Painleve Analysis, Lie Symmetries and Integrability of Nonlinear Ordinary Differential Equations

The Painleve analysis plays an important role in investigating local structure of the solutions of differential equations, while Lie symmetries provide powerful tools in global solvability of equations. In this research, the method of Painleve analysis is applied to discrete nonlinear Schrodinger equations and to a family of second order nonlinear ordinary differential equations. Lie symmetries are studied together with the Painleve property for second order nonlinear ordinary differential equations.In the study of the local singularity of discrete nonlinear Schrodinger equations, the Painleve method shows the existence of solution blow up at finite time. It also determines the rate of blow-up. For second order nonlinear ordinary differential equations, the Painleve test is introduced and demonstrated in detail using several examples. These examples are used throughout the research. The Painleve property is shown to be significant for the integrability of a differential equation.After introducing one-parameter groups, a family of differential equations is determined for discussing solvability and for drawing more meaningful conclusions. This is the most general family of differential equations invariant under a given one-parameter group. The first part of this research is the classification of the integrals in the general solutions of differential equations obtained by quadratures. The second part is the application of Riemann surfaces and algebraic curves in the projective complex space to the integrands. The theories of Riemann surfaces and algebraic curves lead us to an effective way to understand the nature of the integral defined on a curve. Our theoretical work then concentrates on the blowing-up of algebraic curves at singular points. The calculation of the genus, which essentially determines the shape of a curve, becomes possible after a sequence of blowing-ups.The research shows that when combining both the Painleve property and Lie symmetries possessed by the differential equations studied in the thesis, the general solutions can be represented by either elementary functions or elliptic integrals

School and teacher variables associated with performance of students in the senior secondary certificate examinations in Ondo State Nigeria

Available from British Library Document Supply Centre-DSC:DXN027716 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

A Novel Magnetoelastic Immunosensor for Ultrasensitively Detecting Carcinoembryonic Antigen

Abstract A novel wireless immunosensor is developed for the ultra-sensitive detection of carcinoembryonic antigen. The optimum dimension of the microchips, as magnetoelastic sensitive units, was evaluated by simulation and experiments. The unique effects signal amplification and biocompatibility of gold particles contribute to the stability and sensitivity of the sensor. Furthermore, to enhance sensitivity, the working concentrations of antibody and BSA are selected to be 50 mg/mL and 0.1%, respectively. Atom force microscope imaging sheds light on the biological analysis. The Nano-magnetoelastic immunosensor exhibits a linear response to the logarithm of carcinoembryonic antigen (CEA) concentrations ranging from 0.1 to 100 ng/mL, with a detection limit of 2.5 pg/mL. The designed biosensor has merits of excellent stability and sensitivity towards CEA

Effects of Biochar Amendment on Tomato Bacterial Wilt Resistance and Soil Microbial Amount and Activity

Bacterial wilt is a serious soilborne disease of Solanaceae crops which is caused by Ralstonia solanacearum. The important role of biochar in enhancing disease resistance in plants has been verified; however, the underlying mechanism remains not fully understood. In this study, two different biochars, made from peanut shell (BC1) and wheat straw (BC2), were added to Ralstonia solanacearum-infected soil to explore the interrelation among biochar, tomato bacterial wilt, and soil microbial properties. The results showed that both BC1 and BC2 treatments significantly reduced the disease index of bacterial wilt by 28.6% and 65.7%, respectively. The populations of R. solanacearum in soil were also significantly decreased by biochar application. Ralstonia solanacearum infection significantly reduced the densities of soil bacteria and actinomycetes and increased the ratio of soil fungi/bacteria in the soil. By contrast, BC1 and BC2 addition to pathogen-infected soil significantly increased the densities of soil bacteria and actinomycetes but decreased the density of fungi and the ratios of soil fungi/bacteria and fungi/actinomycetes. Biochar treatments also increased soil neutral phosphatase and urease activity. Furthermore, higher metabolic capabilities of microorganisms by biochar application were found at 96 and 144 h in Biolog EcoPlates. These results suggest that both peanut and wheat biochar amendments were effective in inhibiting tomato bacterial wilt caused by R. solanacearum. The results suggest a relationship between the disease resistance of the plants and the changes in soil microbial population densities and activity

Studies of the DMP1 57-kDa Functional Domain both in vivo and in vitro

Dmp1-null mice and patients with mutations in dentin matrix protein 1 (DMP1) resulting in autosomal recessive hypophosphatemic rickets display similar skeletal defects. As mutations were observed in the last 18 amino acids of DMP1 in 1 subset of patients and as fragments of intact DMP1, a 37-kDa N-terminal and a 57-kDa C-terminal fragment, have been purified from bone and dentin, we hypothesized that the cleaved 57-kDa C-terminal fragment is the essential functional domain of DMP1. To test this hypothesis, different forms of recombinant DMP1 were expressed in 293EBNA, CHO and 2T3 cells. The results showed that DMP1 was processed into a 37-kDa N-terminal and a 57-kDa C-terminal fragment in vitro in all cell lines examined. DMP1 processing in CHO cells was blocked by a furin protease inhibitor, decanoyl-Arg-Val-Lys-Arg-chloromethyl ketone, in a dose-dependent manner. Coexpression of PHEX, a potential upstream protease, had no apparent effect on DMP1 cleavage in 293EBNA cells, suggesting that PHEX may not be required for DMP1 processing. To test the in vivo role of the C-terminal fragment, transgenic mice overexpressing full-length DMP1 or the 57-kDa fragment controlled by the 3.6-kb Col1 promoter were generated. Overexpression of these transgenes had no effect on the wild-type skeleton, but on the Dmp1-null background showed expression in the osteoblast layer and throughout the bone matrix leading to the rescue of the null bone phenotype. This suggests that the 57-kDa C-terminal fragment may be able to recapitulate the function of intact DMP1 in vivo

Artificial neural network based mechanical and electrical property prediction of engineered cementitious composites

Engineered cementitious composite (ECC) is a type of cement-based material fabricated with a variety of add-in functional fillers, featuring superior properties of strain-hardening, ductility and energy absorption. Proper composition is essential for designing ECC material, which may lead to different mechanical and electrical properties. However the design for ECC is still a complex process on the basis of micro-mechanism followed by numerical and experimental analyses, and there is no simple model yet for practical engineering application. This study presents the prediction of mechanical and electrical properties of ECC based on the artificial neural network (ANN) technique with the aim of providing a gateway for a more efficient and effective approach in ECC design. Specifically, neural network models were developed for ECCs reinforced with polyvinyl alcohol (PVA) fibre or steel fibre (SF) with experimental data collected from other researchers for training. The development, training and validation of the proposed models were discussed. To assess the capability of well-trained ANN models for property prediction, experimental studies were conducted, including compression test, four-point bending test, tensile test and electrical resistance measurement for ECCs of various composition. Excellent consistency between the predicted and tested results is obtained, demonstrating the feasibility of ANN models for property prediction of ECCs

The retention dynamics of N input within the soil-microbe-plant system in a temperate grassland

In N-limited temperate regions, atmospheric N deposition remains high over the non-growing season. However, the retention dynamics of non-growing season N input within the ecosystem remain unclear. Using an isotopic approach, we investigated the initial retention and subsequent dynamics of N-15 (1.5 g N-15 m(-2)) in the soils, microbes, plants, and litter over three years in grazing-prohibited (PG) and heavily grazed treatments (HG) in northern China. For initial retention (21 days after( 15)N addition), most N-15 was immobilized in soils and microbes, while less was taken up by plants. Soil and microbial N-15 immobilization were significantly higher when grazing was prohibited, although plant 15 Nacquisition was not affected by grazing. After initial retention, rapid N-15 loss was observed in microbes and soils, while N-15 levels were sustained longer in plants and litter. The N-15 residence times were longer when grazing was prohibited. The 15 Nacquisition capacity varies among plant taxa: perennial grasses and forbs accumulated N-15 rapidly, while sagebrush and legumes acted slowly. Although the added N-15 had significant contribution to early spring N demands of soil microbes and plants, it did not increase microbial or plant biomass N. Our results showed that non-growing season exogenous N was primarily retained by soil biota in temperate grasslands in the early stage, but N retention is finally sustained in soil and plants. The findings highlighted the importance of soil microbes in sustaining N upon N input, inferring the needs for considering the microbial role for better understanding N cycling in the temperate grasslands