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

Author(s):  
Qi Ding ◽  
Hongqing Zhang
2017 ◽  
Vol 9 (2) ◽  
pp. 32
Author(s):  
William W. S. Chen

 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.  


2019 ◽  
Vol 12 (2) ◽  
pp. 519-532
Author(s):  
Minoungou Youssouf ◽  
Bagayogo Moussa ◽  
Youssouf Pare

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.


2013 ◽  
Vol 5 (1) ◽  
pp. 89-93
Author(s):  
V.I. Myronyk ◽  
V.V. Mykhaylyuk

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


1867 ◽  
Vol 15 ◽  
pp. 306-310

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 .


1978 ◽  
Vol 1 (3) ◽  
pp. 257-267
Author(s):  
Lloyd K. Williams

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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