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1

Dr. Ravi Prakash Mathur

Abstract:
The present study investigates the influence of a uniform magnetic field on the stability of horizontal viscous fluid layers heated from below. The system represents the classical Rayleigh–Bénard configuration under magnetohydrodynamic (MHD) conditions. By applying the Boussinesq approximation and linear stability theory, a dispersion relation is derived that connects the growth rate of perturbations with parameters such as the Rayleigh number (Ra), Hartmann number (Ha), and Prandtl number (Pr). The analysis shows that the presence of a vertical magnetic field increases the critical Rayleigh number required for the onset of convection, thus stabilizing the system. The magnetic field suppresses the growth of convective cells and delays the transition to turbulence. The stabilizing effect, however, depends on the field orientation, boundary conditions, and the electrical conductivity of the fluid. The results have direct relevance in astrophysical, geophysical, and industrial processes involving magnetized viscous flows such as in molten metals, semiconductor crystal growth, and liquid metal batteries.


29-34
2

Mr. John Abhishek Masih1, Prof. Rajiv Phillip2, Manish Sharma3

Abstract:
A mathematical model presented with the help of delay differential equations and a systematic study of the growth on angiogenesis cancer. This model is investigated using stability theory as well as equilibria. Using the theory of delay differential equations and the basic reproduction R_0 is a measure of the potential for disease spread in a population. We observe that the growth of cancer infection free equilibrium is unstable because the basic reproduction number R_0<1.


11-19
3

Jitendra Singh

Abstract:
One well-known issue with the standard Black-Scholes (BS) approach when attempting to simulate option pricing or asset returns is that it is impossible to duplicate the observed skews/smiles for the second case and the empirical features of asset returns for the first. Adding jumps or stochastic volatility to the underlying process is a popular solution to this issue. This paper studies the stochastic volatility jump diffusion(SVJD) model without shot noise(SN) and compare with Heston model. Further, it is reviewing their theoretical properties, and focusing on their ability to model asset returns by analyzing their statistical properties. The models are calibrated usingU.S. OIL FUND (ETF) (NYSEArca: USO) option prices. Finally, numerical illustration of SVJD models without SN are consistent with the real data in compare to Heston model.


20-28
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