We present a formulation of the incompressible viscous Navier-Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a virtual velocity. We derive a generalization of the inviscid Cauchy formula and obtain certain bounds for the objects introduced.

We determine nonlinear Lorentz transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration as an analogue of the maximal velocity in special relativity follows from the nonlinear Lorentz group of transformtion. The mass formula was derived by the same method as the Thomas precession formula by author. It can play crucial r...

The purpose of this study was to develop a formula to determine and compare the compressibility of selected sport balls. Six balls (basketball, volleyball, soccer ball, baseball, handball, golf ball) were dropped ten times from each of four different heights onto a smooth solid surface overlaid with a white sheet of typing paper, overlaid with a sheet of carbon paper. The diameter of the area o...

This paper investigates the American strangle option in a mean-reversion environment. When underlying asset follows mean-reverting lognormal process, an analytic pricing formula for is explicitly provided. To present formula, we consider partial differential equation (PDE) options with two optimal stopping boundaries and use Mellin transform techniques to derive integral representation arising ...

This paper uses the finite-volume community ocean model (FVCOM) coupled with simulating waves nearshore (SWAN) in a wave–current–sediment to simulate tidal current field, wave and suspended sediment concentration (SSC) field sea area near Weifang Port, China. The three-dimensional water-and-sediment was modified by introducing sediment-settling-velocity formula that considers effect of gradatio...

We consider the dynamics of message passing for spatially coupled codes and, in particular, the set of density evolution equations that tracks the profile of decoding errors along the spatial direction of coupling. It is known that, for suitable boundary conditions and after a transient phase, the error profile exhibits a “solitonic behavior”. Namely, a uniquely-shaped wavelike solution develop...