Ordinary differential equation (ODE), in mathematics, an equation relating a function f of one variable to its derivatives. (The adjective ordinary here refers to those differential equations involving one variable, as distinguished from such equations i
In these,ystands for the function, and eithertorxis the independent variable. The symbolskandmare used here to stand for specific constants. More From Britannica analysis: Newton and differential equations Whichever the type may be, a differential equation is said to be of thenth order if it ...
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To format the A into subscript notation, highlight the A by clicking and dragging the cursor. When you release the mouse button, the A will be highlighted. With the A highlighted, click on the subscript icon, , in the toolbar. The A should now be properly formatted. Note: this alternat...
For the rest of this paper, we assume that our stochastic matrix of interest P is 0/1-valued, meaning that it represents a (single-valued) function \(f:{\cal{X}} \to {\cal{X}}\). Below, in a slight abuse of previous notation, we will use Cspace(f) and Ctime(f, k) to re...
By this example it is also easy to see that the cardinality of the set {R | Z ⊆ R ⊆ R and R is a ring} is equal to the cardinality of the continuum. 5. A function solutions of Eq. (1) which has infinite range In this section we prove the following Theorem: Theorem 5.1....
The starting point of the Boltzmann analysis (but first Maxwell went in the same direction) is to renounce to study the behavior of a gas in terms of the detailed motion of the molecules which constitute it, because of their huge number. It is preferable to investigate a function f(x, ν...
where fp is the body force applied at the point x = x0, and δDx¯ is the Dirac delta function. It can be shown applying the Fourier transformation to Eq. (225) that the velocity field produced by this force in an unbounded fluid is given by the expression [2] (226)Vx=G⋅fp...
Using this code, a moderate laptop can, for example, calculate the coincidence limit [a7(x, x)] and V(x, x¹) to order (σa)20 in a matter of minutes. Results may be output in either a compact notation or in XTENSOR form. In a second application of the approach, we present ...
with a local particle number densityρ(r, t) depending on positionrand timet, a mobility parameterM, an (overdamped) free-energy densityfo(ρ) typically assumed to be a fourth-order polynomial, the notation\({f}_{{{\rm{o}}}^{{\prime} }={\partial }_{\rho }\,{f}_{{{\rm{...