Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Forgetting as a consequence of retrieval: a meta-analytic review of retrieval-induced forgetting

Retrieving a subset of items can cause the forgetting of other items, a phenomenon referred to as retrieval-induced forgetting. According to some theorists, retrieval-induced forgetting is the consequence of an inhibitory mechanism that acts to reduce the accessibility of non-target items that interfere with the retrieval of target items. Other theorists argue that inhibition is unnecessary to account for retrieval-induced forgetting, contending instead that the phenomenon can be best explained by non-inhibitory mechanisms, such as strength-based competition or blocking. The current paper provides the first major meta-analysis of retrieval-induced forgetting, conducted with the primary purpose of quantitatively evaluating the multitude of findings that have been used to contrast these two theoretical viewpoints. The results largely supported inhibition accounts, but also provided some challenging evidence, with the nature of the results often varying as a function of how retrieval-induced forgetting was assessed. Implications for further research and theory development are discussed.