Sentence examples for integral transformations from inspiring English sources

Many boundary value problems can be solved by means of integral transformations, such as the Laplace transform function, which transform a differential equation into an algebraic equation in which the boundary conditions are automatically considered.

The main advantage of the DRBEM over its counterparts, used to model infinite and semi-infinite domains (such as classical BEM formulation, integral transformations, thin layer method), is that it produces time- and frequency-independent matrices (mass and stiffness matrix), by preserving a boundary-only discretization (no internal nodes necessary).

By the method of integral transformations and integral equations, Nowacki [2], Podstrigach [6] and Fichera [7] investigated the initial boundary value problem for the linear homogeneous system.

Due to the size of the domain depending on the time for this type of problems methods of separating the variables and integral transformations not be applied, as remaining within the classical methods of mathematical physics you cannot conform the solution of the heat equation to the motion of the border line of the heat transport domain.

After 2000 trials, the average value of each X* statistic is within ±0.15 of the specified degrees of freedom, and the probability integral transformations yield numbers that are uniformly distributed on the unit interval.

In this paper, it is divided as two steps: (1) Transforming the Copula wind model under the Weibull distribution by probability integral transformation, and then testing the autocorrelation of each transformed series probability to see whether series itself independent; (2) Using Kolmogorov-Smirnov (K-S) principle to check transformed series keeps (0, 1) uniform distribution.

By a peculiar integral transformation, the first order state equation with time delay is transformed into the standard first order state equation, which contains no time delay.

The method of PDE backstepping as well as some special skills is resorted in stabilizing the coupled PDE ODE control system, which is transformed into an exponentially stable PDE ODE cascade with an invertible integral transformation.

First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDE ODE cascade with an invertible integral transformation, where PDE backstepping is employed.

This requires an accurate computation of a specific integral transformation kernel function and its moment integrals.

Using a conceptually novel integral transformation, we obtain extremely simple, explicit formulae for the gain functions.