In this paper, we provide a blow-up mechanism to the modified Camassa-Holm equation with varying linear dispersion. We first consider the case when linear dispersion is absent and derive a finite-time blow-up result with an initial data having a region of mild oscillation. A key feature of the analysis is the development of the Burgers-type inequalities with focusing property on characteristics...

Exponential dispersion models, which are linear exponential families with a dispersion parameter, are the prototype response distributions for generalized linear models. The Tweedie families are those exponential dispersion models with power mean-variance relationships. The normal, Poisson, gamma and inverse Gaussian distributions are Tweedie families. Apart from these special cases, Tweedie di...

For off-zenith observations with ground-based astronomical telescopes, the effect of atmospheric dispersion relative to diffraction on image size increases with telescope diameter. Correction of atmospheric dispersion in extremely large telescopes (ELTs) might become critical. A common solution for ELTs is to use linear atmospheric dispersion correctors (ADCs). In spite of their simplicity, the...

The authors investigate the design of linear dispersion (LD) codes, aiming at flexible encoding schemes that allow various rate–performance tradeoffs under a common coding structure. First, the capacity of LD codes is studied. It is shown that the maximum attainable multiplexing gain of a linear dispersion code is the number of symbols per channel use of the code (i.e. coding rate in symbols). ...

A fully analytic method for computing gradients of dispersion (to any order) for a dielectric multilayer coating is developed, and it is demonstrated how group delay gradients can be used to optimize the dispersion of such a filter. The algorithm complexity is linear with the number of layers and quadratic in dispersion order. To our knowledge, this is the first published algorithm for computin...

In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to linear network error correction coding, i.e., linear network error correction multicast/broadcast/dispersion codes. We further propose the (weakly, strongly) exte...