Related papers: 50 Open Problems: Ultraproduct II$_1$ factors
Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.
Three open problems in analysis are formulated: 1. Injectivity of Radon transform 2. A uniqueness problem for an elliptic system of PDE 3. A problem in operator theory
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
A number of unsolved problems and open questions about the nature and the properties of supernovae are identified and briefly discussed. Some suggestions and directions toward possible solutions are also considered.
The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz,…
In this article we introduce an isomorphism invariant for type II_1 factors using the Connes-Folner condition. We compute bounds of this number for free group factors.
We describe a syntactic method for taking proofs which use ultraproducts and translating them into direct, constructive proofs.
We determine the structure of the Chan-Paton factors of the open strings ending on space filling D-branes in Type II orientifolds. Through the analysis, we obtain a rule concerning possible distribution of O-plane types. The result is…
We examine the properties of existentially closed (R^omega-embeddable) II_1 factors. In particular, we use the fact that every automorphism of an existentially closed (R^omega-embeddable) II_1 factor is approximately inner to prove that…
A brief history of the impurity theories in semiconductors is provided. A bound exciton model is proposed for both donor- and acceptor- like impurities and point defects, which offers a unified understanding for "shallow" and "deep"…
An introduction to and overview of the contents of this Special Issue are given. 32 classes of superconducting materials are discussed, grouped under the three categories "conventional", "possibly unconventional" and "unconventional"…
We solve a problem posed by Cardinali and Sastry [2] about factorization of $2$-covers of finite classical generalized quadrangles. To that end, we develop a general theory of cover factorization for generalized quadrangles, and in…
A list of all possible causal relations in the $2$-dimensional Minkowski space $M$ is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are introduced, all of them encapsulating…
We give a self contained introduction to numerical semigroups, and present several open problems centered on their factorization properties.
The number of ordered factorizations and the number of recursive divisors are two related arithmetic functions that are recursively defined. But it is hard to construct explicit representations of these functions. Taking advantage of their…
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…
The subfactor approach to modular invariants gives insight into the fusion rule structure of the modular invariants.
We describe the theory of "flag paraproducts" and their relationship with the field of differential equations.
Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…
Hyperuniform states of matter exhibit unusual suppression of density fluctuations at large scales, contrasting sharply with typical disordered configurations. Various types of hyperuniformity emerge in multicomponent disordered systems,…