This note is devoted to several inequalities deduced from a special form of the logarithmic Hardy-LittlewoodSobolev, which is well adapted to the characterization of stationary solutions of a Keller-Segel system written in self-similar variables, in case of a subcritical mass. For the corresponding evolution problem, such functional inequalities play an important role for identifying the rate o...

Despite our recent commentary on the article by Resende and Weber, the authors still seem to believe that Sir Charles Bell (1774-1842) himself was affected by facial paralysis. They came to this erroneous conclusion from a paper by Jongkees and by “neurological examination of the photograph of Sir Charles Bell” (Fig 1). However, had they taken the effort to check Jongkees’ German translation wi...

In this paper, we reconstruct the Hardy-Littlewood’s inequality byusing the method of the weight coefficient and the technic of real analysis includinga best constant factor. An open problem is raised.

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...

Blood samples of Mazandaran native chickens were collected. A total of 90 genomic DNAs were isolated through optimized and modified salting-out procedure. The samples were used in Polymerase Chain Reaction (PCR) with 20 micro satellite markers. Amplified PCR-products with the markers were separated on 8% denaturing polyacrylamide gel. One locus (MCW216) was monomorphic. According to allele freq...

1. Interpolation inequalities. A classical problem in analysis is to understand how “smoothness” controls norms that measure the “size” of functions. Maz’ya recognized in his classic text on Sobolev spaces the intrinsic importance of inequalities that would refine both Hardy’s inequality and Sobolev embedding. Dilation invariance and group symmetry play an essential role in determining sharp co...

Abstract We consider Hardy inequalities in IRn, n ≥ 3, with best constant that involve either distance to the boundary or distance to a surface of co-dimension k < n, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm. Résumé Nous étudions des inegalités de Hardy dans IRn, n ≥ 3,...

Evolution at a single multiallelic locus under arbitrary weak selection on both fertility and viability is investigated. Discrete, nonoverlapping generations are posited for autosomal and X-linked loci in dioecious populations, but monoecious populations are studied in both discrete and continuous time. Mating is random. The results hold after several generations have elapsed. With an error of ...

Since the foundations of Population Genetics the notion of genetic equilibrium (in close analogy with Classical Mechanics) has been associated with the Hardy-Weinberg (HW) principle and the identification of equilibrium is currently assumed by stating that the HW axioms are valid if appropriate values of χ(2) (p < 0.05) are observed in experiments. Here we show by numerical experiments with the...

In this article we consider some of the ways in which narrative approaches might contribute towards a better understanding of organisational knowledge management. The telling of stories has a long, rich, and varied tradition, stretching back hundreds of years. In the study of organisations, storytelling can be seen as part of a wider field of enquiry, Organisational Discourse, which seeks to as...