Related papers: The Delone Peak
Nuclear systems are treated within a quantum statistical approach. Correlations and cluster formation are relevant for the properties of warm dense matter, but the description is challenging and different approximations are discussed. The…
For an arithmetic surface $X\to B=\operatorname{Spec} O_K$ the Deligne pairing $\left <\,,\,\right > \colon \operatorname{Pic}(X) \times \operatorname{Pic}(X) \to \operatorname{Pic}(B)$ gives the "schematic contribution" to the Arakelov…
An invariant definition of the operator $\Delta $ of the Batalin-Vilkovisky formalism is proposed. It is defined as the divergence of a Hamiltonian vector field with an odd Poisson bracket (antibracket). Its main properties, which follow…
The detour between two points u and v (on edges or vertices) of an embedded planar graph whose edges are curves is the ratio between the shortest path in in the graph between u and v and their Euclidean distance. The maximum detour over all…
In this article we consider the problem of finding the visibility set from a given point when the obstacles are represented as the level set of a given function. Although the visibility set can be computed efficiently by ray tracing, there…
In these expository notes we focus on selected topics around the themes: Delone sets as models for quasicrystals, inflation symmetries and expansion constants, substitution Delone sets and tilings, and associated dynamical systems.
I want to write about what I know and remember about the activities of Leonid Vital'evich Kantorovich, an outstanding scientist of the 20th century; about his dramatic struggle for recognition of his mathematical economic theories; about…
We survey different perspectives on the stochastic localization process of Eldan, a powerful construction that has had many exciting recent applications in high-dimensional probability and algorithm design. Unlike prior surveys on this…
Dark energy is a premier mystery of physics, both theoretical and experimental. As we look to develop plans for high energy physics over the next decade, within a two decade view, we consider benchmarks for revealing the nature of dark…
In a previous escapade we gave a collection of continued fractions involving Catalan's constant. This paper provides more general formulae governing those continued fractions. Having distinguished different cases associated to regions in…
In his lost notebook, Ramanujan recorded beautiful identities. These include earlier versions of Koshliakov's formula for the divisor function and the transformation formula for the logarithm of Dedekind's $\eta-$function. In this paper we…
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
This paper briefly reviews some of the exciting studies of the local Universe that will be enabled with the European Extremely Large Telescope (E-ELT). As illustrative examples, it summarizes a few of the scientific goals that have been set…
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is an English translation of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825).…
The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the…
Let $C_b(K)$ be the set of all bounded continuous (real or complex) functions on a complete metric space $K$ and $A$ a closed subspace of $C_b(K)$. Using the variational method, it is shown that the set of all strong peak functions in $A$…
Nikol'skii known theorem for the kernels satisfying a condition $A^*_n$, is proved and for kernels from wider class. Explicit formulas for calculating the value of an approximation of classes $\W^{r, \beta}_{p, n} $ by convolution operators…
The history of the very first mathematical contests for high school students is discussed. The main body of the article is dedicated to the mathematical and scientific contests held in imperial Russia in the XIX century. More specifically,…
10 years ago or so Bill Helton introduced me to some mathematical problems arising from semidefinite programming. This paper is a partial account of what was and what is happening with one of these problems, including many open questions…
Seventy-five years ago, Bernardo Dessau passed away. He had been the sole professor of Physics at the University of Perugia for thirty years. With this brief contribution we intend to repay a debt of gratitude, first of all because his…