Let Hp denote the Lebesgue space Lp for p > 1 and the Hardy space Hp for p ≤ 1. For 0 < p, q, r < ∞, we study Hp × Hq → Hr mapping properties of bilinear operators given by finite sums of products of Calderón–Zygmund operators on stratified homogeneous Lie groups. When r ≤ 1, we show that such mapping properties hold when a number of moments of the operator vanish. This hypothesis is natural an...

We present a new two-party attribute-based key agreement protocol that is secure without the random oracle model in groups equipped with a bilinear map. The attribute-based key agreement scheme is one type of the identity-based key agreement scheme, in which the identity can be viewed as a set of descriptive attributes. These kinds of schemes provide some new properties, such as hiding the iden...

We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N = 2 superfield technique and show that in the presence of a scalar N = 2 superpotential the magnetic interaction is implied by the presence of noncommutativity of position vari...

We continue the investigation initiated in [8] of uniform L bounds for the family of bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. ∫ R f(x − αt)g(x − βt) dt t . In this work we show that Hα,β map L1(R) × L2(R) into L(R) uniformly in the real parameters α, β satisfying | β − 1| ≥ c > 0 when 1 < p1, p2 < 2 and 2 3 < p = p1p2 p1+p2 < ∞. As a corollary we obtain L × L∞ → L uniform bounds in the ...

The $S=1$ bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host number of exotic magnetic and nematic orders [Moreno-Cardoner $\textit{et al.}$, Phys. Rev. B $\textbf{90}$, 144409 (2014)], including an extensive region "supersolid" order. In this work, we amend by XXZ in interactions. Tuning limit exactly solvable...

In this paper, a new method for mass air flow (MAF) sensor error compensation and an online updating error map (or lookup table) due to installation and aging in a diesel engine is developed. Since the MAF sensor error is dependent on the engine operating point, the error model is represented as a two-dimensional (2D) map with two inputs, fuel mass injection quantity and engine speed. Meanwhile...

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

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.