The latter is employed to obtain the laws of equivalent orbits, which by definition have the same eccentricity and orbit’s parameter [1]. These laws relate the values of the same physical observables on two equivalent orbits to the corresponding total mass;they include the laws of velocity, angular velocity, radial velocity, areal velocity, acceleration, period, energy and angular momentum. Regardless of the share of the two bodies of a fixed total mass, the same relative orbit occurs for the same initial conditions. Moreover, the same orbit can be traced by different total masses but with different relative velocities. The concept of a gravitational field generated by a set of masses is shown to be meaningful only when the center of mass is not changed by the test mass. The associated concept of the “nothing”, which is an infinitesimal mass that allows for the property just mentioned to be fulfilled, is introduced and its orbits are determined. The perturbation of the nothing orbits due to its replacement by a finite mass is determined. It is proved that such a replacement can have a qualitative effect resulting in a “phase transition” of an orbit from unbound to bound, and that the nothing’s circular orbits cannot be occupied by any material body. The Galileo law of free fall, on which the equivalence principle hinges and which is exact only for “nothing-like” falling objects, is revised to determine the duration of free fall of a body of an arbitrary mass. The wholeness of Newton’s laws and the associated concept of force as an interaction are highlighted, and some contradictions between the Newtonian laws of equivalent Kepler’s orbits and the general relativistic predictions are discussed. It is demonstrated that Newton’s law of gravitation is not an approximation of Einstein field Equations even in the case of a static weak field. However, both theories have a common limit corresponding to the case in which the alien concept of a field can be incorporated in the Newtonian theory. We also show that the relative velocity’s hodograph [2-4], the alternative Laplace-Runge-Lenz (LRL) vector derived by Hamilton [4-6], as well as an infinite set of LRL vectors, result all from one vector. The hodograph is a proper circular arc for hyperbolic motion, a circle less a point for parabolic motion, and a full circle for bound motion.
基金Supported by the National Natural Science Foundation of China(Grant No.61662037)the Scientific Program of Department of Education of Jiangxi Province(Grant Nos.GJJ150894GJJ150905)
文摘Let {X, X_n, n ≥ 1} be a sequence of i.i.d. random vectors with EX =（0,..., 0）_（m×1） and Cov（X, X） = σ~2 Ⅰ_m, and set S_n =∑_（i=1）~n X_i, n ≥ 1. For every d 〉 0 and a_n =o（（log log n）^（-d））, the article deals with the precise rates in the genenralized law of the iterated logarithm for a kind of weighted infinite series of P（｜S_n｜ ≥（ε ＋ a_n）σn^（1/2）（log log n）~d）.
