相关论文: Algebraic Structure of the Varikon Box
In this paper, we present a curious experiment with the hot list strategy in solving sliding block puzzles by paramodulation. The hot list strategy is one of the look-ahead strategies using paramodulation in automated reasoning. We define…
We introduce a new heuristic for the multiple alignment of a set of sequences. The heuristic is based on a set cover of the residue alphabet of the sequences, and also on the determination of a significant set of blocks comprising…
We study the structure of the algebra of polynomial invariants for the usual conjugation action of the complex special, SO_n, and general, O_n, orthogonal group on the space of traceless n by n complex matrices. (Note that these two…
Quantum tunneling across multiple barriers as yet is an unsolved problem for barrier numbers greater than five. The complexity of the mathematical analysis even for small number of barriers pushed it into the realms of Numerical Analysis.…
Origami is the art of folding paper into various patterns without cutting or tearing the paper. By viewing the paper as the complex plane, we iteratively compute and record all intersection points to construct mathematical origami sets.…
In this paper we analyze the geometric structure and properties of a certain class of subsets of $\Bbb R^d$, known in the literature as 1-multicones, and here simply called multicones, which are quite natural generalizations of the…
This contributed conference proceeding reviews some results about a system of a few identical particles with spin trapped in one-dimensional potentials and experiencing two-body interactions. The focus is on how symmetry, integrability, and…
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
We study a variational problem for the perimeter associated with the Grushin plane, called minimal partition problem with trace constraint. This consists in studying how to enclose three prescribed areas in the Grushin plane, using the…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…
The twist construction is a method to build new interesting examples of geometric structures with torus symmetry from well-known ones. In fact it can be used to construct arbitrary nilmanifolds from tori. In our previous paper, we presented…
To a set $\mathcal{B}$ of 4-subsets of a set $\Omega$ of size $n$ we introduce an invariant called the `hole stabilizer' which generalises a construction of Conway, Elkies and Martin of the Mathieu group $M_{12}$ based on Loyd's…
It is well known that the variable ordering can be critical to the efficiency or even tractability of the cylindrical algebraic decomposition (CAD) algorithm. We propose new heuristics inspired by complexity analysis of CAD to choose the…
This paper addresses the two-dimensional bin packing problem with guillotine constraints. The problem requires a set of rectangular items to be cut from larger rectangles, known as bins, while only making use of edge-to-edge (guillotine)…
The dispersion of a point set $P\subset[0,1]^d$ is the volume of the largest box with sides parallel to the coordinate axes, which does not intersect $P$. Here, we show a construction of low-dispersion point sets, which can be deduced from…
The envelope theory is a method to easily obtain approximate, but reliable, solutions for some quantum many-body problems. Quite general Hamiltonians can be considered for systems composed of an arbitrary number of different particles in…
The 15-vertex model of Statistical Mechanics is studied on a square domain with partially oriented boundary. With DWBC the model would reduce to the six-vertex model, but more general boundary configurations are available. After…
In this article a theoretical framework for problems involving fractional equations of hyperbolic type arising in the theory of viscoelasticity is presented. Based on the Galerkin method, a variational problem of the fractionary…
The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching a compact surface (interface). The lower-dimensional piece is a so-called…
A recreational problem from nearly two centuries ago has featured prominently in recent times in the mathematics of designs, codes, and signal processing. The number 15 that is central to the problem coincidentally features in areas of…