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In this article, we quantize the Maxwell ("massless spin one") de Sitter field in a conformally invariant gauge. This quantization is invariant under the SO$_0(2,4)$ group and consequently under the de Sitter group. We obtain a new de…
A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities…
We use mass-transportation as a tool to compare surfaces (2-manifolds). In particular, we determine the "similarity" of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation…
We establish sharp Trudinger-Moser inequalities with logarithmic weights for the $k$-Hessian equation and investigate the existence of maximizers. Our analysis extends the classical results of Tian and Wang to $k$-admissible function spaces…
The goal of this note is to give the explicit solution of Euler-Frahm equations for the Manakov four-dimensional case by elementary means. For this, we use some results from the original papers by Schottky [Sch 1891], Koetter [Koe 1892],…
We present a fully discrete scheme for the numerical approximation of a moving-boundary problem describing diffusants penetration into rubber. Our scheme utilizes the Galerkin finite element method for the space discretization combined with…
In this paper, we study the conformally invariant field equations for vector-spinor field in de Sitter space-time. The solutions are also obtained in terms of the de Sitter-Dirac plane waves. The related two-point functions are calculated…
We present a scalable combinatorial algorithm for globally optimizing over the space of geometrically consistent mappings between 3D shapes. We use the mathematically elegant formalism proposed by Windheuser et al. (ICCV 2011) where 3D…
A small polygon is a polygon of unit diameter. The maximal area of a small polygon with $n=2m$ vertices is not known when $m\ge 7$. Finding the largest small $n$-gon for a given number $n\ge 3$ can be formulated as a nonconvex quadratically…
We introduce and study the maximal-variation locus in families and moduli spaces of projective curves, defined via conductor-level balancing of meromorphic differentials on the normalization. This notion captures precisely when the space of…
We give bounds for the total variation distance between the solutions to two stochastic differential equations starting at the same point and with close coefficients, which applies in particular to the distance between an exact solution and…
In 1985 Hopcroft, Joseph and Whitesides showed it is NP-complete to decide whether a carpenter's ruler with segments of given positive lengths can be folded into a line of at most a given length, such that the folded hinges alternate…
Gravitational perturbations of the de Sitter spacetime are investigated using the Regge--Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heun-type for both electric and…
Multi-robot motion planning is a hard problem. We investigate restricted variants of the problem where square robots are allowed to slide over an arbitrary curve to a new position only a constant number of times each. We show that the…
We study the existence and instability properties of saddle-shaped solutions of the semilinear elliptic equation $-\Delta u = f(u)$ in the whole $\R^{2m}$, where $f$ is of bistable type. It is known that in dimension $2m=2$ there exists a…
Decaying vacuum cosmological models evolving smoothly between two extreme (very early and late time) de Sitter phases are capable to solve or at least to alleviate some cosmological puzzles, among them: (i) the singularity, (ii) horizon,…
We generalize the curved $N$-body problem to spheres and hyperbolic spheres whose curvature $\kappa$ varies in time. Unlike in the particular case when the curvature is constant, the equations of motion are non-autonomous. We first briefly…
Surfaces of revolution in three-dimensional Euclidean space are considered. Several new examples of surfaces of revolution associated with well-known solvable cases of the Schoedinger equation (infinite well, harmonic oscillator, Coulomb…
In this work we consider the problem of finding the minimum-weight loop cover of an undirected graph. This combinatorial optimization problem is called 2-matching and can be seen as a relaxation of the traveling salesman problem since one…
A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement problem. Under low regularity assumptions, convergence is…