The Lamperti–Kiu transformation for real-valued self-similar Markov processes (rssMp) states that, associated to each rssMp via a space-time transformation, is a Markov additive process (MAP). In the case that the rssMp is taken to be an α-stable process with α ∈ (0, 2), [12] and [20] have computed explicitly the characteristics of matrix exponent of the semi-group of the embedded MAP, which we...

ÐMetal matrix composites (MMCs) can be synthesized by aligning metal coated ceramic ®bers in a shaped container and applying pressure at elevated temperatures. The high stresses created at the contacts between neighboring ®bers cause inelastic matrix ̄ow that ®lls inter®ber voids, reduces inter®ber separations and results in composite densi®cation. The rate of densi®cation depends on the contac...

We compute the average characteristic polynomial of Hermitised product M real or complex non-Hermitian Wigner matrices size N×N with i.i.d. matrix elements, and a such times conjugate matrix. Surprisingly, results agree that Ginibre at finite-N, which have Gaussian entries. For latter yields orthogonal for singular values matrix, whereas two polynomials involves kernel eigenvalues. This extends...

The two-terminal conductance of a random flux model defined on a square lattice is investigated numerically at the band center using a transfer matrix method. Due to the chiral symmetry, there exists a critical point where the ensemble averaged mean conductance is scale independent. We also study the conductance distribution function which depends on the boundary conditions and on the number of...

The complexity of matrix multiplication (hereafter MM) has been intensively studied since 1969, when Strassen surprisingly decreased the exponent 3 in the cubic cost of the straightforward classical MM to log2(7) ≈ 2.8074. Applications to some fundamental problems of Linear Algebra and Computer Science have been immediately recognized, but the researchers in Computer Algebra keep discovering mo...

We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63–72]. As a consequence of our analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also s...

2014 A transfer-matrix method is used to calculate the correlation length for strips of finite width in the bond and site percolation problem. From the knowledge of these correlation lengths we compute the thresholds and the critical exponent 03BD by the phenomenological renormalization method. Tome 41 No 20 15 OCTOBRE 1980 LE JOURNAL DE PHYSIQUE LETTRES J. Physique LETTRES 41 (1980) L-473 L-47...

We develop a data-sparse and accurate approximation to parabolic solution operators in the case of a rather general elliptic part given by a strongly P-positive operator [4]. In the preceding papers [12]–[17], a class of matrices (H-matrices) has been analysed which are data-sparse and allow an approximate matrix arithmetic with almost linear complexity. In particular, the matrix-vector/matrixm...

We here establish an a priori Hölder estimate of Krylov and Safonov type for the viscosity solutions of a degenerate quasilinear elliptic PDE of non-divergence form. The diffusion matrix may degenerate when the norm of the gradient of the solution is small: the exhibited Hölder exponent and Hölder constant only depend on the growth of the source term and on the bounds of the spectrum of the dif...