in this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete riemannian manifold floating in space rn+1and is tangent to the space rn at ∂h0(t); (2...

designing and optimization of the intake manifold is one of the important steps in the development of the internal combustion engines. in this paper, the flow inside the intake manifold of an internal combustion engine is investigated by numerical modeling. the convective flux models are adopted to simulate the unsteady compressible flow behavior. to solve the governing equations, for calculati...

Nonlinear dimensionality reduction is an active area of research. In this paper, we present a thematically different approach to detect low-dimensional manifold that lies within set bounds derived from given point cloud. A matrix representing distances on low-rank, and our method based current low-rank Matrix Completion (MC) techniques for recovering partially observed fully entries. MC methods...