We introduce a new solution for Kawahara-KdV equations. The Lie group analysis is used to carry out the integration of this equations. The similarity reductions and exact solutions are obtained based on the optimal system method.

information integration plays an important role in academic environments since it provides a comprehensive view of education data and enables mangers to analyze and evaluate the effectiveness of education processes. however, the problem in the traditional information integration is the lack of personalization due to weak information resource or unavailability of analysis functionality. in this ...

A general uniform convergence theorem for numerical integration of Cauchy principal value integrals is proved. Seven special instances of this theorem are given as corollaries.

In this paper we study the issue of economic integration in Poland between 1924 and 1937 by means of a threshold cointegration analysis of the law of one price. We find that the interwar economy can be regarded as integrated but with obvious restrictions which refer to the existence of relevant transaction costs for arbitrage and differences in the level of prices between cities. Moreover, the ...

We present an efficient approach to evaluate multivariate highly oscillatory integrals on piecewise analytic integration domains. Cubature rules are developed that only require the evaluation of the integrand and its derivatives in a limited set of points. A general method is presented to identify these points and to compute the weights of the corresponding rule. The accuracy of the constructed...

In a recent comparison of methods of highly oscillatory numerical integration the authors appear to have overlooked some works which seem to compete effectively with several of those described. It is the intention briefly to illuminate this with a number of examples reworked. In so doing, it is found that three commonly used Fortran compilers give curiously differing results on a number of occa...