Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
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TL;DR: In this article, the electromagnetic characteristics of biorthogonal rectangular probes were analyzed through finite element simulation and the detection capability of probes according to flaw's width, length and depth were also studied.
23 citations
TL;DR: Application of the D'Arch Thompson method to hominid skull phylogeny has demonstrated three principal axes of evolutionary change anatomically homologous over a fossil sequence.
Abstract: In 1917, D'Arch Thompson suggested that one should study the change from one biological form to another by examining the unique mathematical object that maps between them in accord with biological homologies. Biorthogonal grids provide a particular coordinate system for visualizing such a map and lead to a quantitative syntax in which a change in shape is reduced to differential changes in size. Application of the method to hominid skull phylogeny has demonstrated three principal axes of evolutionary change anatomically homologous over a fossil sequence.
23 citations
TL;DR: In this article, a 3D multiresolution time-domain analysis based on a biorthogonal wavelet expansion is presented for electromagnetic-scattering problems, where wavelets and scaling functions of compact support are used to yield update equations involving a small number of proximate field components.
Abstract: A three-dimensional (3-D) multiresolution time-domain (MRTD) analysis is presented based on a biorthogonal-wavelet expansion, with application to electromagnetic-scattering problems. We employ the Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelet basis, characterized by the maximum number of vanishing moments for a given support. We utilize wavelets and scaling functions of compact support, yielding update equations involving a small number of proximate field components. A detailed analysis is presented on algorithm implementation, with example numerical results compared to data computed via the conventional finite-difference time-domain (FDTD) method. It is demonstrated that for 3-D scattering problems the CDF-based MRTD often provides significant computational savings (in computer memory and run time) relative to FDTD, while retaining numerical accuracy.
23 citations
TL;DR: In this article, the concept of projectable refinable functions was introduced and it was shown that many multivariate refinability functions are projectable, i.e., they essentially carry the tensor product structure of a function even though themselves may be nontensor product (nonseparable) refinability.
23 citations
TL;DR: In this paper, a generalization of those expressions to the case of biorthogonal polynomials is presented, which enables us to compute the determinant of the fundamental solution of the overdetermined system of ODE + PDEs + ΔE.
Abstract: The two-matrix model can be solved by introducing biorthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of biorthogonal polynomials (called windows) satisfy polynomial ODEs as well as deformation equations (PDEs) and finite difference equations (ΔE) which are all Frobenius compatible and define discrete and continuous isomonodromic deformations for the irregular ODE, as shown in previous works of ours. In the one matrix model an explicit and concise expression for the coefficients of these systems is known and it allows to relate the partition function with the isomonodromic tau-function of the overdetermined system. Here, we provide the generalization of those expressions to the case of biorthogonal polynomials, which enables us to compute the determinant of the fundamental solution of the overdetermined system of ODE + PDEs + ΔE.
23 citations