We show that complex coordinates used in conjunction with transformation optics offer an extra degree of freedom that allows control over not only the propagation direction of electromagnetic waves but also their amplitude. We illustrate this idea in two applications. First, we show that in an n-dimensional space one can manipulate the field amplitude for up to n different amplitude distributio...

It has been known that, keeping the outer boundary coordinates intact before and after a coordinate transformation is a sufficient condition for obtaining a reflectionless transformation medium. Here we prove that it is also a necessary condition for reflectionless transformation media in an isotropic and homogenous background. Our analytical results show that the outer boundary coordinates of ...

‎The Lorentz transformation of order $(m=1,n)$‎, ‎$ninNb$‎, ‎is the well-known ‎Lorentz transformation of special relativity theory‎. ‎It is a transformation of time-space coordinates of the ‎pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and ‎$n$ space dimensions ($n=3$ in physical applications)‎. ‎A Lorentz transformation without rotations is called a {it boost}‎. ‎Commonly‎, ‎the ...

Transformation of coordinates usually invokes level-wised processes wherein several sets of complicated equations are calculated. Unfortunately, the accuracy may be corrupted due to the accumulation of inevitable errors between the transformation processes. This paper presents a genetic-based method for generating regressive models for direct transformation from GPS signals to 2-D coordinates. ...

This paper applies a fully post-Newtonian theory (Damour et al. 1991, 1992, 1993, 1994) to the problem of gauge in relativistic reference systems. Gauge fixing is necessary when the precision of time measurement and application reaches 10−16 or better. We give a general procedure for fixing the gauges of gravitational potentials in both the global and local coordinate systems, and for determini...

The elbow-joint angle and the shoulder-joint angle of participants aiming at targets were multiplied in an experiment that used a position-recording system and a cathode-ray tube screen. The linear transformation in joint angles (intrinsic coordinates) corresponded to a nonlinear transformation between the hand coordinates and the screen coordinates (extrinsic coordinates). We examined whether ...

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 ...

A coordinate independent derivation of the Eulerian and Lagrangian strain tensors of finite deformation theory is given based on the parallel propagator, the world function, and the displacement vector field as a three-point tensor. The derivation explicitly shows that the Eulerian and Lagrangian strain tensors are two-point tensors, each a function of both the spatial and material coordinates....