The dilaton theorem implies that the contribution to the dilaton potential from cubic interactions of all levels must be cancelled by the elementary quartic self-coupling of dilatons. We use this expectation to test the quartic structure of closed string field theory and to study the rules for level expansion. We explain how to use the results of Moeller to compute quartic interactions of state...

The critical currents of Nb/AI, A1--oxide, AI/Nb tunnel junctions of various shapes have been measured as a function of the applied magnetic field. For the square junction and for some special shapes like the diamond, "1 + cosine" and quartic junctions the Ic (B) pattern falls off theoretically as 1/B ", with n respectively equal to 1, 2, 3 and 4. In general the measurements are in good agreeme...

This paper is focused on the bifurcation of critical periods from a quartic rigidly isochronous center under any small quartic homogeneous perturbations. By studying the number of zeros of the first several terms in the expansion of the period function in ε, it shows that under any small quartic homogeneous perturbations, up to orders 1 and 2 in ε, there are at most two critical periods bifurca...

We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x - my) = 2(7m - 9)(m - 1)f(x) + 2m²(m² - 1)f(y)-(m - 1)² f(2x) + m²{f(x + y) + f(x - y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stab...

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...

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.