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Some projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T were constructed in [3]. In this paper we describe their integer cohomology rings by generators and relations.
A tautological system, introduced in [16][17], arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete intersections in a complex manifold $X$, equipped with a suitable…
We study tori which are cyclic covers of the standard torus, that is, the deck transformation group of the covering map is cyclic. These covering tori can be parametrized in a natural way and we show that being cyclic is equivalent to…
The period set of a dynamical system is defined as the subset of all integers $n$ such that the system has a periodic orbit of length $n$. Based on known results on the intersection of period sets of torus maps within a homotopy class, we…
The periodic system of chemical elements is represented within the framework of the weight diagram of the Lie algebra of the fourth rank of the rotation group of an eight-dimensional pseudo-Euclidean space. The hydrogen realization of the…
In this note we give a re-interpretation of the algebraic fundamental group for proper schemes that is rather close to the original definition of the fundamental group for topological spaces. The idea is to replace the standard interval…
We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted…
This survey article is the outgrowth of two talks given at the Journ\'ees X-UPS "P\'eriodes et transcendance" at \'Ecole polytechnique. Periods are complex numbers whose real and imaginary parts can be written as integrals of rational…
The TRAPPIST-1 system provides an exquisite laboratory for advancing our understanding exoplanetary atmospheres, compositions, dynamics and architectures. A remarkable aspect of TRAPPIST-1 is that it represents the longest known resonance…
Let $X$ be an algebraic scheme over an algebraically closed field and $\ell$ a prime number invertible on $X$. According to classical results (due essentially to A. Grothendieck, M. Artin and P. Deligne), the \'etale cohomology groups…
In this paper we study the rotation and spatial inversion symmetry of regular tetrahedron. We obtain the representation matrix, multiplication table,the order of all group elements, all possible combinations of generator elements, the…
The periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics. The corresponding partition is mapped to a topological well-ordered symbol plane. In the symbol plane the pruning front is…
The Gregorian calendar -- first established for daily use on Friday, October 15th, 1582 by Pope Gregory XIII in Catholic countries -- is presently the most pervasive calendar in the world. As such, algorithms for performing various…
In general terms, we establish algebraic relations that numbers must satisfy in order for their images to match after one or several transformations. Some groups associated with these relationships are identified, such as the Klein group.…
Deconstructing a time index into time granularities can assist in exploration and automated analysis of large temporal data sets. This paper describes classes of time deconstructions using linear and cyclic time granularities. Linear…
The tetrahedron algebra $\boxtimes$ is an infinite-dimensional Lie algebra defined by generators $\{x_{ij} \mid i, j \in \{0, 1, 2, 3\}, i \neq j\}$ and some relations, including the Dolan-Grady relations. These twelve generators are called…
This paper centers on the collection of accounts on solar eclipses from the era of the Aztecs in Mesoamerica, about 1300 to 1550 AD. We present a list of all eclipse events complying with the topological visibility from the capital…
In this thesis we give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. In his seminal book, Connes constructs a map from the equivariant cohomology of a manifold carrying the…
We introduce Cyclone codes which are rateless erasure resilient codes. They combine Pair codes with Luby Transform (LT) codes by computing a code symbol from a random set of data symbols using bitwise XOR and cyclic shift operations. The…
We present a novel technique to identify calendar-based (annual, monthly and daily) periodicities of an interval-based temporal pattern. An interval-based temporal pattern is a pattern that occurs across a time-interval, then disappears for…