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
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.
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
Since there are some problems in the previous cam of deep-fertilization liquid fertilizer applicator,such as poor precision and low-fertilization performance,a method of the contour line of a cam was proposed based on...Since there are some problems in the previous cam of deep-fertilization liquid fertilizer applicator,such as poor precision and low-fertilization performance,a method of the contour line of a cam was proposed based on Matlab GUI development platform.Bernoulli’equation between the liquid fertilizer and the pressure valve of the fertilizer-spraying needle was founded.Moreover,the motion angles of a rise travel and return travel were corrected and the corresponding parameters of the contour line of the cam were obtained.Equations of cam moving from rise travel to return travel were derived according to the simple harmonic motion.In addition,3D model of cam was established by applying the Pro/E software and the rationality of the cam design was verified.The static analysis of the cam was carried out under working conditions and the corresponding dynamics analysis was performed based on D’Alembert’s principle.And then relationships between the binding force and the drag torque were obtained.A bench test indicates that when the pressure of a hydraulic pump is 0.5 MPa and the velocity of a output shaft is 50 r/min,the average consumption of the fertilizer is 19.7 mL for each measurement,which meets the corresponding agronomic requirement,i.e.20 mL.When the rotation angle of the cam is 8.6°and the rise displacement of a plunger is 0.84 mm,the mouth of the fertilizer-spraying needle sprayed liquid fertilizer as soon as it got into the soil and stopped spraying as soon as it got out of the soil.The results show that the designed contour line of the cam meets the requirement,that is,the mouth of the fertilizer-spraying needle should spray liquid fertilizer as soon as it gets into the soil and stop spraying as soon as it gets out of the soil,which meets the agronomic requirements,that is,fertilizer should be sprayed deeply and precisely.And this study lays a theoretical foundation for designing the cam of intermittent type distributor and provides relevant parameters.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.
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.
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.
基金This research was supported by the National Natural Science Foundation of China(Grant No.51675093)“Young Talents”Project of Northeast Agricultural University(Grant No.18QC19).
文摘Since there are some problems in the previous cam of deep-fertilization liquid fertilizer applicator,such as poor precision and low-fertilization performance,a method of the contour line of a cam was proposed based on Matlab GUI development platform.Bernoulli’equation between the liquid fertilizer and the pressure valve of the fertilizer-spraying needle was founded.Moreover,the motion angles of a rise travel and return travel were corrected and the corresponding parameters of the contour line of the cam were obtained.Equations of cam moving from rise travel to return travel were derived according to the simple harmonic motion.In addition,3D model of cam was established by applying the Pro/E software and the rationality of the cam design was verified.The static analysis of the cam was carried out under working conditions and the corresponding dynamics analysis was performed based on D’Alembert’s principle.And then relationships between the binding force and the drag torque were obtained.A bench test indicates that when the pressure of a hydraulic pump is 0.5 MPa and the velocity of a output shaft is 50 r/min,the average consumption of the fertilizer is 19.7 mL for each measurement,which meets the corresponding agronomic requirement,i.e.20 mL.When the rotation angle of the cam is 8.6°and the rise displacement of a plunger is 0.84 mm,the mouth of the fertilizer-spraying needle sprayed liquid fertilizer as soon as it got into the soil and stopped spraying as soon as it got out of the soil.The results show that the designed contour line of the cam meets the requirement,that is,the mouth of the fertilizer-spraying needle should spray liquid fertilizer as soon as it gets into the soil and stop spraying as soon as it gets out of the soil,which meets the agronomic requirements,that is,fertilizer should be sprayed deeply and precisely.And this study lays a theoretical foundation for designing the cam of intermittent type distributor and provides relevant parameters.
