Related papers: Symmetry gaps for higher order ordinary differenti…
We initiate the study of diameter computation in geometric intersection graphs from the fine-grained complexity perspective. A geometric intersection graph is a graph whose vertices correspond to some shapes in $d$-dimensional Euclidean…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the…
The paper is devoted to studying the orthogonality graph of the matrix ring over a commutative ring. It is proved that the orthogonality graph of the ring of matrices with size greater than 1 over a commutative ring with zero-divisors is…
Systems of two ordinary and partial differential equations (ODEs and PDEs) had been obtained from a scalar complex ODE by splitting it into its real and imaginary parts. The procedure was also carried out to obtain a four dimensional system…
The set of badly approximable $m \times n $ matrices is known to have Hausdorff dimension $mn $. Each such matrix comes with its own approximation constant $c$, and one can ask for the dimension of the set of badly approximable matrices…
We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…
For the largest exceptional simple Lie superalgebra $F(4)$, having dimension $(24|16)$, we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second and third order…
We show that for n>2 the following equivalence problems are essentially the same: the equivalence problem for Lagrangians of order n with one dependent and one independent variable considered up to a contact transformation, a multiplication…
In this review article we discuss four recent methods for computing Maurer-Cartan structure equations of symmetry groups of differential equations. Examples include solution of the contact equivalence problem for linear hyperbolic equations…
We study subclasses of grid intersection graphs from the perspective of order dimension. We show that partial orders of height two whose comparability graph is a grid intersection graph have order dimension at most four. Starting from this…
This paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are…
Recently, the first author together with Jens Marklof studied generalizations of the classical three distance theorem to higher dimensional toral rotations, giving upper bounds in all dimensions for the corresponding numbers of distances…
We study higher dimensional field theories with extra dimensions from a 4d spectrum point of view. It is shown that 4d mass spectra of spinor, gauge and gravity field theories are governed by quantum-mechanical supersymmetry. The 4d…
Some new properties of symmetries that disappear as point symmetries after the first reduction of order of an ODE and reappear after the second are analyzed from the aspect of three-dimensional subalgebra of symmetries of differential…
After the optimal parameters of additive quaternary codes of dimension $k\le 3$ have been determined there is some recent activity to settle the next case of dimension $k=3.5$. Here we complete dimension $k=3.5$ and $k=4$. We also solve the…
We investigate the possibility that supersymmetry is not a fundamental symmetry of nature, but emerges as an accidental approximate global symmetry at low energies. This can occur if the visible sector is non-supersymmetric at high scales,…
We study the breaking of a supersymmetric SO(10) GUT in 6 dimensions by orbifold compactification. In 4 dimensions we obtain a N=1 supersymmetric theory with the standard model gauge group enlarged by an additional U(1) symmetry. The…
It is well known that there exist twenty two symmetry type graphs associated to 4-orbit maps. For this ones we give the feasible values taken by the degree of the vertices and the number appropriate of edges in the boundary of each face of…
We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and provide a comprehensive review of the geometrical foundations…