We study the feasibility of level expansion and test the quartic vertex of closed string field theory by checking the flatness of the potential in marginal directions. The tests, which work out correctly, require the cancellation of two contributions: one from an infinite-level computation with the cubic vertex and the other from a finite-level computation with the quartic vertex. The numerical...

In this paper, we investigate the Hyers-Ulam stability for the system of additive, quadratic, cubicand quartic functional equations with constants coecients in the sense of dectic mappings in non-Archimedean normed spaces.

Let p be a prime = 1 (mod 16). We obtain extensions of known congruences involving parameters of bioctic Jacobi sums (modp). These extensions are used to give an elementary proof of an important congruence of Ήasse relating parameters of quartic and octic Jacobi sums (mod p). This proof leads directly to an elementary resolution of sign ambiguities of parameters of certain quartic, octic, and b...

We compare three diversity-preserving mechanisms, implicit fitness sharing, negative correlation learning, and a new form, root-quartic negative correlation learning, on a standard genetic programming problem, the 6multiplexer. On this problem, root-quartic negative correlation learning significantly outperforms standard negative correlation learning, and marginally outperforms implicit fitness...

This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of B-net representation. In the bivariate setting, a group of new parameters of bivariate quartic and quintic polynomials over a planar simplex is introduced, new formulations of smoothness conditions of bivariate quartic C1 splines and quintic C2 ...

In this article, a generalized form of n -quartic mappings is introduced. The structure such studied, and in fact, it shown that every multiquartic mapping can be described as an equation, namely, the (generalized) functional equation. Moreover, by applying two fixed point techniques, some results corresponding to known ...

Historically, much of the theory and practice in nonlinear optimization has revolved around the quadratic models. Though quadratic functions are nonlinear polynomials, they are well structured and easy to deal with. Limitations of the quadratics, however, become increasingly binding as higher degree nonlinearity is imperative in modern applications of optimization. In the recent years, one obse...

In this paper the number of Fq-isomorphism classes of Jacobi quartic curves, i.e., the number of Jacobi quartic curves with distinct jinvariants, over finite field Fq is enumerated.