We develop a projection-based dimension reduction approach for partial differential equations with high-dimensional stochastic coefficients. This technique uses samples of the gradient of the quantity of interest (QoI) to partition the uncertainty domain into “active” and “passive” subspaces. The passive subspace is characterized by near-constant behavior of the quantity of interest, while the ...

We consider themaximum flow problem with minimum quantities (MFPMQ), which is a variant of the maximum flow problem where the flow on each arc in the network is restricted to be either zero or above a given lower bound (a minimum quantity), which may depend on the arc. This problem has recently been shown to be weakly NP-complete even on series-parallel graphs. In this paper, we provide further...

The paper interprets the concept “operator in separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined “classical” quantum mechanics) by that of “quantum information”. As far wave function characteristic probability (density) distribution for all possible values a certain quantity to be measured, definition mechanics means any unitary change distribution. It c...