This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inf...

The specific force equation has many applications in open channel flow problems. Quantifying of the hydraulic jump phenomenon is an important application of this equation. This equation has a direct solution only for the rectangular channels. The trial and error procedure as well as the graphical solution are the existing methods of solving hydraulic jump equations. No direct solutions are avai...

The multi-scale Gibbs–Helmholtz constrained (GHC) equation is a new predictive cubic equation of state that constrains the energy parameter in the SRK equation to satisfy the Gibbs–Helmholtz equation. It makes use of internal energies of departure calculated from NTP Monte Carlo simulations at the molecular length scale and a novel up-scaling expression to determine the energy parameter at the ...

The propagating chemical fronts found in cubic autocatalytic reactiondiffusion processes are studied. Simulations of the reaction-diffusion equation near to and far from the onset of the front instability are performed and the structure and dynamics of chemical fronts are studied. Qualitatively different front dynamics are observed in these two regimes. Close to onset the front dynamics can be ...

Fourth-order Schrödinger equations have been introduced by Karpman and Shagalov to take into account the role of small fourth-order dispersion terms in the propagation of intense laser beams in a bulk medium with Kerr nonlinearity. In this paper we investigate the cubic defocusing fourth order Schrödinger equation i∂tu +∆ 2 u + |u|u = 0 in arbitrary space dimension R for arbitrary initial data....

Given a cubic equation x1y1z1 + x2y2z2 + · · · + xnynzn = b over a finite field, it is necessary to determine the minimal number of systems of linear equations over the same field such that the union of their solutions exactly coincides with the set of solutions of the initial equation. The problem is solved for arbitrary size of the field. A covering with almost minimum complexity is constructed.

For diagonal cubic surfaces, we give an upper bound for E. Peyre’s Tamagawa type number in terms of the coefficients of the defining equation.