Is The Standard Definition of Knowledge Incomplete?

The aim of this paper is to suggest a new interpretation to the Gettier problem by showing that the standard JTB definition of knowledge is not epistemologically incomplete, being at the same time formally incomplete. The Gettier problem is shown to emerge through the implicit self application of the JTB definition of knowledge to prove its own incompleteness. A conclusion is drawn, which runs counter to the traditional view that the problem necessarily requires a conceptual amendment of the standard definition, in spite of the formal incompleteness of the latter. The Gettier problem is construed to be related to the ancient Meno problem within a contemporary justificational discourse

The boundary rigidity problem in the presence of a magnetic field

For a compact Riemannian manifold with boundary, endowed with a magnetic potential $\alpha$, we consider the problem of restoring the metric $g$ and the magnetic potential $\alpha$ from the values of the Ma\~n\'e action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Ma\~n\'e action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of $\alpha$. For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on $\alpha$. We also show injectivity and stability for $g$ and $\alpha$ in a generic class $\mathcal{G}$ including real analytic ones. For the nonlinear problem, we show rigidity for real analytic simple $g$, $\alpha$. Also, rigidity holds for metrics in a given conformal class, and locally, near any $(g,\alpha)\in \mathcal{G}$.Comment: This revised version contains a proof that 2D simple magnetic systems are boundary rigid. Some references have been adde

Fully Depleted, Monolithic Pinned Photodiode CMOS Image Sensor Using Reverse Substrate Bias

A new pixel design using pinned photodiode (PPD) in a 180 nm CMOS image sensor (CIS) process has been developed as a proof of principle. The sensor can be fully depleted by means of reverse bias applied to the substrate, and the principle of operation is applicable to very thick sensitive volumes. Additional n-type implants under the in-pixel p-wells have been added to the manufacturing process in order to eliminate the large parasitic substrate current that would otherwise be present in a normal device. The new design exhibits nearly identical electro-optical performance under reverse bias as the reference PPD pixel it is based on, and the leakage current is effectively suppressed. The characterisation results from both front- and back-side illuminated sensor variants show that the epitaxial layer is fully depleted

Quantitative Photo-acoustic Tomography with Partial Data

Photo-acoustic tomography is a newly developed hybrid imaging modality that combines a high-resolution modality with a high-contrast modality. We analyze the reconstruction of diffusion and absorption parameters in an elliptic equation and improve an earlier result of Bal and Uhlmann to the partial date case. We show that the reconstruction can be uniquely determined by the knowledge of 4 internal data based on well-chosen partial boundary conditions. Stability of this reconstruction is ensured if a convexity condition is satisfied. Similar stability result is obtained without this geometric constraint if 4n well-chosen partial boundary conditions are available, where $n$ is the spatial dimension. The set of well-chosen boundary measurements is characterized by some complex geometric optics (CGO) solutions vanishing on a part of the boundary.Comment: arXiv admin note: text overlap with arXiv:0910.250