We consider an interior inverse medium problem of reconstructing the shape of a cavity. Both the measurement locations and point sources are inside the cavity.
Due to the lack of a priori knowledge of physical prosperities of the medium inside the cavity and to avoid the computation of background Green's functions, the reciprocity gap method is employed. We prove the related theory and present some numerical examples for validation.
In this paper we will propose a new classifier design based
on the AFS fuzzy theory. First, we will briefly review the current
researches in data classification based on fuzzy and rough set theories and then
present the AFS framework. Second, we will present new
membership functions for fuzzy sets with their logic operations in the AFS
framework and then tackle some theoretical and computational problems related to classifier design. Third,
we will develop a new approach for fuzzy classifier
design based on the proposed membership functions and their logic
operations. Finally, a well-known example is
used to illustrate its effectiveness. The advantage of this classifier is in two-folds. One is
that it can mimic the human reasoning comprehensively and offers a far
more flexible and effective way for the study of large-scale
intelligent systems. The other is its simplicity in methodology and
mathematical beauty in fuzzy theory.
This paper deals positive steady state for predator-prey microorganisms in a flow reactor with diffusion and flow. The coexistence conditions for the predator-prey populations are established. The main method used here is the fixed point index theory.
The scattering of time-harmonic acoustic plane waves by a mixed type scatterer is considered. Such a scatterer is given as the union of
several components with different physical properties. Some of them are impenetrable obstacles with Dirichlet or impedance boundary conditions,
while the others are penetrable inhomogeneous media with compact support.
This paper is concerned with modifications of the factorization method for the following two basic cases,
one is the scattering by a priori separated sound-soft and sound-hard obstacles,
the other one is the scattering by a scatterer with impenetrable (Dirichlet) and penetrable components. The other cases can be dealt with similarly.
Finally, some numerical experiments are presented to demonstrate the feasibility and effectiveness of the modified factorization methods.
This paper concerns inverse source problems for the time-dependent Maxwell equations. The electric current density is assumed to be the product of a spatial function and a temporal function. We prove uniqueness and stability in determining the spatial or temporal function from the electric field, which is measured on a sphere or at a point over a finite time interval.