(N × N)-matrix is called additive when its elements are pair-wise sums of N real numbers ai. For a quadratic binary functional with an additive connection matrix we succeeded in finding the global minimum expressing it through external parameters of the problem. Computer simulations show that energy surface of a quadratic binary functional with an additive matrix is complicate enough.

We propose using discrete dynamical systems to model non-Markovian processes. This implies a whole hierarchy of dynamical systems with dimensionality increasing proportional to the memory. Specific long-range memory effects are investigated for a quadratic, a cubic and a quartic map. Markovian processes transform the quadratic map into a normal form of the logistic equation; the H6non map corre...

In our recent paper I. Gaál: Calculating “small” solutions of relative Thue equations, J. Experiment. Math. (to appear) we gave an efficient algorithm to calculate “small” solutions of relative Thue equations (where “small” means an upper bound of type 10500 for the sizes of solutions). Here we apply this algorithm to calculating power integral bases in sextic fields with an imaginary quadratic...

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for...

The goal of this paper is to investigate the Generalized Hyers - Ulam Rassias (HUR) stability generalquartic functional equation (GQFE) fq(kr1 + (k -1)r2) = 2k4fq(r1) 2(k -1)4fq(r2) +6k2(k -1)2[fq(r1 r2) fq(r1 r2)] 12k2(k 1)2[fq(r1) fq(r2)] in fuzzy normed spaces (F.N. spaces). proved by using direct method. sense and Ulam- Gavruta also studied.

We show how to extract a contour line (or isosurface) from quadratic elements—specifically from quadratic triangles and tetrahedra. We also devise how to transform the resulting contour line (or surface) into a quartic curve (or surface) based on a curved-triangle (curved-tetrahedron) mapping. A contour in a bivariate quadratic function defined over a triangle in parameter space is a conic sect...

We present a computational approach for finding all integral solutions of the equation y2 = 1k + 2k + · · ·+xk for even values of k. By reducing this problem to that of finding integral solutions of a certain class of quartic equations closely related to the Pell equations, we are able to apply the powerful computational machinery related to quadratic number fields. Using our approach, we deter...