Criteria for working-correlation-structure selection in GEE: Assessment via simulation

Efficiency of analysis using generalized estimation equations is enhanced when intracluster correlation structure is accurately modeled. We compare two existing criteria (a quasi-likelihood information criterion, and the Rotnitzky-Jewell criterion) to identify the true correlation structure via simulations with Gaussian or binomial response, covariates varying at cluster or observation level, and exchangeable or AR(l) intracluster correlation structure. Rotnitzky and Jewell's approach performs better when the true intracluster correlation structure is exchangeable, while the quasi-likelihood criteria performs better for an AR(l) structure.

Bi-criteria single machine scheduling problem with a learning effect: Aneja-Nair method to obtain the set of optimal sequences

In this paper, we consider the bi-criteria single machine scheduling problem of n jobs with a learning effect. The two objectives considered are the total completion time (TC) and total absolute differences in completion times (TADC). The objective is to find a sequence that performs well with respect to both the objectives: the total completion time and the total absolute differences in completion times. In an earlier study, a method of solving bi-criteria transportation problem is presented. In this paper, we use the methodology of solvin bi-criteria transportation problem, to our bi-criteria single machine scheduling problem with a learning effect, and obtain the set of optimal sequences,. Numerical examples are presented for illustrating the applicability and ease of understanding.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Stability criteria for single pulse solutions of cw passive mode-locked lasers

The stability of the steady-state solutions of mode-locking of cw lasers by a fast saturable absorber is imvestigated. It is shown that the solutions are stable if the condition (Ps/Pa) = (2/3) (P0Pa) is satisfied, where (Ps/Pa) is the steady-state la ser power, (P0/Pa) is the power at mode-locking threshold, and Pa is the saturated power of the absorber.

Soil nitrogen—crop response calibration relationships and criteria for winter cereal crops grown in Australia

More than 1200 wheat and 120 barley experiments conducted in Australia to examine yield responses to applied nitrogen (N) fertiliser are contained in a national database of field crops nutrient research (BFDC National Database). The yield responses are accompanied by various pre-plant soil test data to quantify plant-available N and other indicators of soil fertility status or mineralisable N. A web application (BFDC Interrogator), developed to access the database, enables construction of calibrations between relative crop yield ((Y0/Ymax) × 100) and N soil test value. In this paper we report the critical soil test values for 90% RY (CV90) and the associated critical ranges (CR90, defined as the 70% confidence interval around that CV90) derived from analysis of various subsets of these winter cereal experiments. Experimental programs were conducted throughout Australia’s main grain-production regions in different eras, starting from the 1960s in Queensland through to Victoria during 2000s. Improved management practices adopted during the period were reflected in increasing potential yields with research era, increasing from an average Ymax of 2.2 t/ha in Queensland in the 1960s and 1970s, to 3.4 t/ha in South Australia (SA) in the 1980s, to 4.3 t/ha in New South Wales (NSW) in the 1990s, and 4.2 t/ha in Victoria in the 2000s. Various sampling depths (0.1–1.2 m) and methods of quantifying available N (nitrate-N or mineral-N) from pre-planting soil samples were used and provided useful guides to the need for supplementary N. The most regionally consistent relationships were established using nitrate-N (kg/ha) in the top 0.6 m of the soil profile, with regional and seasonal variation in CV90 largely accounted for through impacts on experimental Ymax. The CV90 for nitrate-N within the top 0.6 m of the soil profile for wheat crops increased from 36 to 110 kg nitrate-N/ha as Ymax increased over the range 1 to >5 t/ha. Apparent variation in CV90 with seasonal moisture availability was entirely consistent with impacts on experimental Ymax. Further analyses of wheat trials with available grain protein (~45% of all experiments) established that grain yield and not grain N content was the major driver of crop N demand and CV90. Subsets of data explored the impact of crop management practices such as crop rotation or fallow length on both pre-planting profile mineral-N and CV90. Analyses showed that while management practices influenced profile mineral-N at planting and the likelihood and size of yield response to applied N fertiliser, they had no significant impact on CV90. A level of risk is involved with the use of pre-plant testing to determine the need for supplementary N application in all Australian dryland systems. In southern and western regions, where crop performance is based almost entirely on in-crop rainfall, this risk is offset by the management opportunity to split N applications during crop growth in response to changing crop yield potential. In northern cropping systems, where stored soil moisture at sowing is indicative of minimum yield potential, erratic winter rainfall increases uncertainty about actual yield potential as well as reducing the opportunity for effective in-season applications.

Soil phosphorus–crop response calibration relationships and criteria for winter cereal crops grown in Australia

Soil testing is the most widely used tool to predict the need for fertiliser phosphorus (P) application to crops. This study examined factors affecting critical soil P concentrations and confidence intervals for wheat and barley grown in Australian soils by interrogating validated data from 1777 wheat and 150 barley field treatment series now held in the BFDC National Database. To narrow confidence intervals associated with estimated critical P concentrations, filters for yield, crop stress, or low pH were applied. Once treatment series with low yield (<1 t/ha), severe crop stress, or pHCaCl2 <4.3 were screened out, critical concentrations were relatively insensitive to wheat yield (>1 t/ha). There was a clear increase in critical P concentration from early trials when full tillage was common compared with those conducted in 1995–2011, which corresponds to a period of rapid shift towards adoption of minimum tillage. For wheat, critical Colwell-P concentrations associated with 90 or 95% of maximum yield varied among Australian Soil Classification (ASC) Orders and Sub-orders: Calcarosol, Chromosol, Kandosol, Sodosol, Tenosol and Vertosol. Soil type, based on ASC Orders and Sub-orders, produced critical Colwell-P concentrations at 90% of maximum relative yield from 15 mg/kg (Grey Vertosol) to 47 mg/kg (Supracalcic Calcarosols), with other soils having values in the range 19–27 mg/kg. Distinctive differences in critical P concentrations were evident among Sub-orders of Calcarosols, Chromosols, Sodosols, Tenosols, and Vertosols, possibly due to differences in soil properties related to P sorption. However, insufficient data were available to develop a relationship between P buffering index (PBI) and critical P concentration. In general, there was no evidence that critical concentrations for barley would be different from those for wheat on the same soils. Significant knowledge gaps to fill to improve the relevance and reliability of soil P testing for winter cereals were: lack of data for oats; the paucity of treatment series reflecting current cropping practices, especially minimum tillage; and inadequate metadata on soil texture, pH, growing season rainfall, gravel content, and PBI. The critical concentrations determined illustrate the importance of recent experimental data and of soil type, but also provide examples of interrogation pathways into the BFDC National Database to extract locally relevant critical P concentrations for guiding P fertiliser decision-making in wheat and barley.

Information preferences for the evaluation of coastal development impacts on ecosystem services: A multi-criteria assessment in the Australian context

Ecosystem based management requires the integration of various types of assessment indicators. Understanding stakeholders' information preferences is important, in selecting those indicators that best support management and policy. Both the preferences of decision-makers and the general public may matter, in democratic participatory management institutions. This paper presents a multi-criteria analysis aimed at quantifying the relative importance to these groups of economic, ecological and socio-economic indicators usually considered when managing ecosystem services in a coastal development context. The Analytic Hierarchy Process (AHP) is applied within two nationwide surveys in Australia, and preferences of both the general public and decision-makers for these indicators are elicited and compared. Results show that, on average across both groups, the priority in assessing a generic coastal development project is for the ecological assessment of its impacts on marine biodiversity. Ecological assessment indicators are globally preferred to both economic and socio-economic indicators regardless of the nature of the impacts studied. These results are observed for a significantly larger proportion of decision-maker than general public respondents, questioning the extent to which the general public's preferences are well reflected in decision-making processes.

L2-stability of nonstationary feedback systems: Frequency-domain criteria

A frequency-domain positivity condition is derived for linear time-varying operators in2and is used to develop2stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in2with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Studies On Hydrogen Bonds: Part IV. Proposed Working Criteria for Assessing Qualitative Strength of Hydrogen Bonds

The data obtained in the earlier parts of this series for the donor and acceptor end parameters of N-H. O and O-H. O hydrogen bonds have been utilised to obtain a qualitative working criterion to classify the hydrogen bonds into three categories: "very good" (VG), "moderately good" (MG) and weak (W). The general distribution curves for all the four parameters are found to be nearly of the Gaussian type. Assuming that the VG hydrogen bonds lie between 0 and ± la, MG hydrogen bonds between ± 1 and ± 2, W hydrogen bonds beyond ± 2 (where is the standard deviation), suitable cut-off limits for classifying the hydrogen bonds in the three categories have been derived. These limits are used to get VG and MG ranges for the four parameters 1 and θ (at the donor end) and ± and ± (at the acceptor end). The qualitative strength of a hydrogen bond is decided by the cumulative application of the criteria to all the four parameters. The criterion has been further applied to some practical examples in conformational studies such as α-helix and can be used for obtaining suitable location of hydrogen atoms to form good hydrogen bonds. An empirical approach to the energy of hydrogen bonds in the three categories has also been presented.

Time-domain criteria for theL_{2}-stability of nonstationary feedback systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

A multi-criteria approach for hospital capacity analysis

Hospitals are critical elements of health care systems and analysing their capacity to do work is a very important topic. To perform a system wide analysis of public hospital resources and capacity, a multi-objective optimization (MOO) approach has been proposed. This approach identifies the theoretical capacity of the entire hospital and facilitates a sensitivity analysis, for example of the patient case mix. It is necessary because the competition for hospital resources, for example between different entities, is highly influential on what work can be done. The MOO approach has been extensively tested on a real life case study and significant worth is shown. In this MOO approach, the epsilon constraint method has been utilized. However, for solving real life applications, with a large number of competing objectives, it was necessary to devise new and improved algorithms. In addition, to identify the best solution, a separable programming approach was developed. Multiple optimal solutions are also obtained via the iterative refinement and re-solution of the model.

Conservative Design Optimization of Laminated Composite Structures Using Genetic Algorithms and Multiple Failure Criteria

This article analyzes the effect of devising a new failure envelope by the combination of the most commonly used failure criteria for the composite laminates, on the design of composite structures. The failure criteria considered for the study are maximum stress and Tsai-Wu criteria. In addition to these popular phenomenological-based failure criteria, a micromechanics-based failure criterion called failure mechanism-based failure criterion is also considered. The failure envelopes obtained by these failure criteria are superimposed over one another and a new failure envelope is constructed based on the lowest absolute values of the strengths predicted by these failure criteria. Thus, the new failure envelope so obtained is named as most conservative failure envelope. A minimum weight design of composite laminates is performed using genetic algorithms. In addition to this, the effect of stacking sequence on the minimum weight of the laminate is also studied. Results are compared for the different failure envelopes and the conservative design is evaluated, with respect to the designs obtained by using only one failure criteria. The design approach is recommended for structures where composites are the key load-carrying members such as helicopter rotor blades.

Scale-up criteria of square tank surface aerator

Oxygen transfer rate and the corresponding power requirement to operate the rotor are vital for design and scale-up of surface aerators. Present study develops simulation or scale-up criterion correlating the oxygen transsimulation fer coefficient and power number along with a parameter governing theoretical power per unit volume (X, which is defined as equal to (FR1/3)-R-4/3, where F and R are impellers' Fronde and Reynolds number, respectively). Based on such scale-up criteria, design considerations are developed to save energy requirements while designing square tank surface aerators. It has been demonstrated that energy can be saved substantially if the aeration tanks are run at relatively higher input powers. It is also demonstrated that smaller sized tanks are more energy conservative and economical when compared to big sized tanks, while aerating the same volume of water, and at the same time by maintaining a constant input power in all the tanks irrespective of their size. An example illustrating how energy can be reduced while designing different sized aerators is given. The results presented have a wide application in biotechnology and bioengineering areas with a particular emphasis on the design of appropriate surface aeration systems.

Scale-up criteria of square tank surface aerator

Oxygen transfer rate and the corresponding power requirement to operate the rotor are vital for design and scale-up of surface aerators. Present study develops simulation or scale-up criterion correlating the oxygen transsimulation fer coefficient and power number along with a parameter governing theoretical power per unit volume (X, which is defined as equal to (FR1/3)-R-4/3, where F and R are impellers' Fronde and Reynolds number, respectively). Based on such scale-up criteria, design considerations are developed to save energy requirements while designing square tank surface aerators. It has been demonstrated that energy can be saved substantially if the aeration tanks are run at relatively higher input powers. It is also demonstrated that smaller sized tanks are more energy conservative and economical when compared to big sized tanks, while aerating the same volume of water, and at the same time by maintaining a constant input power in all the tanks irrespective of their size. An example illustrating how energy can be reduced while designing different sized aerators is given. The results presented have a wide application in biotechnology and bioengineering areas with a particular emphasis on the design of appropriate surface aeration systems.