The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long WaveBurgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker’s parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational for...

We introduce a general methodology for parameter identification in reaction-diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm is illustrated with the Schnakenberg and Gierer-Meinhardt reaction-diffusion systems using PDE constrained optimization techniques. A quadratic cost functional that measures t...

We show that a novel class of preconditioners, designed by Pravin Vaidya in 1991 but never before implemented, is remarkably robust and can outperform incomplete-Cholesky preconditioners. Our test suite includes problems arising from finitedifferences discretizations of elliptic PDEs in two and three dimensions. On 2D problems, Vaidya’s preconditioners often outperform drop-tolerance incomplete...

We show that calmodulin-dependent phosphodiesterase (CAM-PDE) is selectively expressed in mature olfactory receptor neurons within the olfactory mucosa. Immunocytochemical staining reveals neuronal immunoreactivity that is most pronounced within cilia, dendritic knobs, and axon bundles. Neither sustentacular cells nor basal cells display immunoreactivity. The extent of loss of neuronal immunore...

The problem of state-observation is addressed for nonlinear systems that can bemodeled by an ODE–PDE series association. The ODE subsystem assumes a triangular structure while the PDE element is of heat diffusion type. The aim is to accurately estimate online the state vector of the ODE subsystem and the distributed state of the PDE element. One major difficulty is that the state observation mu...

The critical cell density for relaying in D. discoideum, N*, has been measured as a function of cell density, N, and time after harvesting, t. It has logarithmic dependence on N for 2.5 X 10(4)/cm2 less than N less than 7.5 X 10(5)/cm2 and saturates for N more than 1.0 X 10(6)/cm2. N* is an increasing function of time after harvesting. The phosphodiesterase (PDE) secretion rate on which N* depe...

We studied interactions between the mitogen-activated protein kinase (MAPK) signalling pathway and cAMP-protein kinase (PKA) signaling pathway in regulation of mitogenesis of mesangial cells (MC) determined by [3H]thymidine incorporation, with or without added EGF. Forskolin or dibutyryl cAMP strongly (by 60-70%) inhibited [3H]thymidine incorporation into MC. Cilostamide, lixazinone or cilostaz...

We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, network layer is seen as set of PDE-solvers where geometrically meaningful PDE-coefficients become the layer's trainable weights. Formulating our PDEs on homogeneous spaces allows these networks to be designed with built-in symmetries such rotation in addition standard ...

In this paper, we study the long-time behavior of a class of nonlinear dissipative partial differential equations. By means of the Lyapunov-Perron method, we show that the equation has an inertial manifold, provided that certain gap condition in the spectrum of the linear part of the equation is satisfied. We verify that the constructed inertial manifold has the property of exponential tracking...