A characteristic nonconforming mixed finite element method (MFEM) is proposed for the convection-dominated diffusion problem based on a new mixed variational formulation. The optimal order error estimates for both the original variable u and the auxiliary variable σ with respect to the space are obtained by employing some typical characters of the interpolation operator instead of the mixed (or...

Abstract When solving ill-posed inverse problems, a good choice of the prior is critical for computation reasonable solution. A common approach to include Gaussian prior, which defined by mean vector and symmetric positive definite covariance matrix, use iterative projection methods solve corresponding regularized problem. However, main challenge many these that matrix must be known fixed (up c...

A theorem of Kušnirenko and Bernštein shows that the number of isolated roots of a system of polynomials in a torus is bounded above by the mixed volume of the Newton polytopes of the given polynomials, and this upper bound is generically exact. We improve on this result by introducing refined combinatorial invariants of polynomials and a generalization of the mixed volume of convex bodies: the...

Stromatal fruiting bodies of Cordyceps cardinalis were successfully produced in cereals. Brown rice, German millet and standard millet produced the longest-length of stromata, followed by Chinese pearl barley, Indian millet, black rice and standard barley. Oatmeal produced the shortest-length of fruiting bodies. Supplementation of pupa and larva to the grains resulted in a slightly enhanced pro...