Related papers: Extension operators and geometric decompositions
We interpret a construction of geometric realisation by [Besser], [Grayson], and [Drinfeld] of a simplicial set as constructing a space of maps from the interval to a simplicial set, in a certain formal sense, reminiscent of the Skorokhod…
We establish the first extension results for divergence-free (or solenoidal) elements of $\mathrm{L}^{1}$-based function spaces. Here, the key point is to preserve the solenoidality constraint while simultaneously keeping the underlying…
We construct analytic solutions of open superstring field theory for any exactly marginal deformation in any boundary superconformal field theory when properly renormalized operator products of the marginal operator are given. Our…
We fully solve the long-standing problem of operator basis construction for fields with any masses and spins. Based on the on-shell method, we propose a novel method to systematically construct a complete set of lowest dimensional amplitude…
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…
Discrete exterior calculus (DEC) offers a coordinate-free discretization of exterior calculus especially suited for computations on curved spaces. In this work, we present an extended version of DEC on surface meshes formed by general…
Assumed that the parameters of a generalized hypergeometric function depend linearly on a small variable $\varepsilon$, the successive derivatives of the function with respect to that small variable are evaluated at $\varepsilon=0$ to…
Given a dissipative operator $A$ on a complex Hilbert space $\mathcal{H}$ such that the quadratic form $f\mapsto \mbox{Im}\langle f,Af\rangle$ is closable, we give a necessary and sufficient condition for an extension of $A$ to still be…
We discuss the construction of finite element spaces of differential forms which satisfy the crucial assumptions of the finite element exterior calculus, namely that they can be assembled into subcomplexes of the de Rham complex which admit…
Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to…
This paper highlights how unstructured space-time meshes can be used in production engineering applications with moving domains. Unstructured space-time elements can connect different spatial meshes at the bottom and top level of the…
We introduce a unified method for constructing the basis functions of a wide variety of partially continuous tensor-valued finite elements on simplices using polytopal templates. These finite element spaces are essential for achieving…
We identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to…
Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of the deformation, its…
Hypergeometric functions and their generalizations play an important r\^{o}les in diverse applications. Many authors have been established generalizations of hypergeometric functions by a number ways. In this paper, we aim at establishing…
We extend earlier international efforts to optimise hexahedral-based spectral element methods on GPUs and vectorised CPUs to mixed element meshes additionally involving prismatic, pyramidic, and tetrahedral shapes using tensorial…
Hypergeometric functions provide a useful representation of Feynman diagrams occuring in precision phenomenology. In dimension regularization, the epsilon-expansion of these functions about d=4 is required. We discuss the current status of…
On locally conformally flat manifolds we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the…
We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be…
This paper presents a new concept of geometric multipole expansion for the conductivity or anti-plane elasticity problem in two dimensions by using the Faber polynomials. As an application, we construct semi-neutral inclusions of general…