Related papers: Numerical computation of H-bases
New formulas for approximation of zeta-constants were derived on the basis of a number-theoretic approach constructed for the irrationality proof of certain classical constants. Using these formulas it's possible to approximate certain…
We consider a scheme of Semi-Lagrangian (SL) type for the numerical solution of Hamilton-Jacobi (HJ) equation on unstructured triangular grids. As it is well known, SL schemes are not well suited for unstructured grids, due to the cost of…
The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a new method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of…
We describe a simple algorithm for computing the canonical basis of any finite-dimensional $U_{q}(sp_{2n})$-module.
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
Most variational forms of isogeometric analysis use highly-continuous basis functions for both trial and test spaces. For a partial differential equation with a smooth solution, isogeometric analysis with highly-continuous basis functions…
Following Faber-Pandharipande, we use the virtual localization formula for the moduli space of stable maps to $ \mathbb{P}^1 $ to compute relations between Hodge integrals. We prove that certain generating series of these integrals are…
Let $G$ be a permutation group on a set $\Omega$. A subset of $\Omega$ is a base for $G$ if its pointwise stabilizer is trivial; the base size of $G$ is the minimal cardinality of a base. In this paper we initiate the study of bases for…
Homological stability has shown itself to be a powerful tool for the computation of homology of families of groups such as general linear groups, mapping class groups or automorphisms of free groups. We survey here tools and techniques for…
A new proof for stability estimates for the complex Monge-Amp\`ere and Hessian equations is given, which does not require pluripotential theory. A major advantage is that the resulting stability estimates are then uniform under general…
We prove some stability results for smooth H-minimal hypersurfaces immersed in a sub-Riemannian k-step Carnot group G. The main tools are the formulas for the 1st and 2nd variation of the H-perimeter measure.
This paper presents a novel and efficient method for characteristic mode decomposition in multi-structure systems. By leveraging the translation and rotation matrices of vector spherical wavefunctions, our approach enables the synthesis of…
The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant…
The homology groups of a simplicial complex reveal fundamental properties of the topology of the data or the system and the notion of topological stability naturally poses an important yet not fully investigated question. In the current…
We develop a new algorithm to compute a basis for $M_k(\Gamma_0(N))$, the space of weight $k$ holomorphic modular forms on $\Gamma_0(N)$, in the case when the graded algebra of modular forms over $\Gamma_0(N)$ is generated at weight two.…
We prove a closed formula counting semistable twisted Higgs bundles of fixed rank and degree over a smooth projective curve defined over a finite field. We also prove a formula for the Donaldson-Thomas invariants of the moduli spaces of…
We describe an algorithm for computing the $p$-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke…
The subject of this paper is the design of efficient and stable spectral methods for time-dependent partial differential equations in unit balls. We commence by sketching the desired features of a spectral method, which is defined by a…
Let $R$ be a regular local ring containing a field, let $I$ be an ideal with $d=\text{ht}{I}$, and assume $\text{ht}{p}=d$ for every minimal prime $p$ of $I$. We compute the Bass numbers $\mu^{0}(q,H_{I}^{d}(R))$ and…
The flow in a fixed direction on a translation surface S determines a decomposition of S into closed invariant sets, each of which is either periodic or minimal. We study this decomposition for translation surfaces in the hyperelliptic…