Abstract. We report a new analytical method for solution of a wide class of second-order differential equations with eigenvalues replaced by arbitrary functions. This approach is based on the extension of the previously reported differential transfer matrix method with modified basis functions. Applications of the method to boundary value and initial value problems, as well as several examples ...

Symmetry properties of the Green function in magnetic multilayers with noncollinear magnetization of the layers are investigated on the basis of the transfer matrix method. The Green function symmetric with respect to permutation of its arguments is constructed. It is shown how the boundary conditions can be imposed on this Green function.

We introduce some new classes of words and permutations characterized by the second difference condition π(i − 1) + π(i + 1) − 2π(i) ≤ k, which we call the k-convexity condition. We demonstrate that for any sized alphabet and convexity parameter k, we may find a generating function which counts k-convex words of length n. We also determine a formula for the number of 0-convex words on any fixed...

We study the transmission of electromagnetic waves propagating in three-dimensional disordered photonic crystals that are periodic on the average with a diamond symmetry. The transmission has been calculated using the transfer matrix method. We study two different geometries for the scatterers: spheres and rods connecting nearest neighbors. We find that the gaps of the periodic structure surviv...

C. F. Huang, S. D. Chao, and D. R. Hang 1Department of Physics, National Taiwan University, Taipei, Taiwan, R. O. C. 2National Measurement Laboratory, Center for Measurement Standards, Industrial Technology Research Institute, Hsinchu, Taiwan 300, R. O. C. 3 Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan, R. O. C. 4 Department of Materials Science and Optoelectronic ...

Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper covers the design and implementation of such algorithms. A host of general techniques for improving efficiency are described. Three quite different example prob...

We propose a new fast numerical renormalization group method, the corner transfer matrix renormalization group (CTMRG) method, which is based on a unified scheme of Baxter's corner transfer matrix method and White's density matrix renormalization group method. The key point is that a product of four corner transfer matrices coincides with the density matrix. We formulate the CTMRG method as a r...