These are some notes I have written up for myself. I have compiled what I feel to be some of the most important facts concerning characters on finite abelian groups, especially from a number theoretic point of view. I decided to distribute these because I couldn’t find a single reference that covered everything that I thought was relevant to the material I will discuss on Wednesday. Of course, ...

In this paper, a novel design approach with universal applicability is proposed for realizing low cross-polarized terahertz tri-reflector compact antenna test range (CATR). This not only enables the radiation direction of feed relative to main reflector be designed arbitrarily but also CATR systems corresponding different rotation angles while still maintaining cross-polarization. By using beam...

Using the representation of Eq(2) on the non-commutative space zz ∗−qz∗z = σ; q < 1, σ > 0 summation formulas for the product of two, three and four q-Kummer functions are derived.

Let X be a space of finite type. Set q = 2(p − 1) as usual, and define the mod q support of K(n)∗(X) by S(X,K(n)) = {m ∈ Z/qZ | ⊕ d≡mmod q K(n) d 6= 0} for n > 0. Call K(n)∗(X) sparse if there is no m ∈ Z/qZ with m,m+ 1 ∈ S(X,K(n)). Then we show the relation S(X,K(n)) j S(X,K(n+1)) for any finite type space X with K(n+ 1)∗(X) being sparse. As a special case, we have K(n+ 1)odd(X) = 0 =⇒ K(n)odd...

Smallto medium-sized polynomial eigenvalue problems can be solved by linearizing the matrix polynomial and solving the resulting generalized eigenvalue problem using the QZ algorithm. The QZ algorithm, in turn, requires an initial reduction of a matrix pair to Hessenberg– triangular form. In this paper, we discuss the design and evaluation of high-performance parallel algorithms and software fo...

ABSTRACT AAPSM masks require OPC correction through pitch in order to print a linear dark line response vs the design CDs. The masks also require correction for the clear intensity imbalance caused by the phased etched Qz wall edge. The clear intensity can be balanced by two approaches;(or a combination of the two) data biasing or wet undercut etching of the Qz etched opening. IC manufacturers ...

A simple and cost-effective optical sensing system based on quinizarin fluorescent dye (QZ) for the selective reversible of CH3COO? anions is reported. The anion binding affinity QZ towards different was monitored using electronic absorption fluorescence emission titration studies in DMSO. UV-visible spectrum showed a decrease intensity characteristic peaks at ? = 280, 323, 475 nm, while new pe...

For simplicity, we use the following convention: n denotes a natural number, i denotes an integer, p, x, x0, y denote real numbers, q denotes a rational number, and f denotes a partial function from R to R. Let q be an integer. The functor qZ yields a function from R into R and is defined as follows: (Def. 1) For every real number x holds (qZ)(x) = x q Z. Next we state a number of propositions:...