quartic

As it is well known, Green's functions in the functional-integral approach are defined by means of the so-called generating functional with sources for the boson and fermion fields, but the corresponding functional integrals cannot be evaluated exactly because the interaction part of the Hubbard Hamiltonian is quartic in the Grassmann fermion fields.

Xu, "Bifurcation of limit cycles and isochronous centers for a quartic system," International Journal of Bifurcation and Chaos, vol.

There are several papers by quartic spline interpolation, e.g., [11,12,13] but the interpolation problem which is equivalent to the histopolation with cubic splines is not treated in them in such extent as we do in current paper.

Panel A of Table A6 presents results for linear, cubic, and quartic polynomials.

Liu, "Quartic spline methods for solving one-dimensional telegraphic equations," Applied Mathematics and Computation, vol.

This attracted Makinde and Animasaun [8, 9] to focus on the case of quartic autocatalysis kind of chemical reaction in the flow of an electrically conducting nanofluid containing gyrotactic-microorganism over an upper horizontal surface of a paraboloid of revolution in the presence and absence of thermophoresis and Brownian motion.

In order to capture a possible nonlinear relationship in weight change over polynomial time, terms were calculated and tested (e.g., quadratic, cubic, and quartic).

Collocation method based on cubic, quartic, and septic B-spline functions has been investigated for the numerical solution of the EW equation by Dag and Saka [2], Raslan [20], and Fazal-i-Haq et al.

Among specific topics are the impact of water depth on dynamic characteristics of a bridge, the sensitive frequency of fixed-point loading for a track loading vehicle, an extension of the quartic Said-Bell curve with two parameters, a benchmark study on the finite element analysis of two interacting circular holes, a hybrid algorithm for multi-objective optimization problems, flexible charging power supply of pulse capacitors, and simulating and evaluating marine product virtual factory.

As the divisor is quadratic (and therefore we are not expecting a quartic nor cubic term in the quotient), the middle row of numbers will be offset one place to the right as shown (this means that the first two coefficients of the dividend are written below the line as a first step):

If a terminal angle of attack constraint is found, that is, the constraint [[??].sub.f] is included, the terminal condition ([t.sub.f], [[??].sub.f]) can be further introduced to utilize (11b) quartic spline curve equation to solve the problem

which is a quartic equation in general [11] and its form depends on the medium bidyadic [??].

A quartic B-spline collocation method is proposed for numerical solution of partial integro-differential equations with a weakly singular kernel.

The rest of the team included students Ellen Brown and Cameron Moore, programmer Erin Michno from game studio Quartic Llama and composer Neil Cullen, of the Royal Scottish National Orchestra, who put together the classical music that accompanies the game.