1.3 We argue by contradiction. Thus we suppose that A is infinite and derive a contradiction. As a preliminary, observe that A is non-empty and hence has a ≤-least element, a first element. It also has a ≤∗-least element, a ≤-greatest element, a last element. For each element x let ↑x be the ≤-upper set generated by x, that is y ∈ ↑x ⇐⇒ x ≤ y for each y ∈ A. Consider the subset X ⊆ A given by x...

Insertion element IS121 was mapped between proA and a previously mapped IS5A element in two F-prime plasmids. Results of hybridizations of IS121 to chromosomal DNA from four other strains suggest that IS121 is normally present at this position in the chromosomes of Escherichia coli K-12 strains.

In this work, we analyse the Galerkin Infinite Element method for option pricing. The Infinite Element method is a very simple and efficient modification of the more common Finite Element method. It keeps the best features of Finite Elements, i.e. bandedness, easiness of programming, accuracy, and it is particularly useful when solving problems in unbounded domains. Three main aspects are consi...

Analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (BE/FD) formulation. A semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...

Numerical methods (finite element methods) for the approximate solution of elliptic partial differential equations on unbounded domains are considered, and error bounds, with respect to the number of unknowns which have to be determined, are proven.

The scattering problem from time-harmonic waves by a Neumann type crack in R is considered. A PML technique is used for solving the problem with a bounded domain instead of the infinite domain. A coupled finite-infinite element method is employed in the computation. Because of the singularity of the solution, the infinite element method is used near the crack tip. An error analysis is presented...

This work is devoted to a study and summary of different Infinite Element (IE) formulations for Helmholtz problems in arbitrary exterior domains. The theoretical setting for each of the different formulations is presented and related to the mathematical existence theory. The influences of a bilinear or a sesquilinear formulation are discussed as well as possible extensions to other elements. Th...

The present work solves two-dimensional Advection-Dispersion Equation (ADE) in a semi-infinite domain. A variable source concentration is regarded as the monotonic decreasing function at the source boundary (x=0). Depth-dependent variables are considered to incorporate real life situations in this modeling study, with zero flux condition assumed to occur at the exit boundary of the domain, i.e....