相关论文: Maharam's problem

We prove a computable version of the Hall Harem Theorem where the matching realizes a unary function with controlled sizes of cycles. We apply it to non-amenable computable coarse spaces. As a result, we obtain a computable version of the…

We consider the inverse Calder\'on problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, one usually…

[Inserted by J. Maurice Rojas] We give a formula for the number of complex roots of a generic system of two polynomial equations in two unknowns. The formula is completely combinatorial, ultimately depending just on the convex hull of the…

We interpret all Maurer-Cartan elements in the formal Hochschild complex of a small dg category which is cohomologically bounded above in terms of torsion Morita deformations. This solves the "curvature problem", i.e. the phenomenon that…

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

We present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms. Beginning from basic results developed by Riehm, our solution to this problem hinges on the classification of…

We show that a problem by Yau can not be true in general. The counterexamples are constructed based on the recent work of Wu and Zheng.

In 1934 H. Malmheden discovered an elegant geometric algorithm for solving the Dirichlet problem in a ball. Although his result was rediscovered independently by Duffin 23 years later, it still does not seem to be widely known. In this…

This short communication (preprint) is devoted to mathematical study of evolution equations that are important for mathematical physics and quantum theory; we present new explicit formulas for solutions of these equations and discuss their…

We consider non-negative $\sigma$-finite measure spaces coupled with a proper functional $P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant…

The classic Alternating Direction Method of Multipliers (ADMM) is a popular framework to solve linear-equality constrained problems. In this paper, we extend the ADMM naturally to nonlinear equality-constrained problems, called neADMM. The…

We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including the Porous Medium Equation and the p-Laplacian with a…

It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur--Ulam theorem and find necessary and sufficient conditions under which distance-preserving…

In this paper, we give a negative answer to a problem presented by Bharanedhar and Ponnusamy (Rocky Mountain J. Math. 44: 753--777, 2014) concerning univalency of a class of harmonic mappings. More precisely, we show that for all values of…

According to what has become a standard history of quantum mechanics, in 1932 von Neumann persuaded the physics community that hidden variables are impossible as a matter of principle, after which leading proponents of the Copenhagen…

Supmech, the universal mechanics developed in the previous two papers, accommodates both quantum and classical mechanics as subdisciplines (a brief outline is included for completeness); this feature facilitates, in a supmech based…

In 1967, Kadison asked ``does every type $\mathrm{II}_1$ factor have an orthonormal (with respect to the trace) basis consisting of unitaries?'' Using a noncommutative Lyapunov theorem of Akemann and Weaver, we prove that if $M$ is a…

This paper investigates the structure of fully nonlinear equations and their applications to geometric problems. We solve some fully nonlinear version of the Loewner-Nirenberg and Yamabe problems. Notably, we introduce Morse theory…

We observe that a slight adjustment of a method of Caffarelli, Li, and Nirenberg yields that plurisubharmonic functions extend across subharmonic singularities as long as the singularities form a closed set of measure zero. This solves a…

In this paper, we study uniform perturbations of von Neumann subalgebras of a von Neumann algebra. Let N and M be von Neumann subalgebras of a von Neumann algebra with finite probabilistic index in the sense of Pimsner-Popa. If N and M are…