Hamilton decompositions of 6-regular abelian Cayley graphs

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made: Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian. The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture: Alspach Conjecture: Every 2k-regular, connected Cayley graph on a finite abelian group has a Hamilton decomposition. Alspach’s conjecture is true for k = 1 and 2, but even the case k = 3 is still open. It is this case that this thesis addresses. Chapters 1–3 give introductory material and past work on the conjecture. Chapter 3 investigates the relationship between 6-regular Cayley graphs and associated quotient graphs. A proof of Alspach’s conjecture is given for the odd order case when k = 3. Chapter 4 provides a proof of the conjecture for even order graphs with 3-element connection sets that have an element generating a subgroup of index 2, and having a linear dependency among the other generators. Chapter 5 shows that if Γ = Cay(A, {s1, s2, s3}) is a connected, 6-regular, abelian Cayley graph of even order, and for some1 ≤ i ≤ 3, Δi = Cay(A/(si), {sj1 , sj2}) is 4-regular, and Δi ≄ Cay(ℤ3, {1, 1}), then Γ has a Hamilton decomposition. Alternatively stated, if Γ = Cay(A, S) is a connected, 6-regular, abelian Cayley graph of even order, then Γ has a Hamilton decomposition if S has no involutions, and for some s ∈ S, Cay(A/(s), S) is 4-regular, and of order at least 4. Finally, the Appendices give computational data resulting from C and MAGMA programs used to generate Hamilton decompositions of certain non-isomorphic Cayley graphs on low order abelian groups.

Hamilton-Waterloo problem with triangle and C9 factors

The Hamilton-Waterloo problem and its spouse-avoiding variant for uniform cycle sizes asks if Kv, where v is odd (or Kv - F, if v is even), can be decomposed into 2-factors in which each factor is made either entirely of m-cycles or entirely of n-cycles. This thesis examines the case in which r of the factors are made up of cycles of length 3 and s of the factors are made up of cycles of length 9, for any r and s. We also discuss a constructive solution to the general (m,n) case which fixes r and s.

50th anniversary of the Judd–Ofelt theory: An experimentalist's view of the formalism and its application

The theory on the intensities of 4f-4f transitions introduced by B.R. Judd and G.S. Ofelt in 1962 has become a center piece in rare-earth optical spectroscopy over the past five decades. Many fundamental studies have since explored the physical origins of the Judd–Ofelt theory and have proposed numerous extensions to the original model. A great number of studies have applied the Judd–Ofelt theory to a wide range of rare-earth doped materials, many of them with important applications in solid-state lasers, optical amplifiers, phosphors for displays and solid state lighting, upconversion and quantum-cutting materials, and fluorescent markers. This paper takes the view of the experimentalist who is interested in appreciating the basic concepts, implications, assumptions, and limitations of the Judd–Ofelt theory in order to properly apply it to practical problems. We first present the formalism for calculating the wavefunctions of 4f electronic states in a concise form and then show their application to the calculation and fitting of 4f-4f transition intensities. The potential, limitations and pitfalls of the theory are discussed, and a detailed case study of LaCl3:Er3+ is presented.

Joh. Jacobi Schudt Specimen compendii philologici in usum studiosae juventutis quae in academiis, gymnasiis et scholis inferioribus Philologiae et antiquitatibus ... methodo per quaestiones et responsiones adornandi

Text lat. u. hebr.

Biblisches Lehrbuch der hebräischen Sprache nach der Hamilton'schen Interlinearmethode

bearb. von Creizenach

Na 50 Nachlass Arthur Schopenhauer - 'Schopenhauer-Archiv', 432 - Stichworte zu Kant, Schelling, Jacobi und Fries

4 Seiten

Jacobi Rhenferdii ... dissertationes philologicae de Decem Otiosis Synagogae : in quibus viri clariss. Johannis Lightfooti, aliorum que sententiae de Otiosis examinatur, varia de Synagogis, earumque jure, praefectis, ministris ... adsperguntur

Univ., Diss., 1686

F. W. J. Schelling's Denkmal der Schrift von den göttlichen Dingen &c. des Herrn Friedrich Heinrich Jacobi und der ihm in derselben gemachten Beschuldigung eines absichtlich täuschenden, Lüge redenden Atheismus

Denkmal der Schrift von den göttlichen Dingen & des Herrn Friedrich Heinrich Jacobi und der ihm in derselben gemachten Beschuldigung eines absichtlich täuschenden, Lüge redenden Atheismus

Bernhard von Jacobi als Dorantes, Rollenbild, Kniestück, in: Pierre Carlet de Marivaux: Das Spiel von Liebe und Zufall

Signatur des Originals: S 36/F04765

Bernhard von Jacobi als Dorantes, Rollenbild, in: Pierre Carlet de Marivaux: Das Spiel von Liebe und Zufall

Signatur des Originals: S 36/F04766

Bernhard von Jacobi als Tod, Rollenbild

Signatur des Originals: S 36/F04767

MS 066 Guide to the Howard B. Hamilton, MD, papers; 1945-1997

The Howard B. Hamilton, MD, papers, MS 66, includes material from 1945-1997 related to the Atomic Bomb Casualty Commission (ABCC) and the Radiation Effects Research Foundation (RERF). Hamilton was the Chief of Clinical Laboratories for the Atomic Bomb Casualty Commission from 1956 until its dissolution in 1975. He served in the same capacity for the Radiation Effects Research Foundation, which succeeded the ABCC, until 1984. This collection encompasses this period of time in Dr. Hamilton's career, as well as his related scholarly work after his retirement from RERF. Dr. Hamilton donated his collection of letters, reprints, newspaper articles, photographs, memos, and ephemera to the John P. McGovern Historical Collections and Research Center between 1985 and 2002. The collection is in good condition and consists of 3.75 cubic feet (10 boxes).