Related papers: Some open problems on well-filtered spaces and sob…
We provide a brief topical outline of the persisting problem of the hyperon polarization and consider some future experimental prospects. The predictions which deserve experimental verification are proposed.
In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced…
We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
We construct two dcpo's whose Scott spaces are sober, but the Scott space of their order product is not sober. This answers an open problem on the sobriety of Scott spaces. Meantime, we show that if $M$ and $N$ are special type of sober…
The determination of photospheric abundances in late-type stars from spectroscopic observations is a well-established field, built on solid theoretical foundations. Improving those foundations to refine the accuracy of the inferred…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…
We recall some known and present several new results about Sobolev spaces defined with respect to a measure, in particular a precise pointwise description of the tangent space to this measure in dimension 1. This allows to obtain an…
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness…
This is a survey on special metrics. We shall present some results and open questions on special metrics mainly appeared in the last 10 years
Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to establish the existence of floating areas in Hilbert geometries.…
Thin filters and gas tight windows are used in Space to protect sensitive X-ray detectors from out-of-band electromagnetic radiation, low-energy particles, and molecular contamination. Though very thin and made of light materials, filters…
A brief report on recent work on the sphere-packing problem.
Metrizable spaces are studied in which every closed set is an $\alpha$-limit set for some continuous map and some point. It is shown that this property is enjoyed by every space containing sufficiently many arcs (formalized in the notion of…
Various forms of sorting problems have been studied over the years. Recently, two kinds of sorting puzzle apps are popularized. In these puzzles, we are given a set of bins filled with colored units, balls or water, and some empty bins.…
A class of water wave problems concerns the dynamics of the free interface separating an inviscid, incompressible and irrotational fluid, under the influence of gravity, from a zero-density region. In this note, we present some recent…
Slow sand filtration is most appropriate where there is funding to subsidize the initial cost of the filter, available training for use and maintenance, locally available sand, and a transportation network capable of moving the filter.…