相关论文: Decidable fan theorem and uniform continuity theor…
"Church's thesis" ($\mathsf{CT}$) as an axiom in constructive logic states that every total function of type $\mathbb{N} \to \mathbb{N}$ is computable, i.e. definable in a model of computation. $\mathsf{CT}$ is inconsistent in both…
A cornerstone of current-density functional theory (CDFT) in its paramagnetic formulation is proven. After a brief outline of the mathematical structure of CDFT, the lower semi-continuity and expectation valuedness of the CDFT…
In the author's PhD thesis (2019) universal envelopes were introduced as a tool for studying the continuously obtainable information on discontinuous functions. To any function $f \colon X \to Y$ between $\operatorname{qcb}_0$-spaces one…
The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four point function. The equivalence between PCT theorem and {\it weak local commutativity}, due to Jost,…
Fatou's lemma is a classic fact in real analysis that states that the limit inferior of integrals of functions is greater than or equal to the integral of the inferior limit. This paper introduces a stronger inequality that holds uniformly…
This paper describes and motivates a new decision theory known as functional decision theory (FDT), as distinct from causal decision theory and evidential decision theory. Functional decision theorists hold that the normative principle for…
In this work, we introduce a definition of the Discrete Fourier Transform (DFT) on Euclidean lattices in $\R^n$, that generalizes the $n$-th fold DFT of the integer lattice $\Z^n$ to arbitrary lattices. This definition is not applicable for…
Dynamic density functional theory (DDFT) is a promising approach for predicting the structural evolution of a drying suspension containing one or more types of colloidal particles. The assumed free-energy functional is a key component of…
Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories that can be made all-loop finite. The requirement of all-loop finiteness leads to a severe reduction of the free parameters of the theory and, in turn, to a large…
Urysohn's Lemma is a crucial property of normal spaces that deals with separation of closed sets by continuous functions. It is also a fundamental ingredient in proving the Tietze Extension Theorem, another property of normal spaces that…
In this paper, we investigate the existence and uniqueness of fixed points for self-mappings defined on bipolar metric spaces using a new class of contractive conditions, namely polynomial-type contractions. Our main results establish…
Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories that can be made all-loop finite. The requirement of all-loop finiteness leads to a severe reduction of the free parameters of the theory and, in turn, to a large…
Dynamical density functional theory (DDFT) is a powerful variational framework to study the nonequilibrium properties of colloids by only considering a time-dependent one-body number density. Despite the large number of recent successes,…
In the present article, we introduce a unified notion of multi-tupled fixed points and utilize the same to prove some existence and uniqueness unified multi-tupled fixed point theorems for Boyd-Wong type nonlinear contractions satisfying…
In intuitionistic mathematics, the Brouwer Continuity Theorem states that all total real functions are (uniformly) continuous on the unit interval. We study this theorem and related principles from the point of view of Reverse Mathematics…
Due to efficient scaling with electron number N, density functional theory (DFT) is widely used for studies of large molecules and solids. Restriction of an exact mean-field theory to local potential functions has recently been questioned.…
In this paper, we investigate a problem dual to the unification problem, namely the Common Term (CT) problem for string rewriting systems. Our main motivation was in computing fixed points in systems, such as loop invariants in programming…
N = 1, all-loop Finite Unified Theories (FUTs) are very interesting not only since they realize an old theoretical dream, but also due the remarkable predictive power of particular models as well as for providing candidates that might shed…
This study is on Cauchy's function $f(z)$ and its integral, $J[f(z)]\equiv (2\pi i)^{-1}\oint_C f(t)dt/(t-z)$ taken along a closed simple contour $C$, in regard to their comprehensive properties over the entire $z=x+iy$ plane consisted of…
The aim of this expository article is to present recent developments in the centuries old discussion on the interrelations between continuous and differentiable real valued functions of one real variable. The truly new results include,…