In this paper, we investigate the existence and multiplicity of positive solutions for nonlinear fractional differential equation boundary value problem:0+ is the standard Riemann-Liouville differentiation, and f : [0, 1] × [0, ∞) → [0, ∞) is continuous. By means of some fixed-point theorems on cone, some existence and multiplicity results of positive solutions are obtained. The proofs are based upon the reduction of problem considered to the equivalent Fredholm integral equation of second kind.  2005 Elsevier Inc. All rights reserved.

We consider the boundary value problem ϕ p u + λF t u = 0, with p > 1, t ∈ 0 1 , u 0 = u 1 = 0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed.  2002 Elsevier Science (USA)

During the testing of context-sensitive middleware-based software, the middleware checks the current situation to invoke the appropriate functions of the applications. Since the middleware remains active and the situation may continue to evolve, however, the conclusion of some test cases may not easily be identified. Moreover, failures appearing in one situation may be superseded by subsequent correct outcomes and, therefore, be hidden.We alleviate the above problems by making use of a special kind of situation, which we call checkpoints, such that the middleware will not activate the functions under test. We recommend testers to generate test cases that start at a checkpoint and end at another. Testers may identify relations that associate different execution sequences of a test case. They then check the results of each test case to detect any contravention of such relations. We illustrate our technique with an example that shows how hidden failures can be detected. We also report the experimentation carried out on an RFID-based location-sensing application on top of a context-sensitive middleware.

Pervasive computing software adapts its behavior according to the changing contexts. Nevertheless, contexts are often noisy. Context inconsistency resolution provides a cleaner pervasive computing environment to context-aware applications. A faulty context-aware application may, however, mistakenly mix up inconsistent contexts and resolved ones, causing incorrect results. This paper studies how such faulty context-aware applications may be affected by these services. We model how programs should handle contexts that are continually checked and resolved by context inconsistency resolution, develop novel sets of data flow equations to analyze the potential impacts, and thus formulate a new family of test adequacy criteria for testing these applications. Experimentation shows that our approach is promising.

Abstract:The Ejina Basin is an extremely arid subwatershed in Northwest China. The predominant natural tree species in the area, Populus euphratica, depends on groundwater for sustenance. In recent decades, groundwater overdraft and increased water diversions from the Heihe River caused water table elevations to decline, such that large areas of P. euphratica have withered, creating a highly visible symbol of ecological change and desertification in the Ejina Basin. Ecological restoration efforts aimed at saving existing woodlands and cultivating new stands of P. euphratica are underway. To provide a better scientific basis for ecological restoration plans, it is necessary to understand the effect of water table elevation on P. euphratica water uptake. In this work, we used the HYDRUS-1D software package to study groundwater movement into the root zone and the uptake of groundwater in a 10-year-old P. euphratica woodland. Additionally, we examined the changes in uptake that would occur for different water table elevations. The model calibration was confirmed by comparing predicted soil moisture contents during the P. euphratica growing season with field measured values. The results indicate that in 2000, with an average water table depth of 2Ð64 m, P. euphratica at the study site obtained about 53% of its water from groundwater during the middle part of the growing season (day of year 160-290). Simulations made with constant water table depths found that increasing the water table depth from 2 to 3 metres resulted in a 74% reduction in transpiration. Many factors can influence the optimal water table depth at a given site. An advantage of the modelling approach is that these factors can be systematically varied, creating a site-specific impact assessment of water management options that may alter water table depths, thus aiding ecological restoration efforts.