2 Vector Analysis 6 2.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Scalar Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 The Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 The Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

This paper is the first demonstration of multiplexed wideband data transmission in millimeter-wave range using rectangular-coordinate orthogonal multiplexing (ROM) antennas. spatial wireless multiplex communication method can be applied at several hundred GHz for further improvements rate because much wider bandwidth available and this does not require any signal processing. The achieved throug...

Can we flatten the surface of any 3-dimensional polyhedron P without cutting or stretching? Such continuous flat folding motions are known when P is convex, but the question remains open for nonconvex polyhedra. In this paper, we give a continuous flat folding motion when the polyhedron P is an orthogonal polyhedron, i.e., when every face is orthogonal to a coordinate axis (x, y, or z). More ge...

Recently Shukurov et al [Phys Rev E 72, 025302 (2008)], made use of nonorthogonal curvilinear coordinate system on a dynamo Moebius strip flow, to investigate the effect of stretching by a turbulent liquid sodium flow. In plasma physics, Chui and Moffatt [Proc Roy Soc A 451,609,(1995)] (CM), considered non-orthogonal coordinates to investigate knotted magnetic flux tube Riemann metric. Here it ...

Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x–y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with A’s chosen xor y-axis. It becomes necessary in such cases to develop Lorentz transformations where the line of motion is ...