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...

The efficacy of neem oil on the mortality, growth and feeding responses of epilachna beetle showed that all the larval instars were susceptible to this oil. The LC50 values were higher at 3 instar and it was lowest on 1 instar. The LT50 values of oil increases proportionately with increasing larval age and with decreasing oil concentration. Neem oil significantly prolonged larval and pupal peri...

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,...

subterranean termites are one of the most important pests of buildings, historic monuments and agricultural crops in some parts of iran. using entomopathogenic fungi as microbial insecticides is usually a part of biological control and insect pest management. the pathogenicity of entomopathogenic fungus, metarhizium anisopliae (metschnikoff) sorokin (demi 001) isolated from rhynchophorus ferrug...

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...

Suppose E is a subset of the unit circle T and H∞ ⊂ L∞ is the Hardy subalgebra. We examine the problem of finding the distance from the characteristic function of E to znH∞. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of...

Student populations are diverse such that different types of learners struggle with traditional didactic instruction. Problem-based learning has existed for several decades, but there is still controversy regarding the optimal mode of instruction to ensure success at all levels of students' past achievement. The present study addressed this problem by dividing students into the following three ...