相关论文: 50 Open Problems: Ultraproduct II$_1$ factors

Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type…

We prove many new results about interacting Fock spaces. We pose many open problems; for most of them we prove that their solutions have no choice but being nontrivial. We ask the kind reader to consult the extended abstract in the paper.

A list of open problems on holomorphic symplectic, contact and Poisson manifolds.

This is a review of studies of the behaviour of materials under high pressure in Serbia in the second half of the last century.Theoretical foundations are presented,as well as some examples of the results and a selection of the open…

This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.

For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…

Different q-factor definitions are considered. The formula connecting different q-factors is given. Also it is pointed the way to find all the q-factors from experimental data.

This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…

Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also summarize briefly methods and tools that have led to this collection.

In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and…

In this paper, we extend the definition of hyperinner product defined on weak hypervector spaces with a hyperoperation scalar product to weak hypervector spaces with the hyperoperations sum and scalar products.

We study Cartan subalgebras in the context of amalgamated free product II$_1$ factors and obtain several uniqueness and non-existence results. We prove that if $\Gamma$ belongs to a large class of amalgamated free product groups (which…

Two results on product of compact filters are shown to be the common principle behind a surprisingly large number of theorems.

The intended model of the homotopy type theories used in Univalent Foundations is the infinity-category of homotopy types, also known as infinity-groupoids. The problem of higher structures is that of constructing the homotopy types needed…

A brief introduction into bimodules of $II_1$-factors is presented. Furthermore a version of the following result due to M. Pimsner and S. Popa is derived: Let $N=M_{-1}\subset M=M_0 \subset M_1 \subset M_2 \subset \ldots$ denote the Jones…

We construct `structure invariants' of a one-ended, finitely presented group that describe the way in which the factors of its JSJ decomposition over two-ended subgroups fit together. For groups satisfying two technical conditions, these…

The goal of this paper is to develop methods for the construction of saturated designs that include the mean, main effects and the two-factor interactions of one factor with a subset of the remaining factors. If one factor is interacting…

Some formulas and speculations are presented relative to integrable systems and quantum mechanics.

The paper is devoted to construction of some closed inductive sequence of models of the generalized second-order Dedekind theory of real numbers with exponentially increasing powers. These models are not isomorphic whereas all models of the…