Related papers: Are theoretical results 'Results'?
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally…
In this paper we present some interesting results involving summation of series in particular trigonometric ones. We failed to locate these results in existing literature or in the web like MathWorld (http://mathworld.wolfram.com/) nor…
Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
The purpose of this work is to introduce a general class of $C_G$-simulation functions and obtained some new coincidence and common fixed points results in metric spaces. Some useful examples are presented to illustrate our theorems.…
We apply a classic result in Theoretical Computer Science to solve a sticky problem, and give a neat and slick quick proof of half of it
In modal logic, semantic consequence is usually defined locally by truth preservation at all worlds in all models (with respect to a class of frames). It can also be defined globally by truth preservation in all models (with respect to a…
This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of…
We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems,…
We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are…
This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…
In this paper, we establish some new variants of fixed point theorems for a large class of countably nonexpansive multi-valued mappings. Some fixed point theorems for the sum and the product of three multi-valued mappings defined on…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
High energy physics features many ingenious tools for extracting finite results from formally divergent expressions. This brief note argues from a new perspective that all such formal infinities are meaningful markers of new physics. As…
The following is an extended version of a talk given at the Kinosaki Symposium on Algebraic Geometry in October 2011. The aim is to give an overview of product-quotient surfaces, the results that have been proven so far in collaboration…
Some mathematical theorems represent ideas that are discovered again and again in different forms. One such theorem is Hall's marriage theorem. This theorem is equivalent to several other theorems in combinatorics and optimization theory,…
In this paper peer review reliability is investigated based on peer ratings of research teams at two Belgian universities. It is found that outcomes can be substantially influenced by the different ways in which experts attribute ratings.…
I take a pragmatist perspective on quantum theory. This is not a view of the world described by quantum theory. In this view quantum theory itself does not describe the physical world, nor our observatons, experiences or opinions of it.…