In this paper, we consider some inverse singular value problems for Toeplitz-related matrices. We construct a Toeplitz-plus-Hankel matrix from prescribed singular values including a zero singular value. Then we find a solution to the inverse singular value problem for Toeplitz matrices which have double singular values including a double zero singular value.

The index of matrix A in Cn.n is equivalent to the dimension of largest Jor-dan block corresponding to the zero eigenvalue of A. In this paper, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.

In a preceding paper we have introduced the t-singular homology with integral coefficient of orbifolds, which captures the orbifold structures. In this paper we introduce the s-singular homology of orbifolds, and study the s-singular homology of orbifolds and the t-singular homology with rational coefficient of orbifolds. The main theorems are the following: (i) the s-singular homology group of...

In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximaldimensional geometric type, show that they can generically have only finitely many singular points, and describe all possible locations of singular points. More precisely, we show that singular points must be either vertices, or generalized midpoints and...

In this paper we present a decomposition theorem for generalised quadratic forms over a division algebra with involution in characteristic 2. This is a generalisation of a decomposition result on quadratic forms in characteristic 2 from [3] and extends a generalisation of the Witt decomposition theorem for nonsingular forms to cover forms that may be singular.

The article uses two examples to explore the statement that, contrary to the common wisdom, the properties of singular cardinals are actually more intuitive than those of the regular ones. 1

A certain prima facie implausible idea about the semantics of donkey pronouns has found a surprising number of adherents (Davies 1981, Lappin 1989, Neale 1990, Lappin and Francez 1994, Yoon 1994, 1996, Krifka 1996a) and even crept into a textbook (Larson and Segal 1995).1 According to this idea, syntactically singular donkey pronouns like it in (1) are semantically numberless, so that (2) provi...

A number of generalizations of singular cluacfratic minimization theory for the finitetime case are considered. Also new stahilit,y results are derived for the infinite time problem, and novel techniques are intr(xluccd to facilitate the derivation of singular solutions for this case. of significance is the fact that the ncw results make evident the duality that exists between singular control ...

We derive coupled on-line learning rules for the singular value decomposition (SVD) of a cross-covariance matrix. In coupled SVD rules, the singular value is estimated alongside the singular vectors, and the effective learning rates for the singular vector rules are influenced by the singular value estimates. In addition, we use a first-order approximation of Gram-Schmidt orthonormalization as ...