We produced a set of pseudoisochromatic plates for determining individual color-difference thresholds to assess test performance and test properties, and analyzed the results. We report a high test validity and classification ability for the deficiency type and severity level [comparable to that of the fourth edition of the Hardy-Rand-Rittler (HRR) test]. We discuss changes of the acceptable ch...

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The goal of this paper is to give some information about the following question, posed by Andreas Weiermann (private communication). Is it true that for every β, γ < ε0 there exist α so that whenever A is α–large, A satisfies some inessential assumption, say min(A) ≥ 2, and G : A → β is such that ∀a ∈ A psn(G(a)) ≤ a there must exist γ–large C ⊆ A on which G is nondecreasing. Here ε0 is the sma...

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...

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,...

this study was carried out to investigate the genetic diversity and population structure of 90 specimens of oxynoemacheilus argyrogramma collected from sepidbarg, gamasiab and ghaleji rivers, in the west of iran. analyses using three microsatellite loci indicated that the average number of alleles in the population was 12, which was well above the reported values for freshwater fishes. the expe...