相关论文: Uniqueness vs non-uniqueness in complete connectio…
We establish a one-to-one correspondence between one-sided and two-sided regular systems of conditional probabilities on the half-line that preserves the associated chains and Gibbs measures. As an application, we determine uniqueness and…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
We give several new characterizations of completely monotone functions and Bernstein functions via two approaches: the first one is driven algebraically via elementary preserving mappings and the second one is developed in terms of the…
The study of existence and uniqueness of solutions became important due to the lack of general formula for solving nonlinear ordinary differential equations (ODEs). Compact form of existence and uniqueness theory appeared nearly 200 years…
We determine all entire functions $f$ such that for nonzero complex values $a\neq b$ the implications $f=a \Rightarrow f' =a$ and $f' =b \Rightarrow f=b$ hold. This solves an open problem in uniqueness theory. In this context we give a…
We prove an uniform boundedness principle for the Lipschitz seminorm of continuous, monotone, positively homogeneous and subadditive mappings on suitable cones of functions. The result is applicable to several classes of classically…
We summarize some facts on chains (totally ordered sets), from an order-theoretic and from a topological point of view. We highlight the fact that many classical theorems that are true for partially ordered sets under some completeness…
The union-closed sets conjecture (sometimes referred to as Frankl's conjecture) states that every finite, nontrivial union-closed family of sets has an element that is in at least half of its members. Although the conjecture is known to be…
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object", "everything can possibly exist, unless it yields contradiction", "the ideal elements correctly determine…
We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences…
In this paper, we show that the presence of the Archimedean and the mixture-continuity properties of a binary relation, both empirically non-falsifiable in principle, foreclose the possibility of consistency (transitivity) without…
Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic social choice, these…
The classical and extended deficiency one theorems by Feinberg apply to reaction networks with mass-action kinetics that have independent linkage classes or subnetworks, each with a deficiency of at most one and exactly one terminal strong…
We verify the existence of a purely unrectifiable set in which the typical Lipschitz function has a large set of full differentiability points. The example arises from a construction, due to Cs\"ornyei, Preiss and Ti\v{s}er, of a universal…
We extend Berge's Maximum Theorem to allow for incomplete preferences. We first provide a simple version of the Maximum Theorem for convex feasible sets and a fixed preference. Then, we show that if, in addition to the traditional…
In this paper we confirm that several crucial theorems due to Pommerenke and Becker for the theory of Loewner chains work well without normalization on the complex-valued first coefficient. As applications of those considerations, some new…
We introduce an statistical mechanical formalism for the study of discrete-time stochastic processes with which we prove: (i) General properties of extremal chains, including triviality on the tail $\sigma$-algebra, short-range…
An attempt to come closer to a resolution of the Collatz conjecture is presented. The central idea is the formation of a tree consisting of positive odd numbers with number 1 as root. Functions for generating the tree from the root are…
We consider linear orders of finite alternatives constructed by aggregating individual preferences. Specifically, we focus on linear orders that respect modified collective preference relations derived from supermajority rules, where…
Given a function $f : A \to \mathbb{R}^n$ of a certain regularity defined on some open subset $A \subseteq \mathbb{R}^m$, it is a classical problem of analysis to investigate whether the function can be extended to all of $\mathbb{R}^m$ in…