On reaching him, Heaviside
gave him water, dressed his wounds and then made his way back to his own position with a promise to return with help.
Sotiris Vardoulakis, (1,2,3) Keith Dear, (4) Shakoor Hajat, (3) Clare Heaviside
, (1) Bernd Eggen, (1) and Anthony J.
As a rule, the available analytical solutions are often based on a point force loading whose time dependencies are usually prescribed by Heaviside
or Dirac functions.
save] = standard uncertainty of savings F = cumulative probability density function f = a probability density function H = Heaviside
function HDD = heating degree days (base 65 [degrees]F) I = an identity matrix k = the number of elements in [beta] kWh = kilowatt-hours m = the number of parameters in the model [m.
2010), where r' represents the excitation type; it is 0 for a Dirac impulse or 1 for a Heaviside
Recently the rth powers of the Dirac distribution and the Heaviside
function for negative integers have been defined in  and , respectively.
where H(t) is Heaviside
unit step function function and [p.
New to this edition is coverage of the application of Laplace transforms, the Dirac delta function, and the Heaviside
function; the Cherkaev, Lurie, and Milton (CLM) stress invariance theorem; and recent developments in thermoelasticity.
where [alpha] > -1 and H is the Heaviside
The subsets A and K contain the nodes enriched with Heaviside
function H(x) or crack-tip functions [F.
The most common activation functions are the Heaviside
function, h, defined by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
They cover the fundamentals of laser pulse interaction with matter; the Heaviside
equation for hyperbolic transport processes; the Schrodinger-Newton hyperbolic equation for quantum thermal processes; the Proca equation for relativistic thermal processes; extreme light, lasetron, and Tesla SASE-FEL; beyond orthodox quantum theory; and the Proca equation for heavy photons and gravitons.