In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

In this paper, we prove the generalized Hyers--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.

In 2011 ISO standardized [2] a family of deterministic pseudorandom bit generators MQ—DRBG, based on multivariate quadratic functions satisfying certain properties. The security of the generator could be described in terms of complexity of solving the corresponding system of multivariate quadratic equations. In our previous article [1] we proposed two different techniques for constructing syste...

in this paper, we prove the generalized hyers--ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy banach spaces.

Laser polishing is a finishing process based on melting material, with the objective of improving surface topography. Some operating parameters must be taken into consideration, such as laser power, feed rate, offset, and overlapping. Moreover, because of its dependence on the primary process, the initial topography has also an impact on the final result. This study describes a quadratic model,...

vector notation and then give two different representations. The first representation is the regular gradient space; it has the advantage of simplicity but contains important singularities. The second one is just a regular vector (p, 4, r) in 3-D with the constraint that p* + q* + r* = 1. (5) This can represent the normal of any plane in 3-D, with the added complexity that Eq. (5), a quadratic ...

The structure theory ([3], [8]) for complete flat homogeneous pseudo-riemannian manifolds reduces the classification to the solution of some systems of quadratic equations. There is no general theory for that, but new solutions are found here by essentially the same construction as that used for isoclinic spheres in Grassmann manifolds [4]. It is interesting to speculate on a possible direct ge...

We prove the thrackle conjecture for K5 and K3,3. To do this we reduce the problem to a set of simultaneous quadratic equations over Z2. Parts of this proof are computer assisted.

In the 1950’s I set out to revolutionize logic. I didn’t succeed (not yet!), but it wasn’t for want of trying. Logic has always fascinated me. In the common-sense sense of the word logic was easy; I had no inclination to commit the obvious errors of reasoning, and long chains of deductions were not intimidating. When I was told about syllogisms, I said “sure, obviously”, and didn’t feel that I ...

We propose an efficient search algorithm to solve the equation x3 + y3 + 2z3 = n for a fixed value of n > 0. By parametrizing |z|, this algorithm obtains |x| and |y| (if they exist) by solving a quadratic equation derived from divisors of 2|z|3±n. Thanks to the use of several efficient numbertheoretic sieves, the new algorithm is much faster on average than previous straightforward algorithms. ...