In this work, we present a bilinear Tb theorem for singular integral operators of Calderón-Zygmund type. We prove some new accretive type Littlewood-Paley results and construct a bilinear paraproduct for a para-accretive function setting. As an application of our bilinear Tb theorem, we prove product Lebesgue space bounds for bilinear Riesz transforms defined on Lipschitz curves.

The bilinear Generalized predictive controller is modified to account for unmodelled plant uncertainties and bounded disturbances. First, a generalized predictive control law is derived by means of minimizing a quadratic cost function and then modified by introducing an estimate of the modeling error as a feedback. The robustness results are derived by neither requiring a prior knowledge of the...

In this paper we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of K. de Leeuw’s theorem for bilinear multipliers of strong and weak type. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding b...

The paper presents an algebraic characterization of observability and span-reachability of bilinear hybrid systems without guards, i.e. hybrid systems whose continuous dynamics is determined by bilinear control systems, and whose discrete transitions are triggered externally. The proposed characterization provides necessary and sufficient conditions for observability and spanreachability in ter...

The bilinear map whose domain and range are identical is called self-bilinear map. Once such kind of bilinear map exists, the multilinear map can be constructed easily by using self bilinear map as a component. Yamakawa et al. have introduced the first secure self-bilinear map with auxiliary information based on the integer factoring assumption in Crypto 2014. Inspired by their work, we find th...

Abstract It is proved that the class of c-closed distribution spaces contains extremal domains and codomains to make convolution distributions a well-defined bilinear mapping. The are systematically endowed with topologies bornologies hypocontinuous whenever defined. Largest modules smallest algebras for semigroups constructed along same lines. fact exist within this fundamentally related quant...

This paper presents a novel partial differential equation (PDE)-based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage tasks. We model the ensemble population dynamics as an advection-diffusion-reaction PDE model and formulate the mapping and coverage tasks as identification a...

In many pairing-based cryptosystems, the secret keys are elements of bilinear groups. For safeguarding such secret keys or decrypting or signing in a threshold manner, Verifiable Secret Sharing (VSS) in bilinear groups is required. In this paper, we show a method of verifiably sharing a random secret in a bilinear group. Our method is simple and practical. It can be regarded as a generalisation...