Sentence examples for first kind at from inspiring English sources

Let (x:R^rightarrow R^) be a piecewise continuous function at most with discontinuities of the first kind at the points (tau_{i}).

where and are continuous for and they have a discontinuity of the first kind at the points where they are continuous from the left.

Finally, since a ≠ 0, Eq. (1a) has a singularity of the first kind at the time variable t = 0 because ∫ 0 T 1 t d t = ∞, ∫ 0 T 1 t 2 d t = ∞.

Groundwater flow directions were defined by setting suitable hydraulic heads as a boundary condition of the first kind at the model borders at the depth of the aquitards and the aquifer.

By we denote the set of all functions which are continuous for and continuous from the left with discontinuities of the first kind at Similarly, is the set of functions having derivative.

where is an matrix of functions; is an vector function; is the Banach space of real vector functions continuous for with discontinuities of the first kind at ; are -dimensional column constant vectors;.

Many people have been good at the first kind; few at the second kind, at least today.

We also invoke to the thermal boundary conditions of third kind at the outer boundaries of channel for the conjugate analysis of heat transfer.

An impossible world of the fourth kind, at which some contradiction is true but not everything is, provides a counterexample to ex falso quodlibet.

The heat transfer equations in the fluid and the finite thickness walls of the microchannel are solved analytically using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid wall interfaces.

Using an analytical scheme associated with the thermal boundary conditions of third kind at the outer boundaries of the channel, we bring out the alteration in the underlying thermal transport characteristics of heat as attributable to the nonlinear interactions between flow dynamics and viscous heating.