In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure li...

Key Laboratory of Materials Physics and Anhui Key Laboratory of Nanomaterials and Nanotechnology, Institute of Solid State Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, 230031, China, Department of Materials Science and Engineering, University of Science and Technology of China, Hefei, 230026, China, Institute for Renewable Energy and Environmental Technolog...

In this article, we consider two models of directed polymers in random environment: a discrete model in a general random environment and a continuous model. We consider these models in dimension greater or equal to 3 and we suppose that the normalized partition function is bounded in L (the ”high” temperature case). Under these assumptions, Sinai proved in [11] a local limit theorem for the dis...

A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by ...

In order to determine the optimum rate of Vigna sun-hum seed sowing for rangeland rehabilitation in sandy soil of North Kordofan, Sudan, two trials were conducted separately under managed and unmanaged conditions at El-obeid Agricultural Research Farm in Sheikan locality of North Kordofan State in 2015 and 2016. Seed rates were 1, 2, 3, 4 and 5 Kg/feddan (4200m) and arranged by a Completely Ran...

The study aims to investigate wind effects on the equal area and same height building model having plan cross-sectional shape in form of regular irregular bulidings. ratio modification is kept for shaped models because limited studies are available such type comparison. responses structure resist load increased by applying these modifications corner configuration as cut, chamfer, fillet structu...