The authors conducted VOC measurements using PTR-TOF in Kathmandu, Nepal. PMF was used to separate various source contributions to ambient VOC as a function of time. The authors then used a PMF “nudging” tool and some a priori knowledge of source profiles to move the PMF solution into a more physically realistic space. The various PMF factors are identified by comparing their VOC composition wi...

This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension of the matrix.

Let A be a matrix with nonnegative real entries. The PSD rank of A is the smallest integer k for which there exist k × k real PSD matrices B1, . . . , Bm, C1, . . . , Cn satisfying A(i|j) = tr(BiCj) for all i, j. This paper determines the computational complexity status of the PSD rank. Namely, we show that the problem of computing this function is polynomial-time equivalent to the existential ...

INTRODUCTION The fundamental principle of source/receptor relationships is that mass conservation can be assumed and a mass balance analysis can be used to identify and apportion sources of airborne particulate matter in the atmosphere. This methodology has generally been referred to within the air pollution research community as receptor modeling [Hopke, 1985; 1991]. The approach to obtaining ...

the polynomial interpolation in one dimensional space r is an important method to approximate the functions. the lagrange and newton methods are two well known types of interpolations. in this work, we describe the semi inherited interpolation for approximating the values of a function. in this case, the interpolation matrix has the semi inherited lu factorization.

Routines exist in LAPACK for computing the Cholesky factorization of a symmetric positive definite matrix and in LINPACK there is a pivoted routine for positive semidefinite matrices. We present new higher level BLAS LAPACK-style codes for computing this pivoted factorization. We show that these can be many times faster than the LINPACK code. Also, with a new stopping criterion, there is more r...

This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an m-by-n nonnegative matrix X and an integer k, the PSD factorization problem consists in finding, if possible, symmetric k-by-k positive semidefinite matrices {A, ..., A} and {B, ..., B} such that Xi,j = trace(AB) for i = 1, ...,m, and ...

In this paper, we consider an arbitrary binary polynomial sequence {A_n} and then give a lower triangular matrix representation of this sequence. As main result, we obtain a factorization of the innite generalized Pascal matrix in terms of this new matrix, using a Riordan group approach. Further some interesting results and applications are derived.