Related papers: A constructive proof of the phase-type characteriz…
A theorem, usually attributed to Barr, yields that (A) geometric implications deduced in classical L_{\infty\omega} logic from geometric theories also have intuitionistic proofs. Barr's theorem is of a topos-theoretic nature and its proof…
Constructor theory asserts that the laws of physics are expressible as specifications of which transformations of physical systems can or cannot be brought about with unbounded accuracy by devices capable of operating in a cycle…
We present two new proofs of Simon Henry's result that the category of simplicial sets admits a constructive counterpart of the classical Kan-Quillen model structure. Our proofs are entirely self-contained and avoid complex combinatorial…
In [GW09a] we conjectured that uniformity of degree $k-1$ is sufficient to control an average over a family of linear forms if and only if the $k$th powers of these linear forms are linearly independent. In this paper we prove this…
We present a complete proof synthesis method for the eight type systems of Barendregt's cube extended with $\eta$-conversion. Because these systems verify the proofs-as-objects paradigm, the proof synthesis method is a one level process…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
We generalize the notion of relative phase to completely positive maps with known unitary representation, based on interferometry. Parallel transport conditions that define the geometric phase for such maps are introduced. The interference…
We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-pace based quantum mutual coherence function is…
We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is commonly summarized as a matrix theorem, which we call the…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate…
This note states and proves a representation theorem for regular quantity functions, based on the theory of quantity spaces, thereby giving a new perspective on dimensional analysis and the classical $\pi$ theorem.
The phase structure of QCD remains an open fundamental problem of standard model physics. In particular at finite density, our knowledge is limited. Yet, numerous model studies point towards a rich and complex phase diagram at large…
We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…
We give a proof of the o-minimal version of the Whitney Extension Theorem simplified as compared to the original ones. A new simplifying ingredient is a definable variant of Urysohn's lemma for class $\mathcal{C}^q$ (see Section 3).
In this paper we establish the convergence case of Khintchine's theorem for affine hyperplanes in function field of positive characteristic. Along with that, we also prove a quantitative version of the same. The main technique used in the…
We give a descriptive construction of trees for multi-ended graphs, which yields yet another proof of Stallings' theorem on ends of groups. Even though our proof is, in principle, not very different from already existing proofs and it draws…
We provide a short review of the progress made in the past decade with functional QCD in the description of the phase structure of QCD. We summarise the most important technical aspects of the framework, discuss strategies for truncations…
We give a new proof of the Semistable Reduction Theorem for curves. The main idea is to present a curve $Y$ over a local field $K$ as a finite cover of the projective line $X=\PP^1_K$. By successive blowups (and after replacing $K$ by a…
We prove a structure theorem for projective varieties with nef anticanonical divisors.