In this paper we completed the classification of the phase portraits in the Poincaré disc of uniform isochronous cubic and quartic centers previously studied by several authors. There are three and fourteen different topological phase portraits for the uniform isochronous cubic and quartic centers respectively.

To lowest order of perturbation theory we show that an equivalence can be established between a PT -symmetric generalized quartic anharmonic oscillator model and a Hermitian position-dependent mass Hamiltonian h. An important feature of h is that it reveals a domain of couplings where the quartic potential could be attractive, vanishing or repulsive. We also determine the associated physical qu...

We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in 22 or more variables. Our methods involve the estimation of a certain entangled two-dimensional 21 moment of quartic smooth Weyl sums via a novel cubic moment of Fourier coefficients.

A 1 2 -arc-transitive graph is a vertexand edgebut not arc-transitive graph. In all known constructions of quartic 1 2 -arc-transitive graphs, vertex stabilizers are isomorphic to Z 2,Z 2 2 or to D8. In this article, for each positive integer m ≥ 1, an infinite family of quartic 1 2 -arctransitive graphs having vertex stabilizers isomorphic to Z m

A variationally improved Sturmian approximation for solving time-independent Schrödinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian potential. The results are compared with those of the perturbation theory, the WKB approximation, and the accurate numerical values.

We provide explicit analogues of the Chowla-Selberg formula for quartic abelian CM fields. This consists of two main parts. First, we implement an algorithm to compute the CM points at which we will evaluate a certain Hilbert modular function. Second, we exhibit families of quartic fields for which we can determine the precise form of the analogue of the product of gamma values.

For a binary quartic form φ without multiple factors, we classify the quartic K3 surfaces φ(x, y) = φ(z, t) whose Néron-Severi group is (rationally) generated by lines. For generic binary forms φ, ψ of prime degree without multiple factors, we prove that the Néron-Severi group of the surface φ(x, y) = ψ(z, t) is rationally generated by lines.

The problem of C interpolation of a discrete set of data on the interval [a,b] representing the function f using quartic splines is investigated. An explicit scheme of interpolation is obtained using different quartic splines on even and odd subintervals of interpolation. Mathematical Subject Classification: 41A05, 41A15

We explain how to construct tables of quartic fields of discriminant less than or equal to a given bound in an efficient manner using Kummer theory, instead of the traditional (and much less efficient) method using the geometry of numbers. As an application, we describe the computation of quartic fields of discriminant up to 107, the corresponding table being available by anonymous ftp.

We used Wick’s normal-ordering technique, squeezed creation and annihilation operators, and a variation method, to find the eigenvalues of the general pure ?x2m potential. Numerical results for low-lying energy levels of pure quadratic, quartic, sextic, octic and decatic potentials, for different values of ? were obtained. Some interesting features of these energy levels are explained.