Publications

We show that various representation spaces for continua contain a homeomorphic copy of the harmonic sequence, so even though it is not a T0 space, it contains infinite metrizable subspaces. It remains an open question whether this representation space (topologized using continuous surjections) contains a closed subspace homeomorphic to the harmonic sequence. In fact, the representation space for continua topologized using various kinds of mappings (open, confluent, or monotone mappings, for instance) can be shown to have some closed points, but it remains open in many cases whether there are more than two closed points in most instances. Examples of […]

Previously, the authors used the insights of Robinson's nonstandard analysis as a powerful tool to extend and simplify the construction of some compactifications of regular spaces. They now show that any Hausdorff compactification is obtainable with their method.

When relatively cold fluid is injected to hot host rock featured with fractures, the fluid-rock temperature difference induces cooling of the self-propping fractures and could cause the failure of the asperity. Although fracture sustainability has been extensively studied, little research has focused on thermal effects on asperity failure. A finite-element analysis is conducted to investigate the effect of fluid-rock temperature differences on the asperity failure. In the analysis, rock mechanical properties are coupled with the temperature and stress states of the host rock. The thermally-induced tensile cracks initiate at the junction of asperity and rock matrix and also start at […]

Let p be an odd prime. The unary algebra consisting of the dihedral group of order 2p, acting on itself by left translation, is a minimal congruence lattice representation of 𝕄p+1.

We define a binary metric as a symmetric, distributive lattice ordered magma-valued function of two variables, satisfying a “triangle inequality". Using the notion of a Kuratowski topology, in which topologies are specified by closed sets rather than open sets, we prove that every topology is induced by a binary metric. We conclude with a discussion on the relation between binary metrics and some separation axioms.

In an enhanced geothermal system (EGS), fluid is injected into pre-existing fractures to be heated up and then pumped out for the electricity generation; injected fluid is cold as compared to surrounding bedrock. The rock-fluid temperature difference induces thermal stress along the fracture wall, and the large thermal stress could damage some of the self-propping asperities and result in a change of the topography and lifespan of the fractures. Although fracture sustainability has been extensively studied, the mechanism of asperity damage due to rock-fluid temperature difference remains unknown. We have constructed a finite-element based three-dimensional model, which uses a hemisphere […]

From a measure space, (X, μ𝕏) we define a measure μ ℙ(𝕏) on the power set of X. If (X,τ) is a compactum, whose topology τ is compatible with the measure μ𝕏 on X, then the measure μ ℙ(𝕏) restricts to a natural measure on the hyperspace of closed sets of that given compactum. Surprisingly, under very mild conditions, μℙ(𝕏) is always supported on the hyperspace of finite subsets.

When polluting firms acquire firms in the same industry, do they seek out greener firms to make use of their cleaner technology, especially under threat of penalty for pollution? How does penalty for pollution affect the incentive for acquisition? The result of this study indicates that firms who are penalized for their pollution do not necessarily seek out greener firms to acquire. Our result suggests that it is more profitable for polluting firms to takeover dirtier firms and shut them down. Our result also indicates that, at lower levels of emission tax, the incentive for acquiring a dirtier firm increases […]

The intuitive notion of forming a compactification of a topological space is to “attach” new points to a space to “compactify” it. We use equivalence relations on the remote points of an enlargement of a given topological space to produce the new points. Thus, nonstandard methods are shown to unify the various extant approaches to compactification.

Even though most acquisitions take place among manufacturing firms regulated by environmental policies, there are not many studies which model acquisition decisions when such policies are present. In this book chapter, we model acquisition incentives when polluting firms compete in a Cournot oligopoly market. Our result suggests that emission tax can affect acquisition decisions. The exact relationship between emission tax and acquisition (dis)incentives depends on the pollution intensity of the potential acquisition partners. Furthermore our findings suggest that there may be perverse incentive situations, namely cases in which dirtier firms profitably acquire cleaner firms without making use of their cleaner […]