When plant primary roots grow along a tilted surface that is impenetrable, they can undergo a slanted deviation from the direction of gravity called skewing. Skewing is induced by touch stimuli which the roots experience as they grow along the surface. Touch stimuli also induce the release of extracellular ATP (eATP) into the plant's extracellular matrix, and two apyrases (NTPDases) in Arabidop...

The methods of Shub and Smale [SS93] are extended to the class of multihomogeneous systems of polynomial equations, yielding Theorem 1, which is a formula expressing the mean (with respect to a particular distribution on the space of coefficient vectors) number of real roots as a multiple of the mean absolute value of the determinant of a random matrix. Theorem 2 derives closed form expressions...

We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here “binary matrix” means a matrix whose elements are drawn from {0, 1} or {−1, 1}. We describe efficient parallel algorithms for the search, using Duval’s algorithm for generation of Lyndon words and the well-known representation of the determinant of a circulant in terms of roots of unity....

Abstract. We study the density of the roots of the derivative of the characteristic polynomial Z(U, z) of an N × N random unitary matrix with distribution given by Haar measure on the unitary group. Based on previous random matrix theory models of the Riemann zeta function ζ(s), this is expected to be an accurate description for the horizontal distribution of the zeros of ζ (s) to the right of ...

This paper studies convergence properties of the block gmres algorithm when applied to nonsymmetric systems with multiple right-hand sides. A convergence theory is developed based on a representation of the method using matrix-valued polynomials. Relations between the roots of the residual polynomial for block gmres and the matrix "-pseudospectrum are derived, and illustrated with numerical exp...

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time’s spending. Further, both of them can be used efficiently not only for positive (semi-) definite, but for any non-singular symmetric matrix inversion. We use simulation to verify results, ...

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time’s spending. Further, both of them can be used efficiently not only for positive (semi-) definite, but for any non-singular symmetric matrix inversion. We use simulation to verify results, ...

This paper studies convergence properties of the block GMRES algorithm when applied to nonsymmetric systems with multiple right-hand sides. A convergence theory is developed based on a representation of the method using matrix-valued polynomials. Relations between the roots of the residual polynomial for block GMHES and the matrix &-pseudospectrum are derived, and illustrated with numerical exp...

In this study, it is aimed to use the Lorenz matrix multiplication find n^th powers of some special matrices and reach quadratic equations characteristic roots obtained in way. addition, contribute literature studies field by reaching identities.