A method is introduced for diagnosing a transilient matrix for moist convection. This transilient matrix quantifies the nonlocal transport of air by convective eddies: for every height z, it gives the distribution of starting heights z9 for the eddies that arrive at z. In a cloud-resolving simulation of deep convection, the transilient matrix shows that two-thirds of the subcloud air convecting...

We study the identity problem for matrices, i.e., whether the identity matrix is in a semigroup generated by a given set of generators. In particular we consider the identity problem for the Special Linear Group following recent NP-completeness result for SL(2,Z) and the undecidability for SL(4,Z) generated by 48 matrices. In the seminal paper of Paterson in 1970, an injective morphism from pai...

Using the least element solution of the P0 and Z matrix linear complementarity problem (LCP), we define an implicit solution function for linear complementarity constraints (LCC). We show that the sequence of solution functions defined by the unique solution of the regularized LCP is monotonically increasing and converges to the implicit solution function as the regularization parameter goes do...

The Wolfenstein parametrization of the 3 × 3 Kobayashi-Maskawa (KM) matrix V is modified by keeping its unitarity up to the accuracy of O(λ). This modification can self-consistently lead to the off-diagonal asymmetry of V : |Vij| 2 − |Vji| 2 = Z ∑ k ǫijk with Z ≈ Aλ(1 − 2ρ), which is comparable in magnitude with the Jarlskog parameter of CP violation J ≈ Aλη . We constrain the ranges of J and Z...

A generalized two-dimensional word is a function on Z with a finite number of values. The main problem we are interested in is periodicity of twodimensional words satisfying some local conditions. Let A be a matrix of order n. The function φ : Z → R is a generalized centered function of radius r with the matrix A if ∑ y ∈ Z2 : 0 < |y − x| ≤ r φ(y) = φ(x)A for every x ∈ Z, where for x = (x1, x2)...

This work considers the Real Leja Points Method (ReLPM), [J. Comput. Appl. Math., 172 (2004), pp. 79–99], for the exponential integration of large-scale sparse systems of ODEs, generated by Finite Element or Finite Difference discretizations of 3-D advectiondiffusion models. We present an efficient parallel implementation of ReLPM for polynomial interpolation of the matrix exponential propagato...

Let T be a self-affine tile that is generated by an expanding integral matrix A and a digit set D. It is known that many properties of T are invariant under the Z-similarity of the matrix A. In [LW1] Lagarias and Wang showed that if A is a 2 × 2 expanding matrix with |det(A)| = 2, then the Z-similar class is uniquely determined by the characteristic polynomial of A. This is not true if |det(A)|...

We have implemented a numerical code (ReLPM, Real Leja Points Method) for polynomial interpolation of the matrix exponential propagators exp (∆tA)v and φ(∆tA)v, φ(z) = (exp (z) − 1)/z. The ReLPM code is tested and compared with Krylov-based routines, on large scale sparse matrices arising from the spatial discretization of 2D and 3D advection-diffusion equations.

The role of one-dimensional (I-D) digital FIR lossless matrices in the design of FIR perfect reconstruction QMF banks has been explored in several recent articles. Structures which can realize the complete family of FIR lossless transfer matrices have also been developed, with QMF application in mind. For the case of 2-D QMF banks, the same concept of lossless polyphase matrix has been used to ...

An asymptotic theory for weakly nonlinear, highly oscillatory systems of ordinary differential equations leads to methods which are suitable for accurate computation with large time steps. The theory is developed for systems of the form Z = (A(t)/e)Z + H(Z,t). Z(0, f) = Z„, 0</< 7\0<e« 1, where the diagonal matrix A(t) has smooth, purely imaginary eigenvalues and the components of H(Z, i) are p...