Type IV collagen forms a network that provides the major structural support for basement membranes. Basement membranes are specialized forms of extracellular matrix with important functions in development. One collagen gene (Dcg1) was characterized in Drosophila melanogaster and shown to encode a collagen chain related to vertebrate basement membrane type IV collagen chains. Therefore, to acces...

Applying a few steps of the Arnoldi process to a large nonsymmetric matrix A with initial vector v is shown to induce several quadrature rules. Properties of these rules are discussed, and their application to the computation of inexpensive estimates of the quadratic form 〈f, g〉 := v∗(f(A))∗g(A)v and related quadratic and bilinear forms is considered. Under suitable conditions on the functions ...

Describing the equation of a plane curve C as the determinant of a matrix of linear forms is a classical problem. A related issue is expressing C as the Pfaffian of a skewsymmetric matrix of forms. When the curve is defined by a harmonic homogeneous polynomial (a solution to Laplace’s equation), then the action of the Lie algebra of the orthogonal group SO(3,C) provides a natural such expressio...

for $a,bin m_{nm},$ we say that $a$ is left matrix majorized (resp. left matrix submajorized) by $b$ and write $aprec_{ell}b$ (resp. $aprec_{ell s}b$), if $a=rb$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $r.$ moreover, we define the relation $sim_{ell s} $ on $m_{nm}$ as follows: $asim_{ell s} b$ if $aprec_{ell s} bprec_{ell s} a.$ this paper characterizes all linear p...

for vectors x, y ∈ rn, it is said that x is left matrix majorizedby y if for some row stochastic matrix r; x = ry. the relationx ∼` y, is defined as follows: x ∼` y if and only if x is leftmatrix majorized by y and y is left matrix majorized by x. alinear operator t : rp → rn is said to be a linear preserver ofa given relation ≺ if x ≺ y on rp implies that t x ≺ ty onrn. the linear preservers o...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

In this work we study in detail the conditions under which the stiffness matrix of a spatial system can be transformed into block-diagonal and diagonal form. That is the existence of a coordinate frame in which the stiffness matrix takes on these simple forms. The consequences of a block-diagonal or diagonal stiffness matrix for the invariants of the system, principal screws, von Mises’ invaria...

We report the effect of nickel chloride on fibroblast-mediated collagen gel contraction, fibroblast migration and pattern of matrix metalloproteinase (MMP) activities expressed by human embrzonary lung fibroblasts (HELFs). After the treatment with nickel chloride, gelatin zymography, casein zymography and also western blot assay revealed a significant decrease of MMP-2 and MMP-1 active forms. M...

Inspired by a formal resemblance of certain q-expansions of modular forms and the master field formalism of matrix models in terms of Cuntz operators, we construct a Hermitian onematrix model, which we dub the “modular matrix model.” Together with an N = 1 gauge theory and a special Calabi-Yau geometry, we find a modular matrix model that naturally encodes the Klein elliptic j-invariant, and he...