Jaysie Mher G. Tiongson, Dylan Antonio S. J. Talabis, Lauro L. Fontanil
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引用次数: 0
Abstract
The goal of this paper is to characterize the existence of positive equilibria of power law systems through their kinetics-based decompositions. To achieve this, we consider subclasses of power law systems: PL-RDK and PL-TIK systems. PL-RDK systems are those in which the kinetic order vectors are reactant-determined, that is, branching reactions have identical vectors. PL-TIK systems are characterized by having linearly independent kinetic order vectors per linkage class. We first introduced the notion of Zero Kinetic Deficiency Decomposition of cycle terminal power law systems. Then, by considering non-cycle terminal power law systems, we extend this by introducing the notion of PL-TIK decomposition. Through these novel decomposition classes, we showed that PL-RDK systems with weakly reversible decompositions admit positive equilibria. Moreover, to ensure the existence of PL-TIK decomposition, we developed an algorithm in which any power law system can generate a PL-TIK decomposition. Lastly, we applied the algorithm to Schmitz’ Global Carbon Cycle Model.
期刊介绍：
The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches.
Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.
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