Sheila B Frankfurt, Alanna Coady
Bringing Philosophy to Bear on Moral Injury and Posttraumatic Stress Disorder Construct Validation: Commentary on Farnsworth (2019)
Journal of traumatic stress
spatiotemporal dynamics many natural processes elasticity heat propagation sound waves fluid flows often modeled using partial differential equations pdes certain types pdes closedform analytical solutions permit numerical solutions require appropriate initial boundary conditions others may stable global even wellposed solutions paper focus onespecific type secondorder pde ultrahyperbolic wave equation multiple time dimensions demonstrate wave equation solutions complex time kime show examples cauchy initial value problem spacekime extend classical formulation dynamics wave equation respect positive real longitudinal time solutions cauchy boundary value problem multiple time dimensions derived cartesian polar spherical coordinates include bounded unbounded spatial domains example solutions shown main text additional webbased dynamic illustrations wave equation solutions spacekime shown appendix solving pdes complex time direct connections data science solving underdetermined linear modeling problems specifying initial conditions limited spatial dimensions may insufficient forecast classify predict prospective value parameter statistical model approach extends notion data observations anchored ordered longitudinal events complex time observables need follow strict positivereal structural arrangement instead could traverse entire kime plane