Laguerre polynomials as Jensen polynomials of Laguerre-Polya entire functions

We prove that the only Jensen polynomials associated with an entire function in the Laguerre-Polya class that are orthogonal are the Laguerre polynomials. (C) 2009 Elsevier B.V. All rights reserved.

Schur-SzegA composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Swimmer syndrome affecting an entire litter of kittens

Swimmer syndrome is a developmental abnormality characterized by a delay in the ability to walk and move about and is manifested in newborns between 15 and 20 days of age. These animals exhibit constant coxofemoral articulation abduction, and their pelvic limbs move caudally and laterally. This case reports a litter of three crossbreeds kittens (26 days old) with swimmer syndrome. Each animal was treated with physical therapy and shackle bandages that kept their pelvic limbs bent and close to the body. After seven days, all of the animals exhibited normal ambulation, indicating that this treatment had a curative effect on the kittens.

Dynamics of soil exploration by fine roots down to a depth of 10 m throughout the entire rotation in Eucalyptus grandis plantations

Although highly weathered soils cover considerable areas in tropical regions, little is known about exploration by roots in deep soil layers. Intensively managed Eucalyptus plantations are simple forest ecosystems that can provide an insight into the belowground growth strategy of fast-growing tropical trees. Fast exploration of deep soil layers by eucalypt fine roots may contribute to achieving a gross primary production that is among the highest in the world for forests. Soil exploration by fine roots down to a depth of 10 m was studied throughout the complete cycle in Eucalyptus grandis plantations managed in short rotation. Intersects of fine roots, less than 1 mm in diameter, and medium-sized roots, 1-3 mm in diameter, were counted on trench walls in a chronosequence of 1-, 2-, 3.5-, and 6-year-old plantations on a sandy soil, as well as in an adjacent 6-year-old stand growing in a clayey soil. Two soil profiles were studied down to a depth of 10 m in each stand (down to 6 m at ages 1 and 2 years) and 4 soil profiles down to 1.5-3.0 m deep. The root intersects were counted on 224 m(2) of trench walls in 15 pits. Monitoring the soil water content showed that, after clear cutting, almost all the available water stored down to a depth of 7 m was taken up by tree roots within 1.1 year of planting. The soil space was explored intensively by fine roots down to a depth of 3 m from 1 year after planting, with an increase in anisotropy in the upper layers throughout the rotation. About 60% of fine root intersects were found at a depth of more than 1 m, irrespective of stand age. The root distribution was isotropic in deep soil layers and kriged maps showed fine root clumping. A considerable volume of soil was explored by fine roots in eucalypt plantations on deep tropical soils, which might prevent water and nutrient losses by deep drainage after canopy closure and contribute to maximizing resource uses.

Schur-Szegö composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Ordinary fractional differential equations are in fact usual entire ordinary differential equations on time scales

Despite the huge number of works considering fractional derivatives or derivatives on time scales some basic facts remain to be evaluated. Here we will be showing that the fractional derivative of monomials is in fact an entire derivative considered on an appropriate time scale.