Sentence examples for expansion solutions from inspiring English sources

However, the eigenfunction expansion solutions are incomplete due to the absence of the asymptotic solution corresponding to a crucial eigenvalue.

Further, series expansion solutions are obtained which are valid at small values of α, but the results are found to be applicable over a wide range of values of α.

The use of sensitivity overcomes some of the mathematical obstacles to solving joint CCP problems and, in addition, leads to optimal expansion solutions because uncertain loads are correctly estimated.

A numerical example is given in order to prove the validity of the present study and also to discuss the importance of the completeness of the eigenfunction expansion solutions.

Federico is Founder of Nexxpansion, a global business advisory firm that provides unique sales, operational and capital expansion solutions.

The solution methodology is based on generating the multiple fractional power series expansion solution in the form of a rapidly convergent series with minimum size of calculations.

Without eliminating the secular terms, a valid asymptotic expansion solution for the weakly non-linear equation is analytically determined for the case of primary resonances.

Numerical results are presented to discuss the convergence of the proposed series and to show the accuracy of the calculated response compared to the classical series expansion solution.

An eigenfunction expansion solution for the model reactor closely parallels the full numerical solutions in the round-bottom flask reactor, thus confirming the validity of the simplified model reactor.

Bulk energy storage, CAES (compressed air energy storage) is used as the representative storage technology, and the benefits of optimally allocated storage integration onto the grid are compared with transmission expansion solution.

Instead, the MacDock (and MacDock Mini, which is smallest but with fewer connectors) opt to take advantage of the addition of USB 3.0 to later-generation MacBooks to provide an expansion solution that likely fits the needs of most, in a portable package that retails for less than half what the Thunderbolt expansion options mentioned above are currently going for.