This paper deals with the numerical solution of the Heston partial differential equation (PDE) that plays an important role in financial option pricing theory, Heston (1993). A feature of this time-dependent, twodimensional convection-diffusion-reaction equation is the presence of a mixed spatial-derivative term, which stems from the correlation between the two underlying stochastic processes f...

Using the theory of the symmetry groups for PDEs of order two ([7], [17], [20]), one finds the symmetry group G associated to Ţiţeica surfaces PDE. One proves that Monge-Ampère-Ţiţeica PDE which is invariant with respect to G, where G is the maximal solvable subgroup of the symmetry group G, is just the PDE of Ţiţeica surfaces. One studies the inverse problem and one shows that the Ţiţeica surf...

In the present paper, authors are interested in studying a famous nonlinear PDE referred to as $(2+1)$-dimensional chiral Schrödinger (2D-CS) equation with applications mathematical physics. this respect, real and imaginary portions of 2D-CS firstly derived through traveling wave transformation. Different structures equation, classified bright dark solitons, then retrieved using modified Kudrya...

The M-mode echocardiographic findings of ventricular septal defect (VSD) are nonspecific. A specific pulsed Doppler echocardiographic (PDE) diagnosis of VSD can be made by following the turbulent VSD jet through the septum. To assess the sensitivity, specificity and limitations of PDE diagnosis of VSD, 105 children undergoing cardiac catheterization were examined by PDE. These children had a va...

In this letter, we design a robust stabilizing controller for system composed of two sets linear heterodirectional hyperbolic PDEs, with actuation at one boundary the and couplings middle ODEs in PDE-ODE-PDE configuration. The is underactuated since only PDE systems actuated. approach employs backstepping transformation to move undesired proximal (where located). We can then express target as t...

Drosophila carrying the X-linked mutation dunce (dnc) showed poor learning in a negative reinforcement olfactory conditioning paradigm (Dudai, Y., Y.-N. Jan, D. Byers, W.G. Quinn, and S. Benzer (1976) Proc. Natl. Acad. Sci. U.S.A. 73: 1684-1688). More recently, dnc flies were shown to have reduced activity for one of two cAMP phosphodiesterases (PDEs) present in normal flies, PDE II, whereas PD...

the classical etiology of erectile dysfunction (ed) comprises aging and vascular, neurogenic, psychological and hormonal components. recent studies have shown that ed can be the forerunner of serious cardiovascular disturbances. it has also been reported that peripheral neuropathy and microvascular injuries caused by pathophysiological changes in patients with diabetes and obesity lead to ed in...

iii 1 Background and Significance 1 2 Preliminary Studies 3 2.1 PDE Time Integrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 PDE Nonlinear Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 PDE-constrained Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Linear Solvers . . . ...

Differential evolution (DE) algorithm puts emphasis particularly on imitating the microscopic behavior of individuals, while estimation of distribution algorithm (EDA) tries to estimate the probabilistic distribution of the entire population. DE and EDA can be extended to multi-objective optimization problems by using a Pareto-based approach, called Pareto DE (PDE) and Pareto EDA (PEDA) respect...

In the inherited retinal degeneration of rd mice, cyclic GMP accumulates in affected rod photoreceptors prior to their degeneration. A deficiency in the activity of the visual cell phosphodiesterase apparently results in the accumulation of cyclic GMP. The cyclic GMP phosphodiesterase (PDE) of normal mouse photoreceptors is a heteromeric protein complex of about 170 kDa, consisting of the alpha...