abstract rockfill dams are a type of hydraulic control structures used to protect river bed in cases where a considerable reservoir volume is available behind these structures; it could mitigate the floods and provide a gradual depletion of incoming volume of water so that the discharge passing downstream is decreased. one of the main issues on utilizing rockfill dams is to keep its permeabilit...

We solve the equation of the title for q = 3 and, partially, for q = 2. These are the only prime values of q for which there exist integer solutions. Our arguments are based upon off-diagonal Padé approximation to the binomial function.

We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.

We deduce a nonlinear and inhomogeneous Fokker-Planck equation within a generalized Stratonovich, or stochastic α, prescription (α=0, 1/2, and 1, respectively, correspond to the Itô, Stratonovich and anti-Itô prescriptions). We obtain its stationary state p(st)(x) for a class of constitutive relations between drift and diffusion and show that it has a q-exponential form, p(st)(x)=N(q)[1-(1-q)βV...

A model is developed for the ow of a slightly compressible uid through a saturated inelastic porous medium. The initial-boundary-value problem is a system that consists of the di usion equation for the uid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto-visco-plastic type. The variational form of this...

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial-boundary-value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto-visco-plastic type. The variational form ...

the purpose of this paper is to analyze in detail a special nonlinear partial differentialequation (npde) of the second order which is important in physical, chemical and technicalapplications. the present npde describes nonlinear diffusion and is of interest in several partsof physics, chemistry and engineering problems alike. since nature is not linear intrinsicallythe nonlinear case is there...

This paper studies the robustH∞ filtering problem of nonlinear stochastic systems with time delay appearing in state equation, measurement, and controlled output, where the state is governed by a stochastic Itô-type equation. Based on a nonlinear stochastic bounded real lemma and an exponential estimate formula, an exponential asymptotic mean square H∞ filtering design of nonlinear stochastic t...

We generalize the Toda lattice (or Toda chain) equation to the square lattice, i.e., we construct an integrable nonlinear equation for a scalar field taking values on the square lattice and depending on a continuous (time) variable, characterized by an exponential law of interaction in both discrete directions of the square lattice. We construct the Darboux-Bäcklund transformations for such lat...