The internal motions of biomatter immersed in biofluid are investigated. The interactions between the fragments of biomatter and its surrounding biofluid are modeled using field theory. In the model, the biomatter is coupled to the gauge field representing the biofluid. It is shown that at non-relativistic limit various equation of motions, from the well-known Sine-Gordon equation to the simult...

In this paper, we consider the Cauchy problem for a porous medium equation in Fingero-imbibition phenomena arising in double phase flow through porous media during oil recovery process. Fingero-imbibition is a physical phenomenon which represents the simultaneous occurrence of two special phenomenon viz. fingering and imbibitions in a porous media. We obtain a series solution of porous medium e...

Differential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation mod...

The facility interest rate is one of the most important macroeconomic variables. The bank facility interest rate is associated with other macro-economic variables, one of which is the bank deposit interest rate. Using the time series data of the 1973-2017 period and the simultaneous equation system, the researchers estimated four equations using the three-stage least squares method.The result o...

In this paper, Hamilton’s (1989) Markov-switching model is extended to the simultaneous equations model. Using a framework for an instrumental variable interpretation of full information maximum likelihood (FIML) by Hausman (1975), we can deal with the problem of simultaneous equations based on the Hamilton filter. When we compared the proposed FIML Markov-switching model to LIML Markovswitchin...

We consider the simultaneous diffusion and homogenization limit of the linear Boltzmann equation in a periodic medium in the regime where the mean free path is much smaller than the lattice constant. The resulting equation is a diffusion equation, with an averaged diffusion matrix that is formally obtained by first performing the diffusion limit and then the homogenization one. The rigorous pro...