scholarly journals Gradient Structures Associated with a Polynomial Differential Equation

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 535 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Differential Equation ◽  
Order System ◽  
Mathematical Framework ◽  
Special Significance ◽  
First Order ◽  
System Method ◽  
Polynomial Differential Equation ◽  
The Cauchy Problem ◽  
Finite Set ◽  
Kernel Representation

In this paper, by using the characteristic system method, the kernel of a polynomial differential equation involving a derivation in R n is described by solving the Cauchy Problem for the corresponding first order system of PDEs. Moreover, the kernel representation has a special significance on the space of solutions to the corresponding system of PDEs. As very important applications, it has been established that the mathematical framework developed in this work can be used for the study of some second-order PDEs involving a finite set of derivations.

Corrosion Margins for Redundant Ship Structures

2018 ◽  
Author(s):  
Yordan Garbatov ◽  
C. Guedes Soares
Keyword(s):  
Differential Equation ◽  
Degradation Process ◽  
Step Function ◽  
Order System ◽  
Safety Factors ◽  
Ship Structures ◽  
Degradation Model ◽  
Corrosion Depth ◽  
First Order ◽  
Partial Safety Factors

The work presented here analyses the structural corrosion degradation of two sets of corrosion depth measurements collected with a one-decade difference. The corrosion degradation process is associated to a first order system, subjected to a sudden disturbance, where a step function is used as an input to define the solution of the differential equation of this system leads to the exponential corrosion degradation model as developed earlier. Corrosion margins of redundant ship structures with serious consequences of failure are derived and several conclusions related to the new trend in the ageing structures are presented and discussed. Partial safety factors with respect to the corrosion environment and corrosion margins are developed that can be used in the design, avoiding a complex probabilistic analysis.

scholarly journals Differential Equation in a Banach Space Multiplicatively Perturbed by Random Noise

2017 ◽  
Vol 63 (4) ◽  
pp. 599-614
Author(s):  
V G Zadorozhniy ◽  
M A Konovalova
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Random Noise ◽  
Random Coefficients ◽  
First Order ◽  
The Cauchy Problem ◽  
Moment Functions ◽  
Nonhomogeneous Differential Equation ◽  
Variational Derivatives ◽  
The Moment

We consider the problem of finding the moment functions of the solution of the Cauchy problem for a first-order linear nonhomogeneous differential equation with random coefficients in a Banach space. The problem is reduced to the initial problem for a nonrandom differential equation with ordinary and variational derivatives. We obtain explicit formula for the mathematical expectation and the second-order mixed moment functions for the solution of the equation.

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