In this paper, we define the multicubic-quartic and multimixed cubic-quartic mappings characterize them. other words, unify system of functional equations defining a (resp., multicubic-quartic) mapping to single equation, namely, equation. We also show that under what conditions can be multicubic, multiquartic multicubic-quartic. Moreover, by using fixed point theorem, study generalized Hyers-U...

Let p ≡ 1 (mod 4) be a prime, m ∈ Z and p m. In this paper we obtain a general criterion for m to be a quartic residue (mod p) in terms of appropriate binary quadratic forms. Let d > 1 be a squarefree integer such that ( d p ) = 1, where ( d p ) is the Legendre symbol, and let εd be the fundamental unit of the quadratic field Q( √ d). Since 1942 many mathematicians tried to characterize those p...

We study the capitulation problem for certain number fields K of degree 4 and we show how we can determine the structures of some 2-groups as an application of this study. Let K (2) 1 be the Hilbert 2-class field of K, K (2) 2 be the Hilbert 2-class field of K (2) 1 , CK,2 be the 2component of the ideal class group of K and G2 the Galois group of K (2) 2 /K. We suppose that CK,2 is of type (2, ...

Geometric properties of graphs of solutions for the quartic interaction PDE are studied in the present work. Two classes of solutions are considered. One class is represented by soliton solutions, whereas the other class consists of solutions of a first order PDE system, which generates the quartic interaction PDE, in the sense of least squares type action. We prove that for both classes the gr...

Quartic B-spline time integration method has been recently proposed for solving linear problems in structural dynamics. This paper developed this method to nonlinear dynamic analysis of single-degree-of-freedom (SDOF) systems under exploding loads. Using quartic B-spline basis function, this method gained second order of acceleration at each time-step. Thus it benefits from high accuracy compar...

In the paper [TZ1], we construct new subvarieties in the varieties of power sums for certain quartic hypersurfaces. In this paper, we show that these quartics coincide with the Scorza quartics of general pairs of trigonal curves and ineffective theta characteristics. Among other applications, we give an affirmative answer to the conjecture of Dolgachev and Kanev on the existence of the Scorza q...

In this paper, the authors investigate the generalized Hyers-UlamAoki-Rassias stability of a quartic functional equation g(2x+ y + z) + g(2x+ y − z) + g(2x− y + z) + g(−2x+ y + z) + 16g(y) + 16g(z) = 8[g(x+ y) + g(x− y) + g(x+ z) + g(x− z)] + 2[g(y + z) + g(y − z)] + 32g(x). (1) The above equation (1) is modified and its Hyers-Ulam-Aoki-Rassias stability for the following quartic functional equ...

We will show the general solution of the functional equation f(x + ay) + f(x− ay) + 2(a − 1)f(x) = af(x + y) + af(x− y) + 2a(a − 1)f(y) and investigate the Hyers-Ulam stability of the quartic set-valued functional equation.

In 2003, Pelantová and Twarock did research into the number of, and types of, tiles found in 1-dimensional cut and project quasicrystals associated with 7-order symmetry. In this paper we extend this to symmetries of order 9 (degree 3), as well as orders 15, 16, 20 and 24 (degree 4). Some discussion of the next case, order 11 (degree 5), is given.

This article reviews some recent developments in the analysis of anomalous triple and quartic vector boson couplings that have been discussed at the UK Phenomenology Workshop on Collider Physics 1999 in Durham.