相关论文: Discrete and smooth orthogonal systems: $C^\infty$…

An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…

Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…

In this paper, we characterize all discrete-time systems in quasi-standard form admitting coalgebra symmetry with respect to the Lie--Poisson algebra $\mathfrak{h}_{6}$. The outcome of this study is a family of systems depending on an…

Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…

This paper describes the notion of \sigma -symmetry, which extends the one of \lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider…

We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry…

We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

In a computational topology of digital images, simplexes are replaced by Delta sets in approximating image object shapes. For simplicity, simplexes and Delta sets are restricted to the Euclidean plane. A planar simplex is either a vertex, a…

We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…

H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials (H. Widom. J. Stat. Phys. 94, (1999) 347-363). We obtain similar results for discrete…

We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic differential are invariant under M\"{o}bius transformations.…

We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…

The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the proximal point algorithm. Given the importance of the…

Let $D$ be a closed unit $2$-disk on the plane centered at the origin $O$, and $F$ be a smooth vector field such that $O$ is a unique singular point of $F$ and all other orbits of $F$ are simple closed curves wrapping once around $O$. Thus…

Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidimensional canonical Hamiltonian systems by modifying…

Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can…

The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are general. Studies of this type is fundamental and important. They…

We propose a unified definition for discrete analogues of constant mean curvature surfaces in spaces of constant curvature as a special case of discrete special isothermic nets. B\"acklund transformations and Lawson's correspondence are…

We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as…