Dans Sacre Graal des Monty Python, le personnage de Sir Robin apparait au bout d’une vingtaine minutes en compagnie d’autres chevaliers la Table Ronde. Aux cotes Lancelot Le Brave et Galahad Pur, il est presente comme « Sir-Robin-Celui-Qui-N’est-Pas-Aussi-Brave-Que-Sir-Lancelot ». Il seul dont les exploits sont rapportes : effet, a « quasiment vaincu un dragon », affronte poulet vicieux Bristol...

The main purpose of this paper is the construction of explicit Gauss-Turán quadrature formulas: they are relative to some classes of weight functions, which have the peculiarity that the corresponding s-orthogonal polynomials, of the same degree, are independent of s. These weights too are introduced and discussed here. Moreover, highest-precision quadratures for evaluating Fourier-Chebyshev co...

Interactions are explored through the observation of the dynamics of particles. On the classical level the basic underlying assumption in that scheme is that Newton's second law holds. Relaxing the validity of this axiom by, e.g., allowing for higher order time derivatives in the equations of motion would allow for a more general structure of interactions. We derive the structure of interaction...

We revisit the problem of extending quadrature formulas for general weight functions, and provide a generalization of Patterson’s method for the constant weight function. The method can be used to compute a nested sequence of quadrature formulas for integration with respect to any continuous probability measure on the real line with finite moments. The advantages of the method include that it w...

One 3-D transient temperature field model for a thin uniform plate caused by moving laser heat source is described in present study. The with power density Gaussian-distribution form considered when finite-thin heated. By using the separate variable method and Newton-Cotes method, semi-analytical solution of conduction equation finite obtained. Numerical results show that effect distribution, s...