A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some resul...A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.展开更多
The present paper gives the proof of the set of primes as continuum and evaluates the analytical formula for the integral of the inverse of the primes over the distance. First it starts with the density of the primes,...The present paper gives the proof of the set of primes as continuum and evaluates the analytical formula for the integral of the inverse of the primes over the distance. First it starts with the density of the primes, shortly recapitulates the prime-number-formula and the complete-prime-number-formula, the proof of the set of primes as continuum. The theoretical evaluation is followed in annexes by numerical evaluation of the theoretical results and of different constants, which represent inherent properties of the set of primes.展开更多
文摘A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.
文摘The present paper gives the proof of the set of primes as continuum and evaluates the analytical formula for the integral of the inverse of the primes over the distance. First it starts with the density of the primes, shortly recapitulates the prime-number-formula and the complete-prime-number-formula, the proof of the set of primes as continuum. The theoretical evaluation is followed in annexes by numerical evaluation of the theoretical results and of different constants, which represent inherent properties of the set of primes.
