Related papers: Obstacles problems with measure data
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
We study the regularity of solutions to the obstacle problem for the parabolic biharmonic equation. We analyze the problem via an implicit time discretization, and we prove some regularity properties of the solution.
Big Data bring new opportunities to modern society and challenges to data scientists. On one hand, Big Data hold great promises for discovering subtle population patterns and heterogeneities that are not possible with small-scale data. On…
In this work, we show that very natural, apparently simple problems in quantum measurement theory can be undecidable even if their classical analogues are decidable. Undecidability hence appears as a genuine quantum property here. Formally,…
We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series…
The notorious `measurement problem' has been roving around quantum mechanics for nearly a century since its inception, and has given rise to a variety of `interpretations' of quantum mechanics, which are meant to evade it. We argue that no…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
We study the obstacle problem for unbounded sets in a proper metric measure space supporting a (p,p)-Poincare inequality. We prove that there exists a unique solution. We also prove that if the measure is doubling and the obstacle is…
In this article, we adapt the definition of viscosity solutions to the obstacle problem for fully nonlinear path-dependent PDEs with data uniformly continuous in $(t,\omega)$, and generator Lipschitz continuous in $(y,z,\gamma)$. We prove…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$ during the time interval n. Behavior of…
We review astrophysical, cosmological and terrestrial evidence for and against the constancy of fundamental parameters of particle physics, and discuss theoretical issues of unification and scalar-mediated forces, finding that the current…
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
In this paper we obtain some existence result of solution for general variational inequalities. As applications several coincidence and fixed point results are provided.
Typically, a stochastic model relates stochastic "inputs" and, perhaps, controls to stochastic "outputs". A general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of…
The problem of sequential anomaly detection and identification is considered, where multiple data sources are simultaneously monitored and the goal is to identify in real time those, if any, that exhibit ``anomalous" statistical behavior.…
A variety of physical unknowables are discussed. Provable lack of physical omniscience, omnipredictability and omnipotence is derived by reduction to problems which are known to be recursively unsolvable. "Chaotic" symbolic dynamical…
In this contribution I review rigorous formulations of a variety of limitations of measurability in quantum mechanics. To this end I begin with a brief presentation of the conceptual tools of modern measurement theory. I will make precise…