In this article we prove a collection of new non-linear and non-local integral inequalities. As an example for u ≥ 0 and p ∈ (0,∞) we obtain ∫ R3 dx u(x) ≤ ( p+ 1 p )2 ∫ R3 dx {(−4)−1u(x)}|∇u p 2 (x)|. We use these inequalities to deduce global existence of solutions to a non-local heat equation with a quadratic non-linearity for large radial monotonic positive initial conditions. Specifically,...

Integral transformations have been used for a long time in the solution of differential equations either solely or combined with other methods. These transforms provide great advantage reaching solutions an easy way by transforming many seemingly complex problems into more understandable format. In this study, we integral transform, namely Kashuri Fundo blending homotopy perturbation method non...

We study non-Gaussianity induced by a pseudo Nambu-Goldstone boson with a cosine-type scalar potential. We focus on how the non-Gaussianity is affected when the pseudo Nambu-Goldstone boson rolls down from near the top of the scalar potential where the deviation from a quadratic potential is large. We find that the resultant non-Gaussianity is similar to that obtained in the quadratic potential...

Gradient error can be compensated by optimizing switching sequences of DAC arrays. This paper establishes an absolute lower bound of integral nonlinearity (INL) which may be achieved by optimizing switching sequences. Optimal switching sequences that meet this lower bound are presented for one-dimensional linear gradient error compensation in unary (thermometer decoded) DAC arrays. The sequence...