Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on gene...

The study of spheres dates back to the first century in the book Sphaerica of Menelaus. Spherical trigonometry was thoroughly developed in modern form by Euler in his 1782 paper [?]. Spherical geometry in n-dimensions was first studied by Schläfli in his 1852 treatise, which was published posthumously in 1901 [?]. The most important transformation in spherical geometry, Möbius transformation, w...

Morphing is the process of changing one figure into another. Some numerical methods of 3D surface morphing by deformable modeling and conformal mapping are shown in this study. It is well known that there exists a unique Riemann conformal mapping from a simply connected surface into a unit disk by the Riemann mapping theorem. The dilation and relative orientations of the 3D surfaces can be link...

The flow field, velocity and pressure coefficient distribution of some 2-D ideal flows are presented. Conformal mapping is used to simulate two-dimensional ideal flow for a variety of complex internal and external configurations, based on the numerical integration of Schwarz-Christoffel transformation. The advantages of this method are simplicity and high accuracy. The method presented in this ...

Supersymmetric extensions of the 1D and 2D Swanson models are investigated by applying conformal bridge transformation (CBT) to first order Berry-Keating Hamiltonian multiplied $i$ its conformally neutral enlargements. The CBT plays role Dyson map that transforms into supersymmetric generalizations harmonic oscillator systems, allowing us define pseudo-Hermitian conjugation a suitable inner pro...

where B0 is the trace free part of the second fundamental form of X. It was introduced by Willmore in a slightly different but equivalent form for surfaces in E. The functional is invariant under conformal transformation, and it is natural to extend it for submanifolds in conformal N -sphere S = E ∪ {∞}. Willmore conjecture asks if Clifford torus in S is the unique minimizer of W(X) among all i...