General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

Extending and validating the is-impact model in Saudi Arabia : accounting for computer network quality

Organizations from every industry sector seek to enhance their business performance and competitiveness through the deployment of contemporary information systems (IS), such as Enterprise Systems (ERP). Investments in ERP are complex and costly, attracting scrutiny and pressure to justify their cost. Thus, IS researchers highlight the need for systematic evaluation of information system success, or impact, which has resulted in the introduction of varied models for evaluating information systems. One of these systematic measurement approaches is the IS-Impact Model introduced by a team of researchers at Queensland University of technology (QUT) (Gable, Sedera, & Chan, 2008). The IS-Impact Model is conceptualized as a formative, multidimensional index that consists of four dimensions. Gable et al. (2008) define IS-Impact as "a measure at a point in time, of the stream of net benefits from the IS, to date and anticipated, as perceived by all key-user-groups" (p.381). The IT Evaluation Research Program (ITE-Program) at QUT has grown the IS-Impact Research Track with the central goal of conducting further studies to enhance and extend the IS-Impact Model. The overall goal of the IS-Impact research track at QUT is "to develop the most widely employed model for benchmarking information systems in organizations for the joint benefit of both research and practice" (Gable, 2009). In order to achieve that, the IS-Impact research track advocates programmatic research having the principles of tenacity, holism, and generalizability through extension research strategies. This study was conducted within the IS-Impact Research Track, to further generalize the IS-Impact Model by extending it to the Saudi Arabian context. According to Hofsted (2012), the national culture of Saudi Arabia is significantly different from the Australian national culture making the Saudi Arabian culture an interesting context for testing the external validity of the IS-Impact Model. The study re-visits the IS-Impact Model from the ground up. Rather than assume the existing instrument is valid in the new context, or simply assess its validity through quantitative data collection, the study takes a qualitative, inductive approach to re-assessing the necessity and completeness of existing dimensions and measures. This is done in two phases: Exploratory Phase and Confirmatory Phase. The exploratory phase addresses the first research question of the study "Is the IS-Impact Model complete and able to capture the impact of information systems in Saudi Arabian Organization?". The content analysis, used to analyze the Identification Survey data, indicated that 2 of the 37 measures of the IS-Impact Model are not applicable for the Saudi Arabian Context. Moreover, no new measures or dimensions were identified, evidencing the completeness and content validity of the IS-Impact Model. In addition, the Identification Survey data suggested several concepts related to IS-Impact, the most prominent of which was "Computer Network Quality" (CNQ). The literature supported the existence of a theoretical link between IS-Impact and CNQ (CNQ is viewed as an antecedent of IS-Impact). With the primary goal of validating the IS-Impact model within its extended nomological network, CNQ was introduced to the research model. The Confirmatory Phase addresses the second research question of the study "Is the Extended IS-Impact Model Valid as a Hierarchical Multidimensional Formative Measurement Model?". The objective of the Confirmatory Phase was to test the validity of IS-Impact Model and CNQ Model. To achieve that, IS-Impact, CNQ, and IS-Satisfaction were operationalized in a survey instrument, and then the research model was assessed by employing the Partial Least Squares (PLS) approach. The CNQ model was validated as a formative model. Similarly, the IS-Impact Model was validated as a hierarchical multidimensional formative construct. However, the analysis indicated that one of the IS-Impact Model indicators was insignificant and can be removed from the model. Thus, the resulting Extended IS-Impact Model consists of 4 dimensions and 34 measures. Finally, the structural model was also assessed against two aspects: explanatory and predictive power. The analysis revealed that the path coefficient between CNQ and IS-Impact is significant with t-value= (4.826) and relatively strong with â = (0.426) with CNQ explaining 18% of the variance in IS-Impact. These results supported the hypothesis that CNQ is antecedent of IS-Impact. The study demonstrates that the quality of Computer Network affects the quality of the Enterprise System (ERP) and consequently the impacts of the system. Therefore, practitioners should pay attention to the Computer Network quality. Similarly, the path coefficient between IS-Impact and IS-Satisfaction was significant t-value = (17.79) and strong â = (0.744), with IS-Impact alone explaining 55% of the variance in Satisfaction, consistent with results of the original IS-Impact study (Gable et al., 2008). The research contributions include: (a) supporting the completeness and validity of IS-Impact Model as a Hierarchical Multi-dimensional Formative Measurement Model in the Saudi Arabian context, (b) operationalizing Computer Network Quality as conceptualized in the ITU-T Recommendation E.800 (ITU-T, 1993), (c) validating CNQ as a formative measurement model and as an antecedent of IS Impact, and (d) conceptualizing and validating IS-Satisfaction as a reflective measurement model and as an immediate consequence of IS Impact. The CNQ model provides a framework to perceptually measure Computer Network Quality from multiple perspectives. The CNQ model features an easy-to-understand, easy-to-use, and economical survey instrument.

Analysis of productive performance of crop production systems: an integrated analytical framework

Recent literature has argued that environmental efficiency (EE), which is built on the materials balance (MB) principle, is more suitable than other EE measures in situations where the law of mass conversation regulates production processes. In addition, the MB-based EE method is particularly useful in analysing possible trade-offs between cost and environmental performance. Identifying determinants of MB-based EE can provide useful information to decision makers but there are very few empirical investigations into this issue. This article proposes the use of data envelopment analysis and stochastic frontier analysis techniques to analyse variation in MB-based EE. Specifically, the article develops a stochastic nutrient frontier and nutrient inefficiency model to analyse determinants of MB-based EE. The empirical study applies both techniques to investigate MB-based EE of 96 rice farms in South Korea. The size of land, fertiliser consumption intensity, cost allocative efficiency, and the share of owned land out of total land are found to be correlated with MB-based EE. The results confirm the presence of a trade-off between MB-based EE and cost allocative efficiency and this finding, favouring policy interventions to help farms simultaneously achieve cost efficiency and MP-based EE.