805 research outputs found
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 , we consider the problem of restoring the metric and the
magnetic potential 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 .
For the linearized problem, we show injectivity, up to the natural
obstruction, under explicit bounds on the curvature and on . We also
show injectivity and stability for and in a generic class
including real analytic ones.
For the nonlinear problem, we show rigidity for real analytic simple ,
. Also, rigidity holds for metrics in a given conformal class, and
locally, near any .Comment: This revised version contains a proof that 2D simple magnetic systems
are boundary rigid. Some references have been adde
Recommended from our members
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
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
- …