Related papers: One recent development of the M_3 vs. M_1 problem

I review recent results in three topics of the M-world: (i) Scales. (ii) New dark matter candidates. (iii) Cosmological solutions from p-branes. The three topics are discussed in the framework of Ho\v{r}ava-Witten compactifications. Part…

Recent reverses for the discrete generalised triangle inequality and its continuous version for vector-valued integrals in Banach spaces are surveyed. New results are also obtained. Particular instances of interest in Hilbert spaces and for…

This article demonstrates that the recent proof of the invariant subspace problem, as presented by Khalil et al., is incorrect.

We show that the problem whether a given finite metric space can be embedded into $m$-dimensional rectilinear space can be reformulated in terms of the Gromov--Hausdorff distance between some special finite metric spaces.

This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.

We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber…

There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and…

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

We define a kind of moduli space of nested surfaces and mappings, which we call a comparison moduli space. We review examples of such spaces in geometric function theory and modern Teichmueller theory, and illustrate how a wide range of…

The aim of this paper is to investigate weakly developable spaces. For a comparison with semi-metrizable spaces, we introduce and study a class of spaces among those of weakly developable spaces, semimetrizable spaces and first countable…

In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…

This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of "mubness" is introduced, and applied to some recent calculations in six dimensions (partly done…

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…

The long history of the research concerning the possible existence of bound or resonant states in light multineutron systems, essentially $^3$n and $^4$n, is reviewed. Both the experimental and the theoretical points of view have been…

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

We introduce superequivalence and superuniform spaces.

Some boundedness properties of function spaces (considered as topological groups) are studied.

We study the geometry of spaces of planes on smooth complete intersections of three quadrics, with a view toward rationality questions.

In this paper we examine the multipliers from one model space to another.