Related papers: The architect Kha's protractor
The bricks over preprojective algebras of type A are known to be in bijection with certain combinatorial objects called "arcs". In this paper, we show how one can use arcs to compute bases for the Hom-spaces and first extension spaces…
"What cannot be measured cannot be improved" while likely never uttered by Lord Kelvin, summarizes effectively the driving force behind this work. This paper presents a detailed discussion of automated metrics for evaluating structured 3D…
We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form $H(X)=1+{A}{|X|^{-\gamma}}$ for $|X|$ large, when $A<0$ and…
The theoretical interest in the longitudinal diffractive structure function F_L^D is briefly motivated and possible measurement methods are surveyed. A simulation based on realistic scenarios with a reduced proton beam energy at HERA-II…
Recent results by Keller and Nicol{\'a}s and by Koenig and Yang have shown bijective correspondences between suitable classes of t-structures and co-t-structures with certain objects of the derived category: silting objects. On the other…
We will study commuting properties of the defect functor $\mathrm{Dev}_\beta=\mathrm{Coker}\mathrm{Hom}_\mathcal{C}(\beta,-)$ associate to a homomorphism $\beta$ in a finitely presented category. As an application, we characterize objects…
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of these objects was initiated by Erd\H{o}s in 1950, and over the following decades he asked many questions about them. Most…
In the historical literature there has been an extended discussion on the question, whether the report of Sartorius von Waltershausen about C. F. Gauss checking the largest triangle of the geodetical measurement campaign in the kingdom of…
Economic complexity is a powerful tool to estimate the productive capabilities and future growth of modern economies. Little is known of how economic complexity evolves over long periods in history. In this paper, we use archaeological…
The bra and ket notation introduced by Dirac and the dimensional analysis are two powerful tools for the physicist. Curiously, almost nothing is said about connections between these two topics in the literature. We show here that bras and…
Recent work by J.~Prades and myself on $K\to\pi\pi$ is described. The first part describes our method to connect in a systematic fashion the short-distance evolution with long-distance matrix-element calculations taking the scheme…
An articulated probe is modeled in the plane as two line segments, $ab$ and $bc$, joined at $b$, with $ab$ being very long, and $bc$ of some small length $r$. We investigate a trajectory planning problem involving the articulated…
Consider an input consisting of a set of $n$ disjoint triangular obstacles in $\mathbb{R}^3$ and a target point $t$ in the free space, all enclosed by a large sphere $S$ of radius $R$ centered at $t$. An articulated probe is modeled as two…
Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations have greatly evolved within this time span, and today include dynamically changing and…
Projective Reed-Muller codes(PRM codes) are constructed from the family of projective hypersurfaces of a fixed degree over a finite field $\F_q$. In this paper, we completely determine the minimal distance of the hull of any Projective…
Projective connections first appeared in Cartan's papers in the 1920's. Since then they have resurfaced periodically in, for example, integrable systems and perhaps most recently in the context of so called projectively equivariant…
We computationally investigate the transmission efficiency through moth-eye nanostructures that are fabricated on $\mathrm{SiO}_{2}$ windows in the wavelength range from 0.4 to 2 $\mathrm{\mu m}$. We investigated both truncated cones and…
The Indus Civilization, often denoted by its major city Harappa, spanned almost two millennia from 3200 to 1300 BC. Its tradition reaches back to 7000 BC: a 5000 year long expansion of villages and towns, of trading activity, and of…
Charged-particle trajectories are usually reconstructed with the LHCb detector using combined information from the tracking devices placed upstream and downstream of the 4\,T\,m dipole magnet. Trajectories reconstructed using only…
We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously…