introduction:  the  advent  of  dual-modality  pet/ct  scanners  has  revolutionized  clinical  oncology  by  improving lesion localization and facilitating treatment planning for radiotherapy. in addition, the use of  ct images for ct-based attenuation correction (ctac) decreases the overall scanning time and creates  a noise-free  attenuation  map  (6map).  ctac  methods  include  scaling,  s...

The dual purpose of this article is to establish bilinear Poincaré-type estimates associated to an approximation of the identity and to explore the connections between bilinear pseudo-differential operators and bilinear potential-type operators. The common underlying theme in both topics is their applications to Leibniz-type rules in Sobolev and Campanato-Morrey spaces under Sobolev scaling.

In this paper we develop a Conditional Least Squares (CLS) procedure for estimating bilinear time series models. We apply this method to two general types of bilinear models. A model of type I is a special superdiagonal bilinear model which includes the linear ARMA model as a submodel. A model of type II is a standardized version of the popular bilinear BL(p, 0, p, 1) model (see e.g. Liu and Ch...

In this paper, we determine the $L^p(\mathbb{R})\times L^q(\mathbb{R})\rightarrow L^r(\mathbb{R})$ boundedness of bilinear Hilbert transform $H_{\gamma}(f,g)$ along a convex curve $\gamma$ $$H_{\gamma}(f,g)(x):=\mathrm{p.\,v.}\int_{-\infty}^{\infty}f(x-t)g(x-\gamma(t)) \,\frac{\textrm{d}t}{t},$$ where $p$, $q$, and $r$ satisfy $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$, $r>\frac{1}{2}$, $p>1$, $q>1$...

The N = 2 supersymmetric KdV equations are studied within the framework of Hirota’s bilinear method. For two such equations, namely N = 2, a = 4 and N = 2, a = 1 supersymmetric KdV equations, we obtain the corresponding bilinear formulations. Using them, we construct particular solutions for both cases. In particular, a bilinear Bäcklund transformation is given for the N = 2, a = 1 supersymmetr...

A bilinear Bäcklund transformation is presented for a (3 + 1)-dimensional generalized KP equation, which consists of six bilinear equations and involves nine arbitrary parameters. Two classes of exponential and rational traveling wave solutions with arbitrary wave numbers are computed, based on the proposed bilinear Bäcklund transformation. Published by Elsevier Ltd

In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg uncertainty principle correspond to a description of " off-diagonal " decay. In addition they allow us to prove global continuities in Lebesgue spaces for bilinear ope...