• Accuracy. Result is not identical to that of a previous run of the same job, or does not fall within valid range. • Performance. Observe a performance difference from a previous run of the same job. • Portability. Can’t execute the same job on a distinct software stack, platform, or compute site. • Longevity. Unable to reproduce a result due to lack of identical resources as previous run of t...

If u(x, y) is an infinity harmonic function, i.e., a viscosity solution to the equation −∆∞u = 0 in Ω ⊂ Rm+1 then the function v(x, z) = u(x, ‖z‖) is infinity harmonic in the set {(x, z) : (x, ‖z‖) ∈ Ω} (provided u(x,−y) = u(x, y)).

We will discuss here Dirichlet problems for non linear …rst order partial di¤erential equations. We will present the recent results of DacorognaMarcellini on this subject; mentioning brie‡y, as a matter of introduction, some results on viscosity solutions.

This article considers the problem of building absolutely minimizing Lipschitz extensions to a given function. These extensions can be characterized as being the solution of a degenerate elliptic partial differential equation, the “infinity Laplacian”, for which there exist unique viscosity solutions. A convergent difference scheme for the infinity Laplacian equation is introduced, which arises...

This paper consider various examples of metrics which are contractive w.r.t. an evolution semigroup, and discusses the possibility of an abstract O.D.E. theory on metric spaces, with applications to hyperbolic systems. In particular, using a recently introduced deenition of Viscosity Solutions, it is shown how a strictly hyperbolic system of conservation laws can be reformulated as an abstract ...

block-flexure is the most common mode of toppling failure in natural and excavated rock slopes. in such failure, some rock blocks break due to tensile stresses and some overturn under their own weights and then all of them topple together. in this paper, first, a brief review of previous studies on toppling failures is presented. then, the physical and mechanical properties of experimental mode...

in this paper, sufficient conditions are investigated for the existence of periodic (not necessarily positive) solutions for nonlinear several time delay population system with feedback control. nonlinear system affected by an periodic external source is studied. existence of a control variable provides  the extension of  some previous results obtained in other studies. we give a illustrative e...

the solutions of mathematical models for the estimation of the kinetic, and biokinetic parameters of naphthalene, anthracene and pyrene during degradation in surface and subsurface soils are presented in this work. the models were developed using the twin concepts of rate-determining step and steady-state approximation method. they described the biodegradation of single and a mixture of polycy...

this study presents a comparison between aluminum and iron plate electrodes on phosphate removal from aqueous solutions by electrocoagulation process. the effectiveness of main operational parameters such as initial ph, initial phosphate concentration and current density were examined. in addition, treated solution and sludge characteristics, energy consumption and electrode mass depletion w...