The free variable " x " 0 corresponds to a source vertex " v " 0, thus having no defining equation.
22.
When the coefficients depends only on present and past values of " X ", the defining equation is called a stochastic delay differential equation.
23.
The solution of the telegrapher's equations can be expressed as an ABCD type " two-port network " with the following defining equations
24.
For more advanced treatments the equation may have to be written in an equivalent but alternative form using other defining equations for the definition to be useful.
25.
In order for it to become a proper definition both the quantity and the defining equation, including the value of any constant factor, must be specified.
26.
By the intermediate value theorem, there exists an intermediate t _ r with f ( t _ r ) = 0, the defining equation of the retarded time.
27.
Like PRA, ERA can be defined in an entirely logic-free manner, with just the rules of substitution and induction, and defining equations for all elementary recursive functions.
28.
Shock-wave data for the compressibilities of Cu, Mo, Pd and Ag were available at this time and could be used to define equations of states up to Mbar pressure.
29.
""'Definitions vs . theorems " "': There is a very important difference between defining equations and general or derived results, theorems or laws.
30.
Write x = \ rho \ cos \ theta, y = \ rho \ sin \ theta in the defining equation and solve for \ rho as a function of \ theta.
