Related papers: On C.T.C. Wall's suspension theorem
The finite sum of the squares of the Mie coefficients is very useful for addressing problems of classical light scattering. An approximate formula available in the literature, and still in use today, has been developed to determine a priori…
The main result of this paper is a proof of the continuity of a family of integral functionals defined on the space of functions of bounded variation with respect to a topology under which smooth functions are dense. These functionals occur…
We consider the swampland distance and de Sitter conjectures, of respective order one parameters $\lambda$ and $c$. Inspired by the recent Trans-Planckian Censorship conjecture (TCC), we propose a generalization of the distance conjecture,…
In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the…
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof…
In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent: (i) L is quasi-finite. (ii) There exists a [L]-invertible…
We endow the set of persistence diagrams with the strong topology (the topology of countable direct limit of increasing sequence of bounded subsets considered in the bottleneck distance). The topology of the obtained space is described.…
We prove a new selection theorem for multivalued mappings of C-space. Using this theorem we prove extension dimensional version of Hurewicz theorem for a closed mapping $f\colon X\to Y$ of $k$-space $X$ onto paracompact $C$-space $Y$: if…
The main idea in the present work is the definition of an experimental proposal for the detection of the number of extra{compact dimensions contained as a core feature in String Theory. This goal will be achieved as a consequence of the…
Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors.…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…
We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related. (T.1) A basic property of Cantor space $2^{\mathbb{N}}$…
We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…
In this note we consider a multi-slit Loewner equation with constant coefficients that describes the growth of multiple SLE curves connecting $N$ points on $\mathbb{R}$ to infinity within the upper half-plane. For every $N\in\mathbb{N}$,…
Flexible grid topology has become a key enabler of flexibility in modern power grids, particularly for congestion management. Studying the effects of combinatorial topological changes is therefore of significant interest, though it remains…
Andr\'e's celebrated Theorem of 1998 implies that each complex straight line (apart from obvious exceptions) contains at most finitely many points whose both coordinates are j-invariants of elliptic curves with complex multiplication. We…
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…
This paper describes several classical constructions of thin bases of finite order in additive number theory, and, in particular, gives a complete presentation of a beautiful construction of J. W. S. Cassels of a class of polynomially…
Derrick's theorem on the nonexistence of stable time-independent scalar field configurations [G. H. Derrick, J. Math. Phys. 5, 1252 (1964)] is generalized to finite systems of arbitrary dimension. It is shown that the "dilation" argument…