m-Hilbert Polynomial and Arbitrariness of the General Solution of Partial Differential Equations

2009 ◽  
Author(s):  
Qi Ding ◽  
Hongqing Zhang
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Differential Equations ◽  
Hilbert Polynomial ◽  
Partial Differential

scholarly journals On Finding Geodesic Equation of Student T Distribution

2017 ◽  
Vol 9 (2) ◽  
pp. 32
Author(s):  
William W. S. Chen
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Differential Equations ◽  
Geodesic Equation ◽  
Partial Differential ◽  
Student T Distribution ◽  
Darboux Theorem ◽  
T Distribution ◽  
Two Parameter

 Student t distribution has been widely applied in the course of statistics. In this paper, we focus on finding a geodesic equation of the two parameter student t distributions. To find this equation, we applied both the well-known Darboux Theorem and a triply of partial differential equations taken from Struik D.J. (Struik, D.J., 1961) or Grey A (Grey A., 1993), As expected, the two different approaches reach the same type of results. The solution proposed in this paper could be used as a general solution of the geodesic equation for the student t distribution.  

scholarly journals General Solution of Linear Partial Differential Equations Modeling Homogeneous diffusion-convection-reaction Problems with Cauchy Initial Condition

2019 ◽  
Vol 12 (2) ◽  
pp. 519-532
Author(s):  
Minoungou Youssouf ◽  
Bagayogo Moussa ◽  
Youssouf Pare
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Differential Equations ◽  
Numerical Method ◽  
Initial Condition ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Diffusion Convection

In this paper, we propose the general solution of di¤usion-convection-reaction homogeneous problems with condition initial of Cauchy, using theSBA numerical method. This method is based on the combination of theAdomian Decompositional Method(ADM), the successive approximationsmethod and the Picard principle.

scholarly journals First-order linear partial differential equations in the class of separately differentiable functions

2013 ◽  
Vol 5 (1) ◽  
pp. 89-93
Author(s):  
V.I. Myronyk ◽  
V.V. Mykhaylyuk
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Differential Equations ◽  
Partial Differential ◽  
Order Linear ◽  
First Order ◽  
Linear Partial Differential Equations ◽  
Differentiable Functions

It is obtained a general solution of first-order linear partial differential equations in the class of separately differentiable functions.

scholarly journals I. On Poisson’s solution of the accurate equations applicable to the transmission of sound through a cylindrical tube; and on the general solution of partial differential equations

1867 ◽  
Vol 15 ◽  
pp. 306-310
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Differential Equations ◽  
Cylindrical Tube ◽  
Partial Differential

The pair of equations ± v a = log 2 ρ/D, v = ϕ { v ± a ) t — q }, which constitute Poisson’s solution of the accurate equations applying to the transmission of sound through a cylindrical tube derived by La Grange method, have long attracted the attention of mathematicians. For La Grange’s equations we may substitute the following, viz.— dv / dt + a 2 /D d ρ/ dx =0, dv / dx + D/ρ 2 d ρ/ dt =0. } . . . . . . (A) The first of these is obtained from the equation of the Encyc. Met. (Art. “Sound”), by putting v for dy / dt and D/ρ for dy / dx .

scholarly journals Nonlinear differential equations and algebraic systems

1978 ◽  
Vol 1 (3) ◽  
pp. 257-267
Author(s):  
Lloyd K. Williams
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Asymptotic Series ◽  
Partial Differential ◽  
First Order ◽  
Variation Of Parameters ◽  
Familiar Expression ◽  
First Order Differential Equations

In this paper we obtain the general solution of scalar, first-order differential equations. The method is variation of parameters with asymptotic series and the theory of partial differential equations.The result gives us a form like a differential quotient requiring only that a limit be taken. Like the familiar expression for the solution of linear, first order, ordinary equations, it is the same in all cases.

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