Sentence examples for fractions decomposition from inspiring English sources

A discrete approximation of the spectral measure is derived from a rational (Padé) approximation followed by its partial fractions decomposition.

It is confirmed that a partial fractions decomposition for ( left ({frac {1}{{Agamma + 1}}} right)^{L_{S}} ) can be easily solved via finding A j,j=1,…,L S. Such parameters can be calculated since the fractions in the above equation have the same denominators, following that their numerators must be equal, and then we obtain A j.

Next, we give a q-analog of partial fraction decomposition formula.

For AlH3 between 0.46 and 0.63 mol fraction, decomposition proceeds in two steps.

Firstly, we establish a q-analog of partial fraction decomposition formula by the method of mathematical induction.

We have used many relations of the polygamma functions together with results of reordering of double sums and partial fraction decomposition.

Then, using the relations obtained with the help of q-analog of partial fraction decomposition formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients.

Note that the partial fraction decomposition necessary for the Michaelian kinetics always exists, but is "practical" only with prior knowledge of the poles of the denominator's polynomials.

But thanks to the partial fraction decomposition theorem (see for instance [26]) they can be decomposed in a unique way into a sum of a polynomial and of rational fractions, with irreducible polynomials as denominator and a numerator of strictly smaller degree.

A partial fraction decomposition of the integrand reveals that I2(a) = 2 I(a), and thus we have (A33) t fix (s ) = 2 I (2 N s ) s (1 − e − 2 N s ) Combining this result with Eqs.

On the basis of these elements, taking into account that the employed temperature is equal or higher to 180 °C, it is possible to explain the higher depolymerization of cellulose fraction when microwave irradiation was employed, suggesting a specific relationship between cellulose fraction decomposition and microwave activation of the –CH2OH pendant groups.