In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta RK methods by introducing frequency-depending weights in the update. New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase...

1. Let M be a complex manifold with a smooth boundary which will be denoted bM , dim C M = n. Let us denote M = M ∪ bM and assume for simplicity that M ⊂ ˜ M where˜M is a complex neighbourhood of M , dim C ˜ M = n, so that every point z ∈ bM is an interior point of˜M. Let us take a C ∞-function ρ : ˜ M → R such that M = z | ρ(z) < 0 , bM = z | ρ(z) = 0 ; dρ(z) = 0 for all z ∈ bM. (0.1) For any ...

`=1 ∫ |x|>ε |x| μn`(dx) = 0 for all ε > 0, where x 7→ |x| denotes a fixed homogeneous norm on the Heisenberg group. Professor E. Siebert suggested a way to prove similar results for a Lie group G. The main step is the generalization of Lemma 1 in Pap [4] for an arbitrary Lie group G, which gives an estimation for the Fourier transform of a probability measure on G in terms of integrals of local...

Thermogravimetric analysis of polyethylene oxide (powder and nanofibers obtained by force spinning water or chloroform solutions oxide) was studied using different theoretical models such as Friedman Flynn-Wall-Ozawa. A semiempirical approach for estimating the “sigmoid activation energy” from thermal degradation suggested confirmed experimental data on PEO powder nanofibers' mats. The equation...

Homogeneous coordinates are often used in computer graphics and computer vision applications especially for the representation of geometric transformations. The homogeneous coordinates enable us to represent translation, rotation, scaling and projection operations in a unique way and handle them properly. Today’s graphics hardware based on GPU offers a very high computational power using pixel ...