The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...

We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.

During the support period July 1, 2011 June 30, 2012, seven research papers were published. They consist of three types: • Research that directly addresses the kernel selection problem in machine learning [1, 2]. • Research that closely relates to the fundamental issues of the proposed research of this grant [3, 4, 5, 6]. • Research that is in the general context of computational mathematics [7...

We define and classify matrix linear total differential operators whose images in the Lie algebra g of evolutionary vector fields on the infinite jet space over a fibre bundle are subject to the collective commutation closure,

Via a random construction we establish necessary conditions for L(l) inequalities for certain families of operators arising in harmonic analysis. In particular we consider dilates of a convolution kernel with compactly supported Fourier transform, vector maximal functions acting on classes of entire functions of exponential type, and a characterization of Sobolev spaces by square functions and ...

Let E be a vector valued sequence space with operator valued βdual E . If E satisfies certain gliding hump assumptions, we show that pointwise bounded subsets of E are sequentially equicontinuous. The result is established by considering uniform convergence of the elements in E .

We define a theta operator on p-adic vector-valued modular forms on unitary groups of arbitrary signature, over a quadratic imaginary field in which p is inert. We study its effect on Fourier-Jacobi expansions and prove that it extends holomorphically beyond the μ-ordinary locus, when applied to scalar-valued forms.