Using d'Alembert equation as the approximation of Einstein's equation, a solution is given in this paper to the time-dependent gravitational equation of the Earth in consideration of the Earth's features, ...Using d'Alembert equation as the approximation of Einstein's equation, a solution is given in this paper to the time-dependent gravitational equation of the Earth in consideration of the Earth's features, which describes the characteristics of pulsation of the Earth and the structures of spherical layers of its interior, thus providing a theoretical basis for establishing the idea of mantle pulsation.展开更多
In high voltage networks for the transport of electrical energy, lightning, a phenomenon as dangerous as it is impressive, with an easily recognizable form, can affect a power line by striking either a phase conductor...In high voltage networks for the transport of electrical energy, lightning, a phenomenon as dangerous as it is impressive, with an easily recognizable form, can affect a power line by striking either a phase conductor, a tower or a guard cable, thus causing more dangerous and constraining stresses on the lines for its proper operation. Thus, this article aims to analyze the behavior of a HV line during an atmospheric discharge and assess the spatial and temporal distribution of the lightning current wave. For this purpose, the generalities on the transmissible power in case of link without resistance and the modeling of the atmospheric surge propagation established on the basis of the theory of the lines with distributed constants implementing the wave equation known as the Alembert equation have been developed. Through this research, we are interested in the study of the space-time distribution of the lightning current wave in order to model the radiated electromagnetic field and to examine the influence of the atmospheric discharge induced overvoltage on the transportable power of a High Voltage AC Transmission line, for a good selective protection in order to illuminate the parasites. The 2D simulation based on engineering and “Transmission Line” models have been developed as well as the verification of the coherence of the different models, by comparing the fractal dimensions of the program results with those of the experimentally obtained figures.展开更多
A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
We find on a monoid M the complex-valued solutions f,g:M→C such that f is central and g is continuous of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)g(y),x,y∈M,whereσ:M→M is an involutive automorphism andτ:M...We find on a monoid M the complex-valued solutions f,g:M→C such that f is central and g is continuous of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)g(y),x,y∈M,whereσ:M→M is an involutive automorphism andτ:M→M is an involutive anti-automorphism.The solutions are described in terms of multiplicative functions,additive functions and characters of2-dimensional representations of M.展开更多
文摘Using d'Alembert equation as the approximation of Einstein's equation, a solution is given in this paper to the time-dependent gravitational equation of the Earth in consideration of the Earth's features, which describes the characteristics of pulsation of the Earth and the structures of spherical layers of its interior, thus providing a theoretical basis for establishing the idea of mantle pulsation.
文摘In high voltage networks for the transport of electrical energy, lightning, a phenomenon as dangerous as it is impressive, with an easily recognizable form, can affect a power line by striking either a phase conductor, a tower or a guard cable, thus causing more dangerous and constraining stresses on the lines for its proper operation. Thus, this article aims to analyze the behavior of a HV line during an atmospheric discharge and assess the spatial and temporal distribution of the lightning current wave. For this purpose, the generalities on the transmissible power in case of link without resistance and the modeling of the atmospheric surge propagation established on the basis of the theory of the lines with distributed constants implementing the wave equation known as the Alembert equation have been developed. Through this research, we are interested in the study of the space-time distribution of the lightning current wave in order to model the radiated electromagnetic field and to examine the influence of the atmospheric discharge induced overvoltage on the transportable power of a High Voltage AC Transmission line, for a good selective protection in order to illuminate the parasites. The 2D simulation based on engineering and “Transmission Line” models have been developed as well as the verification of the coherence of the different models, by comparing the fractal dimensions of the program results with those of the experimentally obtained figures.
基金Supported by the Natural Science Foundation of Hubei Province!(992P0 30 7) the National Natural Science Foun-dation of Chi
文摘A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
基金Supported by the National Science Foundation of China(Grant Nos.12061059 and 61763041)。
文摘We find on a monoid M the complex-valued solutions f,g:M→C such that f is central and g is continuous of the functional equation f(xσ(y))+f(τ(y)x)=2f(x)g(y),x,y∈M,whereσ:M→M is an involutive automorphism andτ:M→M is an involutive anti-automorphism.The solutions are described in terms of multiplicative functions,additive functions and characters of2-dimensional representations of M.
