Collocation methods based on quartic splines are presented for second-order two-point boundary value problems. In order to obtain a uniquely solvable linear system for the degrees of freedom of the quartic spline collocation approximation, in addition to the boundary conditions specified by the problem, extra boundary or near-boundary conditions are introduced. Non-optimal (fourth-order) and op...

• Quartic force fields of the highest level provide rotational constants to within, on average, 34 MHz experiment. Tetraatomic species with low anharmonicities can be within 20 MHz. These same methods vibrational frequencies 5.8 cm ?1 . The CcCR quartic field (QFF) methodology is capable computing B 0 and C 35 (0.14%) experiment for triatomic larger molecules at least two heavy atoms. Additiona...

We construct infinite families of elliptic curves with given torsion group structures over quartic number fields. In a 2006 paper, the first two authors and Park determined all of the group structures which occur infinitely often as the torsion of elliptic curves over quartic number fields. Our result presents explicit examples of their theoretical result. This paper also presents an efficient ...

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.

Inflection-point inflation is an interesting possibility to realize a successful slow-roll inflation when inflation is driven by a single scalar field with its initial value below the Planck mass (φI . MP l). In order for a renormalization group (RG) improved effective λφ4 potential to develop an inflection-point, the quartic coupling λ(φ) must exhibit a minimum with an almost vanishing value i...

We show that the quartic Diophantine equations $ax^4+by^4=cz^2$ has only trivial solution in Gaussian integers for some particular choices of $a,b$ and $c$. Our strategy is by elliptic curves method. In fact, we exhibit two null-rank corresponding families over field. also determine torsion groups both families.

Vacuum stability in the Standard Model is problematic as the Higgs quartic self-coupling runs negative at a renormalization scale of about 10 GeV. We consider a non-supersymmetric SO(10) grand unification model for which gauge coupling unification is made possible through an intermediate scale gauge group, Gint = SU(3)C ⊗SU(2)L⊗SU(2)R⊗U(1)B−L. Gint is broken by the vacuum expectation value of a...

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...