No description available.

München, Techn. Univ., Diss., 2002. / Computerdatei im Fernzugriff.

München, Techn. Univ., Diss., 2002. / Computerdatei im Fernzugriff.

München, Techn. Universiẗat, Diss., 2002.

No description available.

In this paper we determine when there exists a matrix M in PGL2(F), and its form, such that L_k = D^M_k where D^M_k is a higher-order Dickson polynomial. We first examine the cases where M has projective orders 3, 4, and 6. For the order 3 case, we find that M has entries in, at worst, a quadratic extension of F. This is also true for the orders 4 and 6, but requires a restriction on the coefficients of h(x), the characteristic polynomial of L. In all cases, an explicit formula for M is given, and in the order 4 case the meaning of the extension is interpreted in terms of the Galois group of h. Lastly, we examine the case where F is finite, and offer a formula for M of order 5.

Texte remanié de: Diss., 1988. / Mention parallèle de titre ou de responsabilité : Andrew D. White in Germany : the representative of the United States in Berlin 1879-1881 and 1897-1902.

We give explicit factorizations of $a$-cyclotomic polynomials of order $2^m 3$, $Q_{2^m3,a}(x)$, over a finite field $F_q$ with $q$ elements where $q$ is a prime power, $m$ is a nonnegative integer and $a$ is a nonnegative element of $F_q$. We use the relation between usual cyclotomic polynomials and $a$-cyclotomic polynomials. Factorizations split into eight categories according to $q \equiv \pm1$ (mod 4), $a$ and $-3$ are square in $F_q$. We find that the coefficients of irreducible factors are primitive roots of unity and in some cases that are related with Dickson polynomials.

Let p be a prime and q = pk. The polynomial gn,q isin Fp[x] defined by the functional equation Sigmaa isin Fq (x+a)n = gn,q(xq- x) gives rise to many permutation polynomials over finite fields. We are interested in triples (n,e;q) for which gn,q is a permutation polynomial of Fqe. In Chapters 2, 3, and 4 of this dissertation, we present many new families of permutation polynomials in the form of gn,q. The permutation behavior of gn,q is becoming increasingly more interesting and challenging. As we further explore the permutation behavior of gn,q, there is a clear indication that gn,q is a plenteous source of permutation polynomials. We also describe a piecewise construction of permutation polynomials over a finite field Fq which uses a subgroup of Fq*, a “selection” function, and several “case” functions. Chapter 5 of this dissertation is devoted to this piecewise construction which generalizes several recently discovered families of permutation polynomials.

This bachelor`s thesis present a study that is based on the castle garden at Tjolöholm Castle in Sweden. The focus is to examine which interesting changes and updates have been made. Many of them have happened in the last decade, others already happened during the time of the castle owners Blanche Dickson's lifetime. Her husband passed away prematurely and was basically not involved in the work of creating the garden. Mrs. Dickson, on the other hand, had the architect Lars Israel Wahlman to do it. He had been involved in the new construction of Tjolöholm's Castle and had thus gained the confidence to take on the castle garden. The planned knot garden at Tjolöholm was not laid out at the beginning of the 20th century because Blanche Dickson passed away very unexpectedly. The establishment of the knot garden therefore never happened then. Since Mrs. Dickson approved architect Wahlman's proposal with a knot garden, so she must have made sure that there was also one planned. But it didn't happen that way because of her passing. The management at Tjolöholm has been based on this knowledge and therefore it has been chosen to be construct. It turned out as Blanche Dickson wished and today it is part of the castle garden where it has now resulted in an interesting part of the well-visited and appreciated garden environment that is found at Tjolöholm Castle. Probably Mrs. Dickson would have preferred well-to-do and noble people who interested visitors to the knot garden. Today can you visit the castle garden. The study is carried out from physical existence with the guidance of Erwin Panofskys analysis method Ikonologi.