We treat the lattice sine-Gordon equation and two of its generalised symmetries as a compatible system. Elimination shifts from yields an integrable NLS-type An auto-Bäcklund transformation superposition formula for system is obtained by elimination down-shifted version. use formulae to calculate three elementary solutions.

We propose a wavefront measurement method based on Talbot effect. It is well known that the wavefront of large aperture long focal lens is difficult to be measured. Here a new method for wavefront measurement of large aperture long focal lens is presented, which is accomplished by fitting the slope of sub-wavefront in the whole aperture while the sub-wavefront slope is got by calculating the sh...

In this paper a univariate discrete distribution, denoted by GIT, is proposed as a generalization of the shifted inverse trinomial distribution, and is formulated as a first-passage time distribution of amodified randomwalk on the half-plane with five transition probabilities. In contrast, the inverse trinomial arises as a random walk on the real line with three transition probabilities. The pr...

The Laplacian of an undirected graph is a square matrix, whose eigenvalues yield important information. We can regard graphs as one-dimensional simplicial complexes, and as whether there is a generalisation of the Laplacian operator to simplicial complexes. It turns out that there is, and that is useful for calculating real Betti numbers [8]. Duval and Reiner [5] have studied Laplacians of a sp...

We propose a wavefront measurement method based on Talbot effect. It is well known that the wavefront of large aperture long focal lens is difficult to be measured. Here a new method for wavefront measurement of large aperture long focal lens is presented, which is accomplished by fitting the slope of sub-wavefront in the whole aperture while the sub-wavefront slope is got by calculating the sh...

A recursion due to Kook expresses the Laplacian eigenvalues of a matroid M in terms of the eigenvalues of its deletion M−e and contraction M/e by a fixed element e, and an error term. We show that this error term is given simply by the Laplacian eigenvalues of the pair (M−e, M/e). We further show that by suitably generalizing deletion and contraction to arbitrary simplicial complexes, the Lapla...

We study the mean square weighted L2 discrepancy of randomized digital (t,m, s)nets over Zp. The randomization method considered here is a digital shift of depth m, i.e., for each coordinate the first m digits of each point are shifted by the same shift whereas the remaining digits in each coordinate are shifted independently for each point. We also consider a simplified version of this shift. ...