In this work we present the formalization of an algorithm to compute the Echelon Form of a matrix. We have proved its existence over Bezout domains and we have made it executable over Euclidean domains, such as Z and K[x]. This allows us to compute determinants, inverses and characteristic polynomials of matrices. The work is based on the HOL-Multivariate Analysis library, and on both the Gauss...

We investigate new algorithms for the solution of nonseparable elliptic equations in irregular domains. Such equations arise frequently in fluid dynamics and other branches of continuum mechanics. We show that the combined use of a fast iteration (involving the use of fast Poisson solvers (FPS) in rectangular domains) and the capacitance matrix method can lead to algorithms which are several ti...

a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...

A region of resistive domains is found in composite superconductors with thermal and electrical contact resistance between the normal metal matrix and the superconductor. The V-I characteristic of 3 sample with resistive domains is found. It is shown that the existence of resistive domains leads to the emergence of hysteresis upon decay and recovery of superconductivity in the presence of trans...

The mitochondrial ADP/ATP carrier imports ADP from the cytosol and exports ATP from the mitochondrial matrix. The carrier cycles by an unresolved mechanism between the cytoplasmic state, in which the carrier accepts ADP from the cytoplasm, and the matrix state, in which it accepts ATP from the mitochondrial matrix. Here we present the structures of the yeast ADP/ATP carriers Aac2p and Aac3p in ...

In previous applications of the finite element method in modeling mechanical behavior of skeletal muscle, the passive and active properties of muscle tissue were lumped in one finite element. Although this approach yields increased understanding of effects of force transmission, it does not support an assessment of the interaction between the intracellular structures and extracellular matrix. I...