The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group...The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.展开更多
In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a ...In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.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
文摘The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.
文摘In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.
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.
