Sentence examples for mathematical analysis shown from inspiring English sources

Given that the Shannon-Nyquist theorem was satisfied the mathematical analysis shown in the last subsection holds true for the 3D discrete Fourier transform of, and, where,, and are the discrete counterparts of,, and, respectively.

A mathematical analysis shows that the concentrations of H2, D2, and HD should be equal to (fH 2, (fD 2, and 2 fH fD), respectively, to a very good approximation.

Some additional mathematical analysis shows that the stochastic differential equation (18) and its solution equation (19) have a precise mathematical interpretation.

Mathematical analysis showed that MPA values would not exceed Cavalieri values if glomeruli had ellipsoidal rather than spherical shape.Similar values for glomerular volume are obtained using the Cavalieri and MPA methods in humans and rats.

Mathematical analysis shows that in active gm-boosted CG LNA, the third input intercept point (IIP3) of LNA depends on interaction between main and auxiliary amplifiers.

Mathematical analysis shows that spray angle depends on the liquid viscosity, the gas and liquid flow rates and the construction of the atomizer.

Mathematical analysis shows that a distinction must be made between the speed of the troughs and crests, called the phase speed, and the speed and direction of the transport of energy or information associated with the wave, termed the group velocity.

Mathematical analysis showed that the dorsal ventral difference in the amount of HSPG is not sufficient to generate the observed difference in pattern, indicating that both extracellular matrix and tissue architecture play a role in this system.

The mathematical analysis shows that the wave propagation excited by the IDT is exactly the surface wave which was studied in Part 1 [Int. J. Solids Struct., 39, 1119 1130] of the research.

A mathematical analysis shows that these solutions decay exponentially at far field.

A mathematical analysis shows that those explicit solutions have exponential behaviors at far field.