Thesis (PH. D.)--University of Illinois, 1914. / Vita. "To be presented at the 301st meeting of the American Institute of Electrical Engineers, New York, November 13, 1914."

Inaug.-diss.--Göttingen. / Lebenslauf.

Inaug.-diss.--Strassburg. / Lebenslauf.

In this thesis, we study alternating virtual knots. We show the Alexander polynomial of an almost classical alternating knot is alternating. We give a characterization theorem for alternating knots in terms of Goeritz matrices. We prove any reduced alternating diagram has minimal genus, and use this to prove the frst Tait Conjecture for virtual knots, namely any reduced diagram of an alternating virtual knot has minimal crossing number. / Thesis / Doctor of Philosophy (PhD)

LD2668 .T4 1941 S55 / Master of Science

Doctor of Philosophy / The alternating Hecke algebra is a q-analogue of the alternating subgroups of the finite Coxeter groups. Mitsuhashi has looked at the representation theory in the cases of the Coxeter groups of type A_n, and B_n, and here we provide a general approach that can be applied to any finite Coxeter group. We give various bases and a generating set for the alternating Hecke algebra. We then use Tits' deformation theorem to prove that, over a large enough field, the alternating Hecke algebra is isomorphic to the group algebra of the corresponding alternating Coxeter group. In particular, there is a bijection between the irreducible representations of the alternating Hecke algebra and the irreducible representations of the alternating subgroup. In chapter 5 we discuss the branching rules from the Iwahori-Hecke algebra to the alternating Hecke algebra and give criteria that determine these for the Iwahori-Hecke algebras of types A_n, B_n and D_n. We then look specifically at the alternating Hecke algebra associated to the symmetric group and calculate the values of the irreducible characters on a set of minimal length conjugacy class representatives.

Doctor of Philosophy / The alternating Hecke algebra is a q-analogue of the alternating subgroups of the finite Coxeter groups. Mitsuhashi has looked at the representation theory in the cases of the Coxeter groups of type A_n, and B_n, and here we provide a general approach that can be applied to any finite Coxeter group. We give various bases and a generating set for the alternating Hecke algebra. We then use Tits' deformation theorem to prove that, over a large enough field, the alternating Hecke algebra is isomorphic to the group algebra of the corresponding alternating Coxeter group. In particular, there is a bijection between the irreducible representations of the alternating Hecke algebra and the irreducible representations of the alternating subgroup. In chapter 5 we discuss the branching rules from the Iwahori-Hecke algebra to the alternating Hecke algebra and give criteria that determine these for the Iwahori-Hecke algebras of types A_n, B_n and D_n. We then look specifically at the alternating Hecke algebra associated to the symmetric group and calculate the values of the irreducible characters on a set of minimal length conjugacy class representatives.

Thesis (Ph. D.)--Ohio state University, 1921. / Autobiography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1929. / Typescript with manuscript equations. With this is bound: A two dimensional boundary value problem for the transmission of alternating currents through a semi-infinite heterogenous conducting medium / by Herbert Pu. Evans. Reprinted from Physical review, vol. 36, no. 10 (15 Nov. 1929), p. 1579-1588. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin. / Bound with v. 3, no. 2-v. 3, no. 6 subsequent to publication. Bibliography: p. 153-162.