相关论文: Separating the Fan Theorem and Its Weakenings

We construct one-parameter complex analytic families whose special fibers are complete toric varieties. Under some assumptions, the general fibers of these families also become toric varieties and we can explicitly describe the…

Credal sets are one of the most important models for describing probabilistic uncertainty. They usually arise as convex sets of probabilistic models compatible with judgments provided in terms of coherent lower previsions or more specific…

A fan is an arcwise-connected continuum, which is hereditarily unicoherent and has exactly one ramification point. Many of the known examples of fans were constructed as 1-dimensional continua that are unions of arcs which intersect in…

A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or…

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of material systems,…

Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to…

We present a relatively simple description of binary, definable subsets of models of weakly quasi-o-minimal theories. In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem. We also…

This paper investigates isomorphisms of Bergman fans of matroids respecting different fan structures, which we regard as matroid analogs of birational maps. We show that isomorphisms respecting the fine fan structure are induced by matroid…

Compactness is one of the core notions of analysis: it connects local properties to global ones and makes limits well-behaved. We study the computational properties of the compactness of Cantor space $2^{\mathbb{N}}$ for uncountable covers.…

The real intersection cohomology of a toric variety is described in a purely combinatorial way using methods of elementary commutative algebra only. We define, for arbitrary fans, the notion of a ``minimal extension sheaf'' on the fan as an…

We develop a formal theory of the weak values with emphasis on the consistency conditions and a probabilistic interpretation in the counter-factual processes. We present the condition for the choice of the post-selected state to give a…

Bell's Theorem was developed on the basis of considerations involving a linear combination of spin correlation functions, each of which has a distinct pair of arguments. The simultaneous presence of these different pairs of arguments in the…

Two closely related classes of topological spaces are fences and fans. A fence is a compact metric space whose components are either arcs or singletons. A fan is a continuum formed by joining arcs at a common vertex, in such a way that…

Recent progress in the theory of fission of hot nuclei is reported. We discuss in particular the properties of the friction formfactor as function of the deformation (and possibly of the temperature) which are necessary to reproduce data…

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$…

The proofs of K. Oka's Coherence Theorems are based on Weierstrass' Preparation (division) Theorem. Here we formulate and prove a Weak Coherence Theorem without using Weierstrass' Preparation Theorem, but only with power series expansions:…

We present two algorithms determining all the complete and simplicial fans admitting a fixed non-degenerate set of vectors $V$ as generators of their 1-skeleton. The interplay of the two algorithms allows us to discerning if the associated…

We distinguish between faint, weak, strong and strict localizations of categories at morphism families and show that this framework captures the different types of derived functors that are considered in the literature. More precisely, we…

We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game.…

The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise when one drops the uniqueness requirement and asks only for…