Related papers: An Episode in The Old Mathematical Intelligencer
We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given bimodal map is. We then define a new class of polymodal…
For a much better-founded theory, check Wing Ip, GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L16203, doi:10.1029/2005GL025386, 2006 (see also http://www.agu.org/journals/gl/gl0616/2005GL025386/)
In Jurek 1985 and 1988 the random integral representations conjecture was stated. It claims that (some) limit laws can be written as probability distributions of random integrals of the form $\int_{(a,b]}h(t)dY_{\nu}(r(t))$, for some…
It is established interconnections between various integral conditions that play an important role in the theory of space mappings and in the theory of degenerate Beltrami equations in the plane.
Takens constructed a residual subset of the state space consisting of initial points with historic behaviour for expanding maps on the circle. We prove that this statistical property of expanding maps on the circle is preserved under small…
We derive key features of the Age-of-Information distribution in a system whose activities are strictly limited to periodic instances on a global time grid. In particular, one agent periodically generates updates while the other agent…
We give a rational form of a generic two-dimensional "quad" map, containing the so-called $Q_4$ case, but whose coefficients are free. Its integrability is proved using the calculation of algebraic entropy.
Given a symmetric matrix $M\in \{0,1,*\}^{D\times D}$, an $M$-partition of a graph $G$ is a function from $V(G)$ to $D$ such that no edge of $G$ is mapped to a $0$ of $M$ and no non-edge to a $1$. We give a computer-assisted proof that,…
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.
We initiate a comprehensive investigation of the geometry of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar N=4 SYM theory. We do so by introducing and studying…
Lecture notes of lectures delivered at the Hodge Theory Summer School in ICTP Trieste, June 2010.
This paper discusses the formulations of the past in quantum mechanics.
E394 in the Enestrom index. Translated from the Latin original, "De partitione numerorum in partes tam numero quam specie datas" (1768). Euler finds a lot of recurrence formulas for the number of partitions of $N$ into $n$ parts from some…
The study of word maps on groups has been of deep interest in recent years. This survey focuses on the case of power maps on groups; $viz.$ the map $x\mapsto x^M$ for a group $G$, and an integer $M\geq 2$. Here, we accumulate various…
Although the Four Color Conjecture originated in cartography, surprisingly, there is nothing in the literature on the number of ways to color an actual geographic map with four or fewer colors. In this paper, we compute these numbers, with…
This article is an expanded version of my talk at the Gathering for Gardner, 2012.
The ancient priest-astronomers constantly watched many heavenly bodies. The record about Halley's Comet of 1682 A.D. has been decoded completely. Good agreement between it and the results of European astronomers is seen. The records about…
The Muon Accelerator Program (MAP) is described, along with its first year of accomplishments.
We consider the mathematical theory of geographical maps, with an emphasis on the eighteenth century works of Euler, Lagrange and Delisle. This period is characterized by the frequent use of maps that are no more obtained by the…
The Cluster-cluster model was introduced by Meakin et al in 1984. Each $x\in \mathbb{Z}^d$ starts with a cluster of size 1 with probability $p \in (0,1]$ independently. Each cluster $C$ performs a continuous-time SRW with rate…