This paper presents a method of component testing based on algebraic specifications. An algorithm for generating checkable test cases is proposed. A prototype testing tool called CASCAT for testing Java Enterprise Beans is developed. It has the advantages of high degree of automation, which include test case generation, test harness construction and test result checking. It achieves scalability by allowing incremental integration. It also allows testing to focus on a subset of used functions and key properties, thus suitable for component testing. The paper also reports an experimental evaluation of the method and the tool.
Abstract. The current paper is devoted to the study of semilinear dispersal evolution equations of the formwhere H = R N or Z N , A is a random dispersal operator or nonlocal dispersal operator in the case H = R N and is a discrete dispersal operator in the case H = Z N , and f is periodic in t, asymptotically periodic in x (i.e. f (t, x, u) − f 0 (t, x, u) converges to 0 as x → ∞ for some time and space periodic function f 0 (t, x, u)), and is of KPP type in u. It is proved that Liouville type property for such equations holds, that is, time periodic strictly positive solutions are unique. It is also proved that if u ≡ 0 is a linearly unstable solution to the time and space periodic limit equation of such an equation, then it has a unique stable time periodic strictly positive solution and has a spatial spreading speed in every direction.
Abstract. The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a system is first introduced via the natural features of spreading speeds. The existence and lower bounds of spreading speed intervals are then established. When the periodic dependence of the habitat is only on the time variable, the existence of a single spreading speed is proved. It also shows that, under certain conditions, the spreading speed interval in any direction is a singleton, and, moreover, the linear determinacy holds.
The current paper is concerned with positive stationary solutions and spatial spreading speeds of KPP type evolution equations with random or nonlocal or discrete dispersal in locally spatially inhomogeneous media. It is shown that such an equation has a unique globally stable positive stationary solution and has a spreading speed in every direction. Moreover, it is shown that the localized spatial inhomogeneity of the medium neither slows down nor speeds up the spatial spreading in all the directions.
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