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.

We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve. It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points ...

This paper presents a generalization of incremental condition estimation, a technique for tracking the extremal singular values of a triangular matrix. While the original approach allowed for the estimation of the largest or smallest singular value, the generalized scheme allows for the estimation of any number of extremal singular values. For example, we can derive estimates for the three smal...

The purpose of this paper is to extend and clarify the methods of the papers [G1] and [G2] by using the methods of [G3], incorporating ideas from Carnot-Caratheodory geometry such as those of the fundamental paper [NSW]. We will thereby prove an analogue for singular Radon transforms to the T (1) theorem of David and Journe [DJ]. As in [G1] and [G2], we will associate a singular integral operat...

A graph is said to be non-singular if it has no eigenvalue equal to zero; otherwise it is singular. Molecular graphs that are non-singular and also have the property that all subgraphs of them obtained by deleting a single vertex are themselves singular, known as NSSD graphs, are of importance in the theory of molecular π-electron conductors; NSSD = non-singular graph with a singular deck. Wher...

In this note, we study singular integrals with rough kernels, which belong to a class of singular Radon transforms. We prove certain estimates for the singular integrals that are useful in an extrapolation argument. As an application, we prove L p boundedness of the singular integrals under a certain sharp size condition on their kernels.

A QR–method for computing the singular values via semiseparable matrices. Abstract The standard procedure to compute the singular value decomposition of a dense matrix, first reduces it into a bidiagonal one by means of orthogonal transformations. Once the bidiagonal matrix has been computed, the QR–method is applied to reduce the latter matrix into a diagonal one. In this paper we propose a ne...

In this paper, we consider the singular values and singular vectors of finite, low rank perturbations of large rectangular random matrices. Specifically, we prove almost sure convergence of the extreme singular values and appropriate projections of the corresponding singular vectors of the perturbed matrix. As in the prequel, where we considered the eigenvalues of Hermitian matrices, the non-ra...

The particle size control of drug is one of the most important factors affecting the efficiency of the nano-drug production in confined liquid impinging jets. In the present research, for this investigation the confined liquid impinging jet was used to produce nanoparticles of Carbamazepine. The effects of several parameters such as concentration, solution and anti-solvent flow rate and solvent...

Finite element method (FEM) is one of the most famous methods which has many applications in varies studies such as the study of crack propagation in engineering structures. However, unless extremely fine meshes are employed, problem arises in accurately modelling the singular stress field in the singular element area around the crack tip. In the present study, the crack growth simulation has b...