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.

Envelopes of families of framed surfaces and singular solutions of first-order partial differential equations

2020 ◽  
pp. 1-28
Author(s):  
Masatomo Takahashi ◽  
Haiou Yu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Singular Solutions ◽  
Uniqueness Theorems ◽  
Singular Surfaces ◽  
Partial Differential ◽  
First Order ◽  
Existence Conditions ◽  
Two Parameter

In order to investigate envelopes for singular surfaces, we introduce one- and two-parameter families of framed surfaces and the basic invariants, respectively. By using the basic invariants, the existence and uniqueness theorems of one- and two-parameter families of framed surfaces are given. Then we define envelopes of one- and two-parameter families of framed surfaces and give the existence conditions of envelopes which are called envelope theorems. As an application of the envelope theorems, we show that the projections of singular solutions of completely integrable first-order partial differential equations are envelopes.

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 .

An eigenfunction expansion associated with a two-parameter system of differential equations. I

1981 ◽  
Vol 89 (1-2) ◽  
pp. 143-155 ◽  
Author(s):  
M. Faierman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Uniform Convergence ◽  
Ordinary Differential Equations ◽  
Eigenfunction Expansion ◽  
Second Order ◽  
System Of Differential Equations ◽  
Parameter System ◽  
Partial Differential ◽  
Two Parameter

SynopsisTechniques from the theory of partial differential equations are employed to prove the uniform convergence of the eigenfunction expansion associated with a left definite two-parameter system of ordinary differential equations of the second order.

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