We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of refinement. Given a finite element solution a...

General strategy for developing finite elements of general geometric shape explained on quadrilateral folded plate structure element ensuring invariance properties is presented in this paper. The basic idea of this strategy consists in using the natural coordinate system only for defining the element geometry and performing the element integration in a mapped biunit square. For defining the app...

By a result of Gallai, every finite graph G has a vertex partition into two parts each inducing an element of its cycle space. This fails for infinite graphs if, as usual, the cycle space is defined as the span of the edge sets of finite cycles in G. However we show that, for the adaptation of the cycle space to infinite graphs recently introduced by Diestel and Kühn (which involves infinite cy...

Complex variable methods are used to obtain exact and closed expressions for Goursat’s functions for the stretched infinite plate weakened by two inner holes which are free from stresses. The plate considered is conformally mapped on the area of the right half-plane. Previous work is considered as special cases of this work. Cases of different shapes of holes are included. Also, many new cases ...

The Time-Domain Boundary Element Method (TDBEM) is a well known numerical technique that handles quite properly dynamic analyses considering infinite dimension media. However, when these analyses are also related to nonlinear behavior, very complex numerical procedures arise considering the TD-BEM, which may turn its application prohibitive. In order to avoid this drawback and model nonlinear i...

Extensive studies have been conducted on the generation of unstructured meshes of triangles for the purpose of nite element analysis. Delaunay triangulation has been the basis of several such methods, and has lead to algorithms that can produce unstructured meshes of triangles for any planar domain. However, there have not been many robust methods for producing unstructured meshes of quadrilate...

There exist infinite, finitely presented, torsion-free groups G such that Aut(G) and Out(G) are torsion-free but G has an automorphism sending some non-trivial element to its inverse.

We consider embeddings between infinite graphs. In particular, We establish that there is no universal element in the class of countable graphs into which the random graph is not embeddable.

An integral part of scattering theory calculations in continuum quantum systems involves identifying appropriate boundary conditions addition to writing down the correct Hamiltonian. In simplest problem one dimensional lattice, due an on-site potential and unequal bond (in otherwise translationally invariant lattice) give different results for amplitudes. While problems lattice models can be ma...

— We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.