The purpose of this paper is to study the boundedness in the context of Triebel-Lizorkin spaces for some multilinear operators related to certain convolution operators. The operators include Littlewood-Paley operator, Marcinkiewicz integral, and Bochner-Riesz operator. 1. Introduction. Let T be a Calderon-Zygmund operator. A well-known result of Coif-man et al. [6] states that the commutator [b...

A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficien...

We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficients may depend on space and time. Pointwise convergence of the global analytic expansion is proved. This leads to analytic representations of solutions of initial-boundary problems of first and second type in terms of convol...

Line integral convolution (LIC) has become a well-known and popular method for visualizing vector elds. The method works by convolving a random input texture along the integral curves of the vector eld. In order to accelerate image synthesis signiicantly, an eecient algorithm has been proposed that utilizes pixel coherence in eld line direction. This algorithm, called \fast LIC", originally was...

This paper presents a new visualization technique for flow fields in 2D. It utilizes a physical model of smearing ink over a sheet of paper as an intuitive metaphor for the representation of a dynamical system. This technique is capable of producing images that are comparable to those generated with line integral convolution (LIC), which is a well-known and established visualization technique f...

A stochastic differential equation model is considered for nonlinear oscillators under excitations of combined Gaussian and Poisson white noise. Since the solutions of stochastic differential equations can be interpreted in terms of several types of stochastic integrals, it is sometimes confusing about which integral is actually appropriate. In order for the energy conservation law to hold unde...

We study stochastic perturbed Volterra equations of convolution type in an infinite dimensional case. Our interest is directed towards the existence and regularity of stochastic convolutions connected to the equations considered under some kind of perturbations. We use an operator theoretical method for the representation of solutions.

In this paper, we shall firstly illustrate why we should introduce set-valued stochastic integrals, and then we shall discuss some properties of set-valued stochastic processes and the relation between a set-valued stochastic process and its selection set. After recalling the Aumann type definition of stochastic integral, we shall introduce a new definition of Lebesgue integral of a set-valued ...

This paper proposes an extension to the existing automatic pencil drawing generation technique based on Line Integral Convolution (LIC). The original LIC pencil filter utilizes image segmentation and texture direction detection techniques for defining outlines and stroke directions, and the quality of a resulting image depends largely on the result of the white noises and the texture directions...