PDE , Part II

MATH348-Advanced Engineering Mathematics Homework Solutions: PDE Part II

PDE-PEDA: A New Pareto-Based Multi-objective Optimization Algorithm

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...

Human bronchial cyclic nucleotide phosphodiesterase isoenzymes: biochemical and pharmacological analysis using selective inhibitors.

1 The aims of the present study were to characterize the cyclic nucleotide phosphodiesterase (PDE) isoenzyme activities present in human bronchi and to examine the ability of selective isoenzyme inhibitors to relax histamine and methacholine precontracted preparations of human bronchi. 2 Three separations of pooled human bronchial tissue samples were performed. Ion-exchange chromatography showe...

Cyclic adenosine 3':5'-monophosphate phosphodiesterase and its role in learning in Drosophila.

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...

Arbitrage-Free Pricing of XVA – Part II: PDE Representation and Numerical Analysis

We study the semilinear partial differential equation (PDE) associated with the non-linear BSDE characterizing buyer’s and seller’s XVA in a framework that allows for asymmetries in funding, repo and collateral rates, as well as for early contract termination due to counterparty credit risk. We show the existence of a unique classical solution to the PDE by first proving the existence and uniqu...