REVIEW 3 cited by
Extending the Choquet theory: Trace convexity
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We introduce the notion of trace convexity for functions and respectively, for subsets of a compact topological space. This notion generalizes both classical convexity of vector spaces, as well as Choquet convexity for compact metric spaces. We provide new notions of trace-convexification for sets and functions as well as a general version of Krein-Milman theorem. We show that the class of upper semicontinuous convex-trace functions attaining their maximum at exactly one Choquet-boundary point is residual and we obtain several enhanced versions of the maximum principle which generalize both the classical Bauer's theorem as well as its abstract version in the Choquet theory. We illustrate our notions and results with concrete examples of three different types.
Forward citations
Cited by 3 Pith papers
-
A discrete adjoint method for deterministic and probabilistic eikonal-equation-based inversion of traveltime for velocity and source location
A discrete adjoint state method, built on a second-order fast marching solver, provides self-consistent gradients for velocity and source location in eikonal traveltime tomography and enables deterministic and probabi...
-
3D Wave-Equation-Based Finite-Frequency Tomography for Ultrasound Computed Tomography
Finite-frequency traveltime tomography, with analytic sensitivity kernels in a water background, is applied to ultrasound computed tomography and used to reconstruct 2D and 3D sound-speed images from transmission data.
-
Effects of stochastic and natural seismic noise on the performance of waveform cross-correlation used to recover low-magnitude seismicity prior to the July 29, 2025, Kamchatka earthquake
Random-noise simulations and a Tohoku side-sensitivity test are used to argue that low-magnitude waveform-correlation detections before the July 29, 2025, Kamchatka earthquake are statistically significant and not ran...
Discussion (0). Continue with ORCID to comment.