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.

As mentioned several times in class, the arithmetic of quaternionic Shimura varieties is strongly controlled by the behavior of the class of CM points (just as in the case of modular curves). Just as for elliptic curves, if o is an order in an imaginary quadratic field K, one has a notion of a QM-surface with o-CM. Namely, let ι : O ↪→ A be a QM structure on an abelian surface (we are still wor...

In this paper we will propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structures of class semigroups of imaginary quadratic orders which were given by Zanardo and Zannier [8], and we will give a general algorithm for calculating power of ideals/classes via the Dirichlet composition of quadratic forms which is applicable to...