A scheme of combined reflection and transmission ellipsometry on light-transmitting ambient-film-substrate systems is proposed and the required sample design and instrument operation are investigated. A comparative study of the sensitivity of external and internal reflection and transmission ellipsometry is carried out based on unified linear approximations of the exact equations. These approxi...

In this paper, a review of the methodology for the computation of transmission and reflection coefficients for the surface waves, propagated through a vertical contact, will be presented and discussed. The surface-wave transmission and reflection coefficients will be obtained using a simple method. This method will be very briefly described and compared with a more sophisticate method, obtainin...

The motivation of this paper comes from statistical physics as well as from combinatorics and topology. The general setup in statistical mechanics can be outlined as follows. Let G be a graph and let C be a finite set of “states” or “colors”. We think of G as a crystal in which either the edges or the vertices are regarded as “sites” which can have states from C. In the first case we speak abou...

a potential V (x), when the height of the potential exceeds the particle’s energy for a < x < b. Elementary derivations of this result can be found in most textbooks[1]. Quantum mechanics also predicts that a particle with energy E, greater than a barrier V (x) for all x, will reflect from the barrier. This can also be estimated using semiclassical methods. A derivation can be found in Landau a...

in this paper, we introduce the concept of semihyperring $(r,+,cdot)$ together with a suitable partial order $le$. moreover, we introduce and study hyperideals in ordered semihyperrings. simple ordered semihyperrings are defined and its characterizations are obtained. finally, we study some properties of quasi-simple and $b$-simple ordered semihyperrings.

The big theorem of this section gives us that a finite reflection group, call it W , is generated by simple reflections (reflections of simple roots for a given simple system). We also get a useful corollary that, given a simple system the W orbit of any root meets this simple system. Exercise 1 Let Φ be a root system of rank n consisting of unit vectors. If Ψ ⊂ Φ is a set of n roots whose mutu...

A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, results are extended to case when theory consideration finitely many constraints.

We give a simple formula for the essential dimension of a finite pseudoreflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the “poor man’s essential dimension” of an arbitrary finite group, an intermediate notion between the absolute essential dimension and the essential dimension at a prime p.