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.

I classified bilinear differential operators acting in the spaces of tensor fields on any real or complex manifold and invariant with respect to diffeomorphisms 1980. Here give details proof.

The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results. First, the class of bilinear stochastic systems (or linear systems with multiplicative noise) is discussed. The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a so...

Bilinear models have been proposed to separate the factors from the observations for joint factors identification or translation tasks. However, the performance of existing bilinear models may degrade under challenging conditions when local image information cannot be obtained caused by occlusions or image noises. In this paper, a novel sub-pattern bilinear model (SpBM) is proposed. Different f...

The algebraic and geometric structure of certain classes of nonlinear stochastic systems is exploited in order to obtain useful stability and estimation results. First, the class of bilinear stochastic systems (or linear systems with multiplicative noise) is discussed. The stochastic stability of bilinear systems driven by colored noise is considered; in the case that the system evolves on a so...

A proper bilinear form is proposed for the N = 1 supersymmetric modified Korteweg-de Vries equation. The bilinear Bäcklund transformation for this system is constructed. As applications, some solutions are presented for it.