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- In this paper, a mathematical model of a cancer sub-network is analysed from the view point of Lie symmetry methods. This model discusses a human cancer cell which is developed due to the dysfunction of some genes at the R-checkpoint during the cell cycle. The primary purpose of this paper is to apply the techniques of Lie symmetry to the model and present some approximated solutions for the three-dimensional system of first-order ordinary differential equations describing a cancer sub-network. The result shows that the phosphatase gene (Cdc25A) regulates the cyclin-dependent kinases inhibitor (𝑃27𝐾𝑖𝑝1). Furthermore, this research discovered that the activity that reverses the inhibitory effects on cell cycle progression at the R-checkpoint initiates a pathway.
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- This study examines a classical Black-Scholes (BC) model for stochastic volatility with Heston process from Lie symmetry perspective. In the same way the study includes a classification of point symmetries and the corresponding modified local one-parameter transformations. Lie symmetry analysis is presented for the case where the volatility is a stochastic process.Furthermore, an invariant solutions are calculated and illustrated numerically.
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- This paper analyses the model of Black–Scholes option pricing from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the Black–Scholes equation. Furthermore, corresponding determining equations were constructed and new symmetries were found. As a result, the findings of the study demon strate of the integrability of the model to present an invariant solution for the Ornstein–Uhlenbeck stochastic process.
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