This paper is concerned with α– and D–negative imaginary systems. The definition of α–negative imaginary transfer functions is firstly introduced. Then, the relationship between negative imaginary and α–negative imaginary transfer functions is studied. By means of the generalized inverse, an α–negative imaginary lemma is proposed to test the α–negative imaginary property of transfer functions. ...

An imaginary cube is a three dimensional object which has square projections in three orthogonal directions just as a cube has. In this paper, we study imaginary cubes and present sculptures based on imaginary cubes. We show that there are 16 kinds of minimal convex imaginary cubes. The list of 16 representative minimal convex imaginary cubes contains, as well as a regular tetrahedron and a cub...

Silicon thin layers are deposited on glass substrates with the thickness of 103 nm, 147 nm and 197 nm. The layers are produced with electron gun evaporation method under ultra-high vacuum condition. The optical Reectance and the Transmittance of produced layers were measured by using spectrophotometer. The optical functions such as, real and imaginary part of refractive index, real and imaginar...

Nonlinear dynamical modeling of interaction between automatic and conscious processes in the human brain is considered in terms of the quaternion fields. The interaction is due, particularly, to the nonlinear firing rate of neu-rons. Possible connection of consciousness with the general field theory is indicated. A new type of symmetry between dynamics of real and imaginary fields is pointed ou...

is called the 2-class field tower of k. If n is the minimal integer such that kn = kn+1, then n is called the length of the tower. If no such n exists, then the tower is said to be of infinite length. At present there is no known decision procedure to determine whether or not the (2-)class field tower of a given field k is infinite. However, it is known by group theoretic results (see [2]) that...

Imaginary cubes are three-dimensional objects that have square projections in three orthogonal ways, just like a cube has. In this paper, we introduce higherdimensional extensions of imaginary cubes and study their properties.

Multi-layer orthotropic finite cylindrical shells with a viscoelastic core in contact with fluids are gaining increasing importance in engineering. Vibrational control of these structures is essential at higher modes. In this study, an extended version of the wave propagation approach using first-order shear deformation theory of shell motion is employed to examine the free vibration of damped ...