For a bilinear map $*:\mathbb R^d\times \mathbb R^d\to R^d$ of nonnegative coefficients and vector $s\in positive entries, among an exponentially number ways combining $n$ instances $s$ using $n-1$ applications $*$ for given $n$, we are interested in the largest entry over all resulting vectors. An asymptotic behavior is that $n$-th root this converges to growth rate $\lambda$ when tends infini...

We provide a direct proof for the boundedness of pseudodifferential operators with symbols in the bilinear Hörmander class BS 1,δ, 0 ≤ δ < 1. The proof uses a reduction to bilinear elementary symbols and Littlewood-Paley theory.

Toe-in gait and crouch gait can make children with mild cerebral palsy fall and suffer improper balance during walking or ambulation training. A customized external strap orthosis for correcting leg alignment was used to resolve this problem. The purpose of this study was to research the immediate effects while wearing the customized external strap orthosis. Pressure platform was used to assess...