We consider a time discrete kinetic scheme (known as “transport collapse method”) for the inviscid Burgers equation ∂tu+ ∂x u 2 = 0. We prove the convergence of the scheme by using averaging lemmas without bounded variation estimate. Then, the extension of this result to the kinetic model of Brenier and Corrias is discussed.

Aim of this note is to provide a brief outline of the theory of shift-differentials, introduced in [2], and show how their construction can be extended to the case of vector valued functions. In the following, we consider the space BV of scalar integrable functions having bounded variation, endowed with the L norm. We recall that, given a map Φ : X 7→ Y between normed linear spaces, its differe...

Multiple-scale homogenization problems are treated in the space BV of functions of bounded variation, using the notion of multiple-scale convergence developed in [35]. In the case of one microscale Amar’s result [3] is recovered under more general conditions; for two or more microscales new results are obtained. AMS Classification Numbers (2010): 49J45, 35B27, 26A45

We present a very short derivation of the integral representation of the two-sided Skorokhod reflection Z of a continuous function X of bounded variation, which is a generalization of the integral representation of the one-sided map featured in [1, 4]. We also show that Z satisfies a simpler integral representation when additional conditions are imposed on X.

What is cryptic genetic variation? Cryptic genetic variation refers to unexpressed, bottled-up genetic potential. It is not normally seen, but is expressed under abnormal conditions such as in a new environment or a different genetic background. In a sense, the measurable component of normal variation is just the tip of an iceberg of genetic possibilities that are hidden below the visible surface.

A frequency-dependent selection model proposed by Huang, Singh and Kojima (1971) was found to be more effective at maintaining genetic variation in a finite population than the overdominant model. The fourth moment parameter of the distribution of unfixed states showed that there was a more platykurtic distribution for the frequency-dependent model. This agreed well with the expected gene frequ...