相关论文: Minimal cubature rules on an unbounded domain

We provide explicit expressions for quadrature rules on the space of $C^1$ quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention…

A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…

We discover a family of closed, embedded minimal surfaces in the three-dimensional round sphere which includes new examples with low genus. The existence proof relies on an equivariant min-max procedure applied to a novel sweepout which is…

We consider minimal graphs u(x,y)>0 over unbounded domains D (with u vanishing on the boundary of D). Assuming D contains a sector properly containing a halfplane, we obtain estimates on growth and provide examples illustrating a range of…

We first define the trace on a domain $\Omega$ which is definable in an o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$ vanishing on the boundary in the trace sense satisfies Poincar\'e inequality. We finally…

It is established a continuous boundary extension of some class of mappings. Under some additional conditions, we have established that this extension is light in the closure of the definition domain. Under some stronger conditions, we also…

For fixed large genus, we construct families of complete immersed minimal surfaces in R3 with four ends and dihedral symmetries. The families exist for all large genus and at an appropriate scale degenerate to the plane.

We give lower bounds for the degree of the discriminant with respect to y of separable polynomials f in K[x,y] over an algebraically closed field of characteristic zero. Depending on the invariants involved in the lower bound, we give a…

Bound state poles in the $S$-matrix of perturbative QED are generated by the {\em divergence} of the expansion in $\alpha$. The perturbative corrections are necessarily singular when expanding around free, \order{\alpha^0} $in$ and $out$…

We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.

We study a local behavior of one class of mappings, which are defined in a domain of $n$-measured Euclidean space, in a case, when corresponding images of this domain are variable. Under some conditions on a function defining a behavior of…

We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.

Gau{\ss} cubature (multidimensional numerical integration) rules are the natural generalisation of the 1D Gau{\ss} rules. They are optimal in the sense that they exactly integrate polynomials of as high a degree as possible for a particular…

The purpose of this paper is to provide a detailed description of the spaces that can be specified as $L^2$ domains for the operators of a first order elliptic complex on a compact manifold with conical singularities. This entails an…

This article focuses on long-time existence for quasilinear wave equations with small initial data in exterior domains. The nonlinearity is permitted to fully depend on the solution at the quadratic level, rather than just the first and…

We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and…

Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$…

Definable continuous injective maps defined on definable open sets into the Euclidean spaces of the same dimension are open maps in definably complete locally o-minimal expansions of ordered groups.

An infinite family of Boolean polynomials which correspond to the discrete average maps, defined in [2], is constructed and their algebraic and combinatorial properties are investigated. They turn out to be balanced, and some recurrence…

Boundedness is demonstrated for the fifth derivative of the one-particle reduced density matrix for non-relativistic Coulombic wavefunctions in the vicinity of the diagonal. To prove this result, strong pointwise bounds are obtained for…