Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise

A Wentzell-Freidlin type large deviation principle is established for the two-dimensional Navier-Stokes equations perturbed by a multiplicative noise in both bounded and unbounded domains. The large deviation principle is equivalent to the Laplace principle in our function space setting. Hence, the weak convergence approach is employed to obtain the Laplace principle for solutions of stochastic Navier-Stokes equations. The existence and uniqueness of a strong solution to (a) stochastic Navier-Stokes equations with a small multiplicative noise, and (b) Navier-Stokes equations with an additional Lipschitz continuous drift term are proved for unbounded domains which may be of independent interest. © 2006 Elsevier Ltd. All rights reserved

On the grid generation methods in harmonic mapping on plane and curved surfaces

Harmonic grid generation methods for multiply connected plane regions and regions on curved surfaces are discussed. In particular, using a general formulation on an analytic Riemannian manifold, it is proved that these mappings are globally one-to-one and onto

Conditional value-at-risk for water management in Lake Burley Griffin

Copyright © Australian Mathematical SocietyAs the centrepiece of Canberra, Lake Burley Griffin provides the setting for buildings of national importance and a venue for aquatic recreation while, as part of the Molonglo River, the lake has a role in the ecological processes of its broader setting. For the purposes of recreation and landscape a constant water level is preferred: the management plan requires the lake to be maintained at a prescribed normal level. In years of low rainfall this requirement could conflict with the water demands of other users. Episodes of high rainfall may also require compromise between competing objectives. For example, drawdown of lake levels for flood mitigation could impact on the lake's recreational and amenity values and the spill may not be a good use of water. Conditional Value at Risk, a risk measure developed by the financial industry for portfolio management, is defined as the expected loss given that some loss threshold is exceeded. Here, Conditional Value at Risk is applied as decision support for strategic planning and day-to-day operational problems in the hydraulic management of Lake Burley Griffin.R. B. Webby, J. Boland, P. G. Howlett, A. V. Metcalfe, T. Srithara

Recognition of some perfectly orderable graph classes

AbstractThis paper presents new algorithms for recognizing several classes of perfectly orderable graphs. Bipolarizable and P4-simplicial graphs are recognized in O(n3.376) time, improving the previous bounds of O(n4) and O(n5), respectively. Brittle and semi-simplicial graphs are recognized in O(n3) time using a randomized algorithm, and O(n3log2n) time if a deterministic algorithm is required. The best previous time bound for recognizing these classes of graphs is O(m2). Welsh–Powell opposition graphs are recognized in O(n3) time, improving the previous bound of O(n4). HHP-free graphs and maxibrittle graphs are recognized in O(mn) and O(n3.376) time, respectively

Tailoring of Abiotic Stress Adaptive Traits to Diminish the Eff ect of Changing Climate on Crop Productivity

The world population is likely to exceed 10 billion by 2050, thereby increasing food, feed and fuel production demand. On the other hand, global climate change (drought, heat, salinity, elevated CO2 and extreme cold) hostile the global agricultural productions. The changes in climatic factors perhaps influence the crop distribution, affect the crop growth and yield, and increase the risks of farming and human health consequences in developing countries. Crop breeding is one of the approaches to fight environmental challenges in agriculture. Available literatures imply that genotypes of different crop species are expressing greater phenotypic variability to tolerate abiotic stresses by inherent constitutional. Hence, there is an opportunity for utilizing the existing variability in abiotic stress tolerance traits. The gene sources for abiotic tolerance are available in germplasm collection, landraces, or wild relatives, if not, with less frequency it can be created as transgenes, so moclones or mutants. However, to make significant advancement in abiotic stress breeding requires accurate and reproducible phenotyping under well-imposed stress environment. The targeted trait for abiotic stress tolerance should have high positive correlation with yield attributes and be amenable for scoring in given environment. The traits introgressed for abiotic stress tolerance vary with stress scenario, timing and intensity of stress encountered by the crop species. Most of the traits that confer abiotic stress tolerance are quantitative in nature. The conventional crop improvement strategy followed to transfer abiotic stress tolerance is by recurrent selection and backcross breeding, which delivered limited success. The recent advancement through rapid and high-throughput phenotyping and genotyping have given much hope for tailoring desirable traits to evolve climate-resilient cultivars. The gene pyramiding strategy is useful to accumulate desirable abiotic tolerant traits into a commercially preferred cultivar. Further, transgenic and double haploid approaches will help in accelerating the trait pyramiding strategy. The climate-resilient cultivars with climate-smart farming will offer sustainable and cost-effective solution to the changing agro-climatic situations

Agricultural bio-waste recycling through efficient microbial consortia

In India and other countries, rice straw, a byproduct of rice production, is burned in enormous amounts, which contributes to environmental pollution and climate change by releasing greenhouse gases viz., CO2, N2O, CH4, into the atmosphere. This study aimed to accelerate the degradation of this enormous amount of agricultural biomass via microbial inoculants. Four treatments—rice straw (RS), rice straw plus water (RSW), rice straw plus water plus Pusa decomposer (RSWF), and rice straw plus water plus Tamil Nadu Agricultural University (TNAU) biomineralizer (RSWB) were used in the current investigation. The study's findings demonstrated that rice straw treated with microorganisms decomposed more quickly than RS and RSW treatments. According to EDAX spectra of elemental composition, the carbon content of rice straw in the RS, RSW, RSWF, and RSWB treatments was 33.66%, 29.75%, 13.33%, and 20.65% w/w, respectively. The RSWF treatment of rice straw was found to have the highest nitrogen concentration (0.64% w/w), followed by RSWB (0.61% w/w), RSW (0.45%) w/w, and RS (0.43% w/w). Treatments RSWF and RSWB had lower C/N ratios 20.83, and 33.85, respectively, than that RSW (66.11) and RS (78.28). The RSWF and RSWB treatments' porous, distorted, and rough surface structures provided further evidence that both microbial consortia could decompose rice straw more quickly than the RSW and RS treatments. Therefore, the results of this study imply that rice straw could be added to the soil to improve soil fertility for sustainable crop production rather than being burned

Effect of different herbicide spray volumes on weed control efficiency of a battery-operated Unmanned aerial vehicle sprayer in transplanted rice (Oryza sativa L.)

The effect of spray volume on weed control in transplanted rice ecosystems using the Unmanned aerial vehicle (UAV) needs to be better understood for management in the advancements of UAV-based spraying technology. The present study aimed to find out the influence of varied spray volumes of 15 L/ha, 20 L/ha and 25 L/ha using the UAV and 500 L/ha using a Knapsack sprayer (KS) to compare the weed density, weed dry matter and weed control efficiency and yield in transplanted rice (Oryza sativa L.). Pre-emergence (PE) application of Pyrazosulfuron-ethyl at 25 g a.i./ha at three days after transplanting (DAT) and post-emergence (PoE) application of Bis-pyribac sodium at 25 g a.i./ha at 25 DAT were used as herbicide treatments. The results revealed that varied spray volumes significantly influenced the weed density, dry matter, and weed control efficiency of the UAV and KS. Application of herbicides using KS (500 L/ha) and UAV (25 L/ha) had better control on the weeds by reducing weed density and dry matter at 20, 40, and 60 DAT, with no significant difference. Higher grain yield and straw yield were recorded in KS (500 L/ha) and UAV (25 L/ha), with no significant difference. However, applying 25 L/ha had better weed control efficiency and higher yield, possibly due to optimum deposition. Considering the low volume application of UAV (25 L/ha) as compared with KS (500 L/ha), it is better to go for the optimal application of 25 L/ha, which is an energy-efficient and cost-effective, labour-saving approach compared to KS