Homogenization of low-cost control problems on perforated domains

AbstractThe aim of this paper is to study the asymptotic behaviour of some low-cost control problems in periodically perforated domains with Neumann condition on the boundary of the holes. The optimal control problems considered here are governed by a second order elliptic boundary value problem with oscillating coefficients. It is assumed that the cost of the control is of the same order as that describing the oscillations of the coefficients. The asymptotic analysis of small cost problem is more delicate and need the H-convergence result for weak data. In this connection, an H-convergence result for weak data under some hypotheses is also proved

Selection of culture medium and conditions for the production of selenium enriched Saccharomyces cerevisiae

Selenium (Se) yeast is a recognized source of organic food-form of Se and it plays a vital role in animal and human nutrition. The organic Se supplementation in the form of yeast has been shown to have beneficial effects on growth, immune status and reproduction in many animal species, thereby improving the productivity and economical benefits in livestock production. Subsequently, strategies to supplement animal feeds with Se yeast have led to the development of industrial production of Se yeast. The aim of the present study was to improve the yeast biomass production measured as dry cell weight (DCW) and Se enrichment of yeast cells through optimization of the culture conditions and culture media. The culture conditions were optimized by the shake flask experiments. Maximum cell density (2.93 g/LDCW) was observed at pH 5 to 5.5, at 30 °C (2.88 g/L DCW). Significantly higher DCW was recorded when glucose was used as the carbon source (3.09 g/L DCW). The media optimization study carried out in fermentors with five different media (defined medium–A, defined medium-B, synthetic medium, rich medium and industrial medium) showed that the synthetic medium yielded maximum yeast biomass (12.8 g/LDCW) followed by rich medium (11.7 g/L DCW) and defined medium B (10.5 g/LDCW). The Se accumulation was also significantly higher in synthetic medium (2718.3 ppm), followed by industrial medium (2457.7 ppm) and defined medium-B (2251.3 ppm). The methylene blue reduction time (MBRT) was very high ( >15 m) in synthetic medium indicating the highest accumulation of organically bound Se, and MBRT was moderate for defined medium-A and industrial medium ( <10 m).Keywords: Saccharomyces cerevisiae, synthetic medium, carbon source, selenium enrichment, methylene blue reduction time (MBRT)African Journal of Biotechnology Vol. 12(20), pp. 2972-297

Low-cost control problems on perforated and non-perforated domains

We study the homogenization of a class of optimal control problems whose state equations are given by second order elliptic boundary value problems with oscillating coefficients posed on perforated and non-perforated domains. We attempt to describe the limit problem when the cost of the control is also of the same order as that describing the oscillations of the coefficients. We study the situations where the control and the state are both defined over the entire domain or when both are defined on the boundary

Role of edaphic factors on VAM fungal colonization and Spore populations in certain tropical wild legumes

Four nodulating annual tropical wild legumes, viz., Alysicarpus monilifer, Desmodium triflorum, Indigofera linnaei and Tephrosia purpurea from three different regions in the Western Ghats ecosystem were investigated to assess their mycorrhizal status. The response ofvesicular-arbuscular mycorrhizal (VAM) root colonization and spore number to edaphicfactors such as soil moisture, pH and available Nand P was analysed. Though the spore number varied significantly both within and between sites, a uniformly high degree ofroot colonization was observed for all the plants in the present study. The spore number recorded was high, rangingfrom 15 to 165 spores gl soil. Spores of sixteen VAM fungal species belonging to Acaulospora, Glomus and Scutellospora were isolated from the rhizosphere soils. Soil moisture generally had a positive influence on VAM colonization and sporulation except in I. linnaei. The pH correlated negatively with root infection in I. linnaei and T. purpurea, but had no influence in the other two species. The effect of 2-pH on sporulation varied with host species and sites. No general correlation existed between available soil nutrients, root colonization and spore number but the influence ofNand P was counteractive on VAM infection. The present study indicates that the response of root colonization and spore number to edaphic factors is a localised rather than a generalised phenomenon

Quasiparticles as composite objects in the RVB superconductor

We study the nature of the superconducting state, the origin of d-wave pairing, and elementary excitations of a resonating valence bond (RVB) superconductor. We show that the phase string formulation of the t-J model leads to confinement of bare spinon and holon excitations in the superconducting state, though the vacuum is described by the RVB state. Nodal quasiparticles are obtained as composite excitations of spinon and holon excitations. The d-wave pairing symmetry is shown to arise from short range antiferromagnetic correlations

Polymers pushing Polymers: Polymer Mixtures in Thermodynamic Equilibrium with a Pore

We investigate polymer partitioning from polymer mixtures into nanometer size cavities by formulating an equation of state for a binary polymer mixture assuming that only one (smaller) of the two polymer components can penetrate the cavity. Deriving the partitioning equilibrium equations and solving them numerically allows us to introduce the concept of "polymers-pushing-polymers" for the action of non-penetrating polymers on the partitioning of the penetrating polymers. Polymer partitioning into a pore even within a very simple model of a binary polymer mixture is shown to depend in a complicated way on the composition of the polymer mixture and/or the pore-penetration penalty. This can lead to enhanced as well as diminished partitioning, due to two separate energy scales that we analyse in detail.Comment: 10 pages, 6 figure

Efficient Set Sharing Using ZBDDs

Set sharing is an abstract domain in which each concrete object is represented by the set of local variables from which it might be reachable. It is a useful abstraction to detect parallelism opportunities, since it contains definite information about which variables do not share in memory, i.e., about when the memory regions reachable from those variables are disjoint. Set sharing is a more precise alternative to pair sharing, in which each domain element is a set of all pairs of local variables from which a common object may be reachable. However, the exponential complexity of some set sharing operations has limited its wider application. This work introduces an efficient implementation of the set sharing domain using Zero-suppressed Binary Decision Diagrams (ZBDDs). Because ZBDDs were designed to represent sets of combinations (i.e., sets of sets), they naturally represent elements of the set sharing domain. We show how to synthesize the operations needed in the set sharing transfer functions from basic ZBDD operations. For some of the operations, we devise custom ZBDD algorithms that perform better in practice. We also compare our implementation of the abstract domain with an efficient, compact, bit set-based alternative, and show that the ZBDD version scales better in terms of both memory usage and running time

Spontaneous breaking of the Fermi surface symmetry in the t-J model: a numerical study

We present a variational Monte Carlo (VMC) study of spontaneous Fermi surface symmetry breaking in the t-J model. We find that the variational energy of a Gutzwiller projected Fermi sea is lowered by allowing for a finite asymmetry between the x- and the y-directions. However, the best variational state remains a pure superconducting state with d-wave symmetry, as long as the underlying lattice is isotropic. Our VMC results are in good overall agreement with slave boson mean field theory (SBMFT) and renormalized mean field theory (RMFT), although apparent discrepancies do show up in the half-filled limit, revealing some limitations of mean field theories. VMC and complementary RMFT calculations also confirm the SBMFT predictions that many-body interactions can enhance any anisotropy in the underlying crystal lattice. Thus, our results may be of consequence for the description of strongly correlated superconductors with an anisotropic lattice structure.Comment: 6 pages, 7 figures; final versio

Response of Siratro (Macroptilium atropurpureum Urb. Rabaceae) to Vesicular-arbuscular Mycorrhizal Fungi and Rhizobium sp. in Sterilized Soil

The effect of inoculation of six species of vesicular-arbuscular mycorrhizal fungi viz., Gigaspora margarita, Glomus mosseae, G. monosporum, G. versiformis, G. fasciculatum, G. deserticola and Rhizobium sp. on growth and NPK content in siratro (Macroptilium atropurpureum) was studied. The mycorrhizal species were isolated from the rhizosphere forest soils of the Western Ghats and multiplied in pot culture with Sorghum bicolor as the host plant. Rhizobium sp. isolated from fresh nodules of siratro was cultured and maintained in yeast extract mannitol broth. The influence of VAM fungi and Rhizobium sp. either singly or in combination on growth and nutrient contents of siratro showed statistically significant increase after only 60 days of plant growth. Dual inoculation with VAM fungi and Rhizobium increased plant nodule number and tissue NPK content. Highest growth and nutrient content were exhibited by plants inoculated with Rhizobium together with multiple VAM fungi