Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.

Existence Theorems for Non-Cooperative Elliptic Systems

2010 Mathematics Subject Classification: 35J65, 35K60, 35B05, 35R05.

Zenith angle distributions at Super-Kamiokande and SNO and the solution of the solar neutrino problem

We have performed a detailed study of the zenith angle dependence of the regeneration factor and distributions of events at SNO and SK for different solutions of the solar neutrino problem. In particular, we discuss the oscillatory behavior and the synchronization effect in the distribution for the LMA solution, the parametric peak for the LOW solution, etc. A physical interpretation of the effects is given. We suggest a new binning of events which emphasizes the distinctive features of the zenith angle distributions for the different solutions. We also find the correlations between the integrated day-night asymmetry and the rates of events in different zenith angle bins. The study of these correlations strengthens the identification power of the analysis.

Branch and price solution approach for order acceptance and capacity planning in make -to -order operations

The increasing emphasis on mass customization, shortened product lifecycles, synchronized supply chains, when coupled with advances in information system, is driving most firms towards make-to-order (MTO) operations. Increasing global competition, lower profit margins, and higher customer expectations force the MTO firms to plan its capacity by managing the effective demand. The goal of this research was to maximize the operational profits of a make-to-order operation by selectively accepting incoming customer orders and simultaneously allocating capacity for them at the sales stage. ^ For integrating the two decisions, a Mixed-Integer Linear Program (MILP) was formulated which can aid an operations manager in an MTO environment to select a set of potential customer orders such that all the selected orders are fulfilled by their deadline. The proposed model combines order acceptance/rejection decision with detailed scheduling. Experiments with the formulation indicate that for larger problem sizes, the computational time required to determine an optimal solution is prohibitive. This formulation inherits a block diagonal structure, and can be decomposed into one or more sub-problems (i.e. one sub-problem for each customer order) and a master problem by applying Dantzig-Wolfe’s decomposition principles. To efficiently solve the original MILP, an exact Branch-and-Price algorithm was successfully developed. Various approximation algorithms were developed to further improve the runtime. Experiments conducted unequivocally show the efficiency of these algorithms compared to a commercial optimization solver.^ The existing literature addresses the static order acceptance problem for a single machine environment having regular capacity with an objective to maximize profits and a penalty for tardiness. This dissertation has solved the order acceptance and capacity planning problem for a job shop environment with multiple resources. Both regular and overtime resources is considered. ^ The Branch-and-Price algorithms developed in this dissertation are faster and can be incorporated in a decision support system which can be used on a daily basis to help make intelligent decisions in a MTO operation.^

Branch and Price Solution Approach for Order Acceptance and Capacity Planning in Make-to-Order Operations

The increasing emphasis on mass customization, shortened product lifecycles, synchronized supply chains, when coupled with advances in information system, is driving most firms towards make-to-order (MTO) operations. Increasing global competition, lower profit margins, and higher customer expectations force the MTO firms to plan its capacity by managing the effective demand. The goal of this research was to maximize the operational profits of a make-to-order operation by selectively accepting incoming customer orders and simultaneously allocating capacity for them at the sales stage. For integrating the two decisions, a Mixed-Integer Linear Program (MILP) was formulated which can aid an operations manager in an MTO environment to select a set of potential customer orders such that all the selected orders are fulfilled by their deadline. The proposed model combines order acceptance/rejection decision with detailed scheduling. Experiments with the formulation indicate that for larger problem sizes, the computational time required to determine an optimal solution is prohibitive. This formulation inherits a block diagonal structure, and can be decomposed into one or more sub-problems (i.e. one sub-problem for each customer order) and a master problem by applying Dantzig-Wolfe’s decomposition principles. To efficiently solve the original MILP, an exact Branch-and-Price algorithm was successfully developed. Various approximation algorithms were developed to further improve the runtime. Experiments conducted unequivocally show the efficiency of these algorithms compared to a commercial optimization solver. The existing literature addresses the static order acceptance problem for a single machine environment having regular capacity with an objective to maximize profits and a penalty for tardiness. This dissertation has solved the order acceptance and capacity planning problem for a job shop environment with multiple resources. Both regular and overtime resources is considered. The Branch-and-Price algorithms developed in this dissertation are faster and can be incorporated in a decision support system which can be used on a daily basis to help make intelligent decisions in a MTO operation.

Transiting exoplanets from the CoRoT space mission XIII. CoRoT-13b: a dense hot Jupiter in transit around a star with solar metallicity and super-solar lithium content

We announce the discovery of the transiting planet CoRoT-13b. Ground-based follow-up in CFHT and IAC80 confirmed CoRoT's observations. The mass of the planet was measured with the HARPS spectrograph and the properties of the host star were obtained analyzing HIRES spectra from the Keck telescope. It is a hot Jupiter-like planet with an orbital period of 4.04 days, 1.3 Jupiter masses, 0.9 Jupiter radii, and a density of 2.34 g cm(-3). It orbits a G0V star with T(eff) = 5 945 K, M(*) = 1.09 M(circle dot), R(*) = 1.01 R(circle dot), solar metallicity, a lithium content of +1.45 dex, and an estimated age of between 0.12 and 3.15 Gyr. The lithium abundance of the star is consistent with its effective temperature, activity level, and age range derived from the stellar analysis. The density of the planet is extreme for its mass, implies that heavy elements are present with a mass of between about 140 and 300 M(circle plus).

Novel and facile solution-phase synthesis of 2,5-diketopiperazines and O-glycosylated analogs

This work describes the synthesis in Solution of a series of related diketopiperazines with potential biological activities: cyclo(L-Pro-L-Ser), cyclo(L-Phe-L-Ser), cyclo(D-Phe-L-Ser) and the corresponding glycosylated analogs of the latter, cyclo[D-Phe-L-Ser(alpha GlcNAc)] and cyclo[D-Phe-L-Ser(beta GlcNAc)]. The synthetic approach involved coupling reactions of -OH or O-glycosylated serine benzyl esters with NFmoc-protected amino acids (Pro or Phe), followed by one-pot deprotection-cyclization reaction in the presence of 20% piperidine in DMF. (C) 2009 Elsevier Ltd. All rights reserved.

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

Quantum integrability is established for the one-dimensional supersymmetric U model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric U chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system. [S0163-1829(98)00425-1].

Influence of Mg content on the microstructure and solid solution chemistry of Al-7%Si-Mg casting alloys during solution treatment

The solution treatment stage of the T6 heat-treatment of Al-7%Si-Mg foundry alloys influences microstructural features such as Mg2Si dissolution, and eutectic silicon spheroidisation and coarsening. Microstructural and microanalytical studies have been conducted across a range of Sr-modified Al-7%Si alloys, with an Fe content of 0.12% and Mg contents ranging from 0.3-0.7wt%. Qualitative and quantitative metallography have shown that, in addition to the above changes, solution treatment also results in changes to the relative proportions of iron-containing intermetallic particles and that these changes are composition-dependent. While solution treatment causes a substantial transformation of pi phase to beta phase in low Mg alloys (0.3-0.4%), this change is not readily apparent at higher Mg levels (0.6-0.7%). The pi to beta transformation is accompanied by a release of Mg into the aluminum matrix over and above that which arises from the rapid dissolution of Mg2Si. Since the level of matrix Mg retained after quenching controls an alloy's subsequent precipitation hardening response, a proper understanding of this phase transformation is crucial if tensile properties are to be maximised.

Integrability and exact solution of an electronic model with long range interactions

We present an electronic model with long range interactions. Through the quantum inverse scattering method, integrability of the model is established using a one-parameter family of typical irreducible representations of gl(211). The eigenvalues of the conserved operators are derived in terms of the Bethe ansatz, from which the energy eigenvalues of the Hamiltonian are obtained.

Integrability and exact solution for coupled BCS systems associated with the su(4) Lie algebra

We introduce an integrable model for two coupled BCS systems through a solution of the Yang-Baxter equation associated with the Lie algebra su(4). By employing the algebraic Bethe ansatz, we determine the exact solution for the energy spectrum. An asymptotic analysis is conducted to determine the leading terms in the ground state energy, the gap and some one point correlation functions at zero temperature. (C) 2002 Published by Elsevier Science B.V.

Attributes of irrigated rice and soil solution as affected by salinity levels of the water layer

In the State of Rio Grande do Sul, Brazil, flooded rice fields using Patos Lagoon as the source of water for irrigation are subject to be damaged by salinity, since this source is bound to the sea on its southern end. The sensitivity of rice is variable during plant development, being higher in the seedling and reproductive periods. However, there is not enough information about the behavior of plants under salt stress during the course of its development, especially in the vegetative stage. This study evaluated the effect of different levels of salinity of irrigation water on the salinity of soil solution over time and on some plant attributes, during the vegetative stage of rice. The study was conducted in a greenhouse, where seeds of the variety IRGA 424 were sown in pots and irrigated with water with electrical conductivity (ECi) levels of: 0.3, 0.75, 1.5, 3.0 and 4.5 dS m-1; from the tillering initiation (V4) until the panicle initiation (PI). The evaluations made were the electrical conductiviy of soil solution (ECe), the dry biomass of plants and stems, tillering, height and the transpiration of plants. The ECe increased with the ECi over time, and was determined by water transpiration flux in pots. The ECe values at the end of the experiment were high and, in most cases, higher than the critical values for flooded rice. The growth attributes of rice were negatively affected from ECi of 2.0 dS m-1 and ECe of 4.0 dS m-1.

Monitoring the clinical introduction of a glutamine and antioxidant solution in critically ill trauma and burn patients

OBJECTIVE: Enteral glutamine supplementation and antioxidants have been shown to be beneficial in some categories of critically ill patients. This study investigated the impact on organ function and clinical outcome of an enteral solution enriched with glutamine and antioxidant micronutrients in patients with trauma and with burns. METHODS: This was a prospective study of a historical control group including critically ill, burned and major trauma patients (n = 86, 40 patients with burns and 46 with trauma, 43 in each group) on admission to an intensive care unit in a university hospital (matching for severity, age, and sex). The intervention aimed to deliver a 500-mL enteral solution containing 30 g of glutamine per day, selenium, zinc, and vitamin E (Gln-AOX) for a maximum of 10 d, in addition to control treatment consisting of enteral nutrition in all patients and intravenous trace elements in all burn patients. RESULTS: Patients were comparable at baseline, except for more inhalation injuries in the burn-Gln-AOX group (P = 0.10) and greater neurologic impairment in the trauma-Gln-AOX group (P = 0.022). Intestinal tolerance was good. The full 500-mL dose was rarely delivered, resulting in a low mean glutamine daily dose (22 g for burn patients and 16 g for trauma patients). In burn patients intravenous trace element delivery was superior to the enteral dose. The evolution of the Sequential Organ Failure Assessment score and other outcome variables did not differ significantly between groups. C-reactive protein decreased faster in the Gln-AOX group. CONCLUSION: The Gln-AOX supplement was well tolerated in critically ill, injured patients, but did not improve outcome significantly. The delivery of glutamine below the 0.5-g/kg recommended dose in association with high intravenous trace element substitution doses in burn patients are likely to have blunted the impact by not reaching an efficient treatment dose. Further trials testing higher doses of Gln are required.

Critical values of nitrogen indices in tomato plants grown in soil and nutrient solution determined by different statistical procedures

The objective of this study was to establish critical values of the N indices, namely soil-plant analysis development (SPAD), petiole sap N-NO3 and organic N in the tomato leaf adjacent to the first cluster (LAC), under soil and nutrient solution conditions, determined by different statistical approaches. Two experiments were conducted in randomized complete block design with four repli-cations. Tomato plants were grown in soil, in 3 L pot, with five N rates (0, 100, 200, 400 and 800 mg kg-1) and in solution at N rates of 0, 4, 8, 12 and 16 mmol L-1. Experiments in nutrient solution and soil were finished at thirty seven and forty two days after transplanting, respectively. At those times, SPAD index and petiole sap N-NO3 were evaluated in the LAC. Then, plants were harvested, separated in leaves and stem, dried at 70ºC, ground and weighted. The organic N was determined in LAC dry matter. Three statistical procedures were used to calculate critical N values. There were accentuated discrepancies for critical values of N indices obtained with plants grown in soil and nutrient solution as well as for different statistical procedures. Critical values of nitrogen indices at all situations are presented.

Multidata inverse problems and Bayesian solution methods in astronomy

Statistical analyses of measurements that can be described by statistical models are of essence in astronomy and in scientific inquiry in general. The sensitivity of such analyses, modelling approaches, and the consequent predictions, is sometimes highly dependent on the exact techniques applied, and improvements therein can result in significantly better understanding of the observed system of interest. Particularly, optimising the sensitivity of statistical techniques in detecting the faint signatures of low-mass planets orbiting the nearby stars is, together with improvements in instrumentation, essential in estimating the properties of the population of such planets, and in the race to detect Earth-analogs, i.e. planets that could support liquid water and, perhaps, life on their surfaces. We review the developments in Bayesian statistical techniques applicable to detections planets orbiting nearby stars and astronomical data analysis problems in general. We also discuss these techniques and demonstrate their usefulness by using various examples and detailed descriptions of the respective mathematics involved. We demonstrate the practical aspects of Bayesian statistical techniques by describing several algorithms and numerical techniques, as well as theoretical constructions, in the estimation of model parameters and in hypothesis testing. We also apply these algorithms to Doppler measurements of nearby stars to show how they can be used in practice to obtain as much information from the noisy data as possible. Bayesian statistical techniques are powerful tools in analysing and interpreting noisy data and should be preferred in practice whenever computational limitations are not too restrictive.