We study the problem of estimating the size of an inclusion embedded inside a two dimensional body with discontinuous conductivity by one voltage-current measurement. This problem is practically important because the conductivity of a human body is discontinuous. The proofs rely on quantitative uniqueness estimates for the conductivity equation with discontinuous coefficients.

We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuous H(div) and first-order error estimate in L(2).

In this paper we give stability analysis and error estimates for the recently introduced central discontinuous Galerkin method when applied to linear hyperbolic equations. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitative conclusions from the a...

DNA polymerases catalyze the synthesis of DNA using a continuous uninterrupted template strand. However, it has been shown that a 3'-->5' exonuclease-deficient form of the Klenow fragment of Escherichia coli DNA polymerase I as well as DNA polymerase of Thermus aquaticus can synthesize DNA across two unlinked DNA templates. In this study, we used an oligonucleotide-based assay to show that disc...

Intuitively, discontinuous changes can be seen as very rapid continuous changes. A couple of alternative methods based on this ontology are presented and compared. One, called the approximation method, approximates discontinuous change by continuous function and then calculates a limit. The other, called the direct method, directly creates a chain of hypothetical intermediate states (mythical i...

We study discontinuous Galerkin methods for solving elliptic variational inequalities, of both the first and second kinds. Analysis of numerous discontinuous Galerkin schemes for elliptic boundary value problems is extended to the variational inequalities. We establish a priori error estimates for the discontinuous Galerkin methods, which reach optimal order for linear elements. Results from so...

This article introduces a novel transition system for discontinuous lexicalized constituent parsing called SR-GAP. It is an extension of the shift-reduce algorithm with an additional gap transition. Evaluation on two German treebanks shows that SR-GAP outperforms the previous best transitionbased discontinuous parser (Maier, 2015) by a large margin (it is notably twice as accurate on the predic...

Let M be a manifold, on which a real reductive Lie group G acts transitively. The action of a discrete subgroup Γ on M is not always properly discontinuous. In this paper, we give a criterion for properly discontinuous actions, which generalizes our previous work [6] for an analogous problem in the continuous setting. Furthermore, we introduce the discontinuous dual t(H:G) of a subset H of G , ...

This paper offers insights into the diffusion and impact of artificial intelligence in science. More specifically, we show that neural network-based technology meets essential properties emerging technologies scientific realm. It is novel, because it shows discontinuous innovations originating domain put to new uses many application domains; quick growing, its dimensions being subject rapid cha...

Failures of road embankments on discontinuous permafrost commonly occur during thawing of the foundation soil. As an approximation, weak zones created by thawing of discontinuous permafrost can be considered as ‘voids’ within the foundation. Geosynthetic reinforcements have been used to bridge these ‘voids’ and provide support to the embankment fill. This paper presents results of a numerical i...