Related papers: Vector variational principle
We construct variations for the classes of regular solutions to degenerate Beltrami equations with restrictions of the set-theoretic type for the complex coefficient. On this basis, we prove the variational maximum principle and other…
We give a new simpler proof of a theorem of Jayne and Rogers.
We prove a structure theorem for projective varieties with nef anticanonical divisors.
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
We prove a stability version of the Pr\'ekopa-Leindler inequality.
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
We provide a short proof of the 1-dimensional flat chain conjecture.
We study flat vector bundles over complex parallelizable manifolds.
In order to solve an initial value problem by the variational iteration method, a sequence of functions is produced which converges to the solution under some suitable conditions. In the nonlinear case, after a few iterations the terms of…
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.
In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li, Shi, J. Math. Anal. Appl. 246, 308-319 (2000), clarify the assumptions and conclusions of their Theorem 1 as…
We prove a simple uncertainty principle and show that it can be applied to prove Wegner estimates near fluctuation boundaries. This gives new classes of models for which localization at low energies can be proven.
Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational…
For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof…
In this short communication, we present a generalization of the Ekeland variational principle. The main result is established through standard tools of functional analysis and calculus of variations. The novelty here is a result involving…
Consider an election between k candidates in which each voter votes randomly (but not necessarily independently) and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for…
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.
It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still…