Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated kernels in the nonparametric estimation for discrete functions. The extension from one to two orders around the mode provides a large family of discrete distributions having a finite support. Establishing a bridge between Dirac and discrete uniform distributions, some different shapes are also obtained and their properties are investigated. In particular, the mean and variance are pointed out. Applications to discrete kernel estimators are given with a solution to a boundary bias problem. (C) 2010 Elsevier B.V. All rights reserved.

Evaluating responses of maize (Zea mays L.) to soil physical conditions using a boundary line approach

The functional relation between the decline in the rate of a physiological process and the magnitude of a stress related to soil physical conditions is an important tool for uses as diverse as assessment of the stress-related sensitivity of different plant cultivars and characterization of soil structure. Two of the most pervasive sources of stress are soil resistance to root penetration (SR) and matric potential (psi). However, the assessment of these sources of stress on physiological processes in different soils can be complicated by other sources of stress and by the strong relation between SR and psi in a soil. A multivariate boundary line approach was assessed as a means of reducing these cornplications. The effects of SR and psi stress conditions on plant responses were examined under growth chamber conditions. Maize plants (Zea mays L.) were grown in soils at different water contents and having different structures arising from variation in texture, organic carbon content and soil compaction. Measurements of carbon exchange (CE), leaf transpiration (ILT), plant transpiration (PT), leaf area (LA), leaf + shoot dry weight (LSDW), root total length (RTL), root surface area (RSA) and root dry weight (RDW) were determined after plants reached the 12-leaf stage. The LT, PT and LA were described as a function of SR and psi with a double S-shaped function using the multivariate boundary line approach. The CE and LSDW were described by the combination of an S-shaped function for SR and a linear function for psi. The root parameters were described by a single S-shaped function for SR. The sensitivity to SR and psi depended on the plant parameter. Values of PT, LA and LSDW were most sensitive to SR. Among those parameters exhibiting a significant response to psi, PT was most sensitive. The boundary line approach was found to be a useful tool to describe the functional relation between the decline in the rate of a physiological process and the magnitude of a stress related to soil physical conditions. (C) 2009 Elsevier B.V. All rights reserved.

Plant availability of phosphorus in four superphosphate fertilizers varying in water-insoluble phosphate compounds

There is concern that the use of lower quality phosphate rock can result in elevated amounts of Fe-Al-P water-insoluble compounds in fertilizers and, consequently, low agronomic effectiveness. Therefore, studies were conducted to evaluate the effect of some of these compounds on plant growth. Four commercial superphosphates varying in chemical composition (two single and two triple superphosphates) were selected for the study. Fertilizer impurities were collected as water-insoluble residues by washing each P source with deionized water. A modal analysis, based primarily on elemental chemical analysis and x-ray diffractometry, was used to estimate the chemical composition of each P source. Water-soluble monocalcium phosphate (MCP) and the water-leached fertilizer residues were prepared to give a range of fertilizers in terms of water-soluble phosphorus (WSP) (0-100% of the available P as MCP). The water-leached fractions, MCP, and the mixtures of MCP with water-leached fractions were applied to supply 40 mg available P kg(1) to a thermic Rhodic Kanhapludult with pH values of 5.2 +/- 0.05 (unlimed) and 6.4 +/- 0.08 (limed). Wheat (Triticum aestivum L.) grown in a greenhouse for 101 d served as the test crop. The requirement for WSP was source and pH dependent. At a soil pH of 5.2, the fertilizers required 73 to 95% WSP to reach the maximum dry-matter yield, while they required 60 to 86% WSP at pH 6.4. To reach 90% of the maximum yield, all superphosphate fertilizers required <50% WSP. These results show that it is not always necessary to have high water solubility as required by legislation in many countries.

Growth and haematology of pacu, Piaractus mesopotamicus, fed diets with varying protein to energy ratio

Haematopoiesis and blood cells` functions can be influenced by dietary concentration of nutrients. This paper studied the effects of dietary protein:energy ratio on the growth and haematology of pacu, Piaractus mesopotamicus. Fingerling pacu (15.5 +/- 0.4 g) were fed twice a day for 10 weeks until apparent saciety with diets containing 220, 260, 300, 340 or 380 g kg(-1) crude protein (CP) and 10.88, 11.72, 12.55, 13.39, 14.22 MJ kg(-1) digestible energy (DE) in a totally randomized experimental design, 5 x 5 factorial scheme (n=3). Weight gain and specific growth rate were affected (P < 0.05) by protein level only. Protein efficiency ratio decreased (P < 0.05) with increasing dietary protein at all levels of dietary energy. Daily feed intake decreased (P < 0.05) with increasing dietary energy. Mean corpuscular haemoglobin concentration was affected (P < 0.05) by DE and interaction between dietary CP and DE. Total plasma protein increased (P < 0.05) with dietary protein and energy levels. Plasma glucose decreased (P < 0.05) with increasing dietary protein. The CP requirement and optimum protein:energy ratio for weight gain of pacu fingerlings, determined using broken-line model, were 271 g kg(-1) and 22.18 g CP MJ(-1) DE respectively. All dietary CP and DE levels studied did not pose damages to fish health.

Side boundary wall, Q House, Chelmer, Brisbane

Stepped out lower section of wall houses seating, shelving and water features to outdoor room and living areas.

View along western boundary; paperbark trees between private and public housing, Cotton Tree Housing Estate, Maroochydore

This pilot project at Cotton Tree, Maroochydore, on two adjacent, linear parcels of land has one of the properties privately owned while the other is owned by the public housing authority. Both owners commissioned Lindsay and Kerry Clare to design housing for their separate needs which enabled the two projects to be governed by a single planning and design strategy. This entailed the realignment of the dividing boundary to form two approximately square blocks which made possible the retention of an important stand of mature paperbark trees and gave each block a more useful street frontage. The scheme provides seven two-bedroom units and one single-bedroom unit as the private component, with six single-bedroom units, three two-bedroom units and two three-bedroom units forming the public housing. The dwellings are deployed as an interlaced mat of freestanding blocks, car courts, courtyard gardens, patios and decks. The key distinction between the public and private parts of the scheme is the pooling of the car parking spaces in the public housing to create a shared courtyard. The housing climbs to three storeys on its southern edge and falls to a single storey on the north-western corner. This enables all units and the principal private outdoor spaces to have a northern orientation. The interiors of both the public and private units are skilfully arranged to take full advantage of views, light and breeze.

Gauge P-representations for quantum-dynamical problems: Removal of boundary terms

P-representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum-dynamical many-body calculations such as Bose-Einstein condensation. We introduce a representation called the gauge P representation, which greatly widens the range of tractable problems. Our treatment results in an infinite set of possible time evolution equations, depending on arbitrary gauge functions that can be optimized for a given quantum system. In some cases, previous methods can give erroneous results, due to the usual assumption of vanishing boundary conditions being invalid for those particular systems. Solutions are given to this boundary-term problem for all the cases where it is known to occur: two-photon absorption and the single-mode laser. We also provide some brief guidelines on how to apply the stochastic gauge method to other systems in general, quantify the freedom of choice in the resulting equations, and make a comparison to related recent developments.

Calculation of line integrals in boundary integral methods

We propose quadrature rules for the approximation of line integrals possessing logarithmic singularities and show their convergence. In some instances a superconvergence rate is demonstrated.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium

Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered: isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered.

Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium

Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered: isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Integrable eight-state supersymmetric U model with boundary terms and its Bethe ansatz solution

A class of integrable boundary terms for the eight-state supersymmetric U model are presented by solving the graded reflection equations. The boundary model is solved by using the coordinate Bethe ansatz method and the Bethe ansatz equations are obtained. (C) 1998 Elsevier Science B.V.

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property. (C) 1998 Elsevier Science B.V.

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.