Abstract Space separation within the Proper Generalized Decomposition—PGD—rationale allows solving high dimensional problems as a sequence of lower ones. In our former works, different geometrical transformations were proposed for addressing complex shapes and spatially non-separable domains. Efficient implementation separated representations needs expressing domain product characteristic funct...

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...

We present a generalisation of the standard well known and widely used Metropolis-Hastings algorithm which, unlike the Metropolis-Hastings sampler, can mix well over a target distribution which has separated and possibly narrow modes. The idea arose via a consideration of a space augmented slice sampler where the uniform space required to be sampled for the slice sampler, say I , is augmented w...

In this paper, several geometries of a class of grounded coplanar waveguide (GCPW) are investigated using the finite difference time domain (FDTD) method, and their losses are computed. A uniform grounded coplanar waveguide (GCPW) structure is used as a reference case for the other non-uniform geometries. First, four geometries are proposed to study the transmission and loss effect of replacing...

Analytic calculations of the electric field of a parallel-plate capacitor are notoriously difficult [1, 2, 3, 4, 5, 6, 7, 8]. The usual goal of such efforts is a calculation of the correction to the hard-edge approximation, C = A/4πd (in Gaussian units), of the capacitance for plates of area A separated by distance d. Calculate instead the electromagnetic momentum of the parallel-plate capacito...