Kuki Shuzo was a philosopher at the margins of the Kyoto School; his most significant contribution was the short work 'Iki' no kozo, in which he located Japanese uniqueness in the Edo demimonde aesthetic of iki, style or chic. This thesis surveys the major Western critiques of Kuki's aesthetics, focussing particularly on the work done by Peter Dale, Leslie Pincus, and Harry Harootunian revealing Kuki's borrowing from European modernism, especially fascist modernism, and attempts to uncover an alternative genealogy for Kuki in Japanese Pure Land thought. It finally asserts that Kuki's valorization of resignation, and his own retreat into the aesthetic, can be read as a form of resistance to Japanese nationalism.

<p>Given a positive integer k, Conrey, Farmer, Keating, Rubinstein and Snaith conjectured a formula for the asymptotics of the k-th moments of the central values of quadratic Dirichlet L-functions. The conjectured formula for the moments is expressed as sum of a k(k+1)/2 degree polynomial in log |d|. In the sum, d varies over the set of fundamental discriminants. This polynomial, called the moment polynomial, is given as a k-fold residue. In Part I of this thesis, we derive explicit formulae for first k lower order terms of the moment polynomial.</p> <p> In Part II, we present a formula bounding the average of S(t,f), the remainder term in the formula for the number of zeros of an L-function, L(s,f), where f is a newform of weight k and level N. This is Turing's method applied to cuspforms. We carry out the improvements to Turing's original method including using techniques of Booker and Trudgian. These improvements have application to the numerical verification of the Riemann Hypothesis.</p>

The goal of this thesis is to define and study the Fourier algebra A(G) of a locally compact groupoid G. If G is a locally compact group, its Fourier-Stieltjes algebra B(G) and its Fourier algebra A(G) were defined by Eymard in 1964. Since then, a rich theory has been developed. For the groupoid case, the algebras B(G) and A(G) have been studied by Ramsay and Walter (borelian case, 1997), Renault (measurable case, 1997) and Paterson (locally compact case, 2004). In this work, we present a new definition of A(G) in the locally compact case, specially well suited for studying locally trivial groupoids. Let G be a locally compact proper groupoid. Following the group case, in order to define A(G), we consider the closure under certain norm of the span of the left regular G-Hilbert bundle coefficients. With the norm mentioned above, the space A(G) is a commutative Banach algebra of continuous functions of G vanishing at infinity. Moreover, A(G) separates points and it is also a B(G)-bimodule. If, in addition, G is compact, then B(G) and A(G) coincide. For a locally trivial groupoid G we present an easier to handle definition of A(G) that involves "trivializing" the left regular bundle. The main result of our work is a decomposition of A(G), valid for transitive, locally trivial groupoids with a "nice" Haar system. The condition we require the Haar system to satisfy is to be compatible with the Haar measure of the isotropy group at a fixed unit u. If the groupoid is transitive, locally trivial and unimodular, such a Haar system always can be constructed. For such groupoids, our theorem states that A(G) is isomorphic to the Haagerup tensor product of the space of continuous functions on Gu vanishing at infinity, times the Fourier algebra of the isotropy group at u, times space of continuous functions on Gu vanishing at infinity. Here Gu denotes the elements of the groupoid that have range u. This decomposition provides an operator space structure for A(G) and makes this space a completely contractive Banach algebra. If the locally trivial groupoid G has more than one transitive component, that we denote Gi, since these components are also topological components, there is a correspondence between G-Hilbert bundles and families of Gi-Hilbert bundles. Thanks to this correspondence, the Fourier-Stieltjes and Fourier algebra of G can be written as sums of the algebras of the Gi components. The theory of operator spaces is the main tool used in our work. In particular, the many properties of the Haagerup tensor product are of vital importance. Our decomposition can be applied to (trivially) locally trivial groupoids of the form X times X and X times H times X, for a locally compact space X and a locally compact group H. It can also be applied to transformation group groupoids X times H arising from the action of a Lie group H on a locally compact space X and to the fundamental groupoid of a path-connected manifold.

Given natural numbers n and k, with n>k, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of Z, say X={x_1,...,x_n} and Y={y_1,...,y_n}, such that x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for i=1,...,k. Many partial solutions to this problem were found in the late 19th century and early 20th century. When k=n-1, we call a solution X=(n-1)Y ideal. This is considered to be the most interesting case. Ideal solutions have been found using elementary methods, elliptic curves, and computational techniques. This thesis focuses on the ideal case. We extend the framework of the problem to number fields, and prove generalizations of results from the literature. This information is used along with computational techniques to find ideal solutions to the PTE problem in the Gaussian integers. We also extend a computation from the literature and find new lower bounds for the constant C_n associated to ideal PTE solutions. Further, we present a new algorithm that determines whether an ideal PTE solution with a particular constant exists. This algorithm improves the upper bounds for C_n and in fact, completely determines the value of C_6. We also examine the connection between elliptic curves and ideal PTE solutions. We use quadratic twists of curves that appear in the literature to find ideal PTE solutions over number fields.

The cohomology ring of a finite cyclic group was explicitly computed by Cartan and Eilenberg in their 1956 book on Homological Algebra. It is surprising that the cohomology ring for the next simplest example, that of a finite abelian group, has still not been treated in a systematic way. The results that we do have are combinatorial in nature and have been obtained using "brute force" computations. In this thesis we will give a systematic method for computing the cohomology ring of a finite abelian group. A major ingredient in this treatment will be the Tate resolution of a commutative ring R (with trivial group action) over the group ring RG, for some finite abelian group G. Using the Tate resolution we will be able to compute the cohomology ring for a finite cyclic group, and confirm that this computation agrees with what is known from Cartan-Eilenberg. Then we will generalize this technique to compute the cohomology ring for a finite abelian group. The presentation we will give is simpler than what is in the literature to date. We will then see that a straightforward generalization of the Tate resolution from a group ring to an arbitrary ring defined by monic polynomials will yield a method for computing the Hochschild cohomology algebra of that ring. In particular we will re-prove some results from the literature in a much more unified way than they were originally proved. We will also be able to prove some new results.

Given natural numbers n and k, with n>k, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of Z, say X={x_1,...,x_n} and Y={y_1,...,y_n}, such that x_1^i+...+x_n^i=y_1^i+...+y_n^i\] for i=1,...,k. Many partial solutions to this problem were found in the late 19th century and early 20th century. When k=n-1, we call a solution X=(n-1)Y ideal. This is considered to be the most interesting case. Ideal solutions have been found using elementary methods, elliptic curves, and computational techniques. This thesis focuses on the ideal case. We extend the framework of the problem to number fields, and prove generalizations of results from the literature. This information is used along with computational techniques to find ideal solutions to the PTE problem in the Gaussian integers. We also extend a computation from the literature and find new lower bounds for the constant C_n associated to ideal PTE solutions. Further, we present a new algorithm that determines whether an ideal PTE solution with a particular constant exists. This algorithm improves the upper bounds for C_n and in fact, completely determines the value of C_6. We also examine the connection between elliptic curves and ideal PTE solutions. We use quadratic twists of curves that appear in the literature to find ideal PTE solutions over number fields.

In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are polynomials over Q in the so-called elementary prime symmetric functions, whose values lie in Z. The latter are defined on the nonnegative integers and take the values of the elementary symmetric functions applied to the multi-set of prime factors (with repetition) of an integer n. Initially we look at basic properties of prime symmetric functions, and consider analogues of questions posed for the usual sum of proper divisors function, such as those concerning perfect numbers or Aliquot sequences. We consider the inverse question of when, and in how many ways a number $n$ can be expressed as f(m) for certain prime symmetric functions f. Then we look at asymptotic formulae for the average orders of certain fundamental prime symmetric functions, such as the arithmetic function whose value at n is the sum of k-th powers of the prime divisors (with repetition) of n. For these last functions in particular, we also look at statistical results by comparing their distribution of values with the distribution of the largest prime factor dividing n. In addition to average orders, we look at the modular distribution of prime symmetric functions, and show that for a fundamental class, they are uniformly distributed over any fixed modulus. Then our focus shifts to the related area of partitions into prime powers. We compute the appropriate asymptotic formulae, and demonstrate important monotonicity properties. We conclude by looking at iteration problems for some of the simpler prime symmetric functions. In doing so, we consider the empirical basis for certain conjectures, and are left with many open problems.

Diss. (sammanfattning) Stockholm : Karol. inst., 2002. / Härtill 5 uppsatser.

xviii, 124 p. : ill. (some col.) / This dissertation discusses three topics on scenarios beyond the Standard Model. Topic one is the effects from a fourth generation of quarks and leptons on electroweak baryogenesis in the early universe. The Standard Model is incapable of electroweak baryogenesis due to an insufficiently strong enough electroweak phase transition (EWPT) as well as insufficient CP violation. We show that the presence of heavy fourth generation fermions solves the first problem but requires additional bosons to be included to stabilize the electroweak vacuum. Introducing supersymmetric partners of the heavy fermions, we find that the EWPT can be made strong enough and new sources of CP violation are present. Topic two relates to the lepton avor problem in supersymmetry. In the Minimal Supersymmetric Standard Model (MSSM), the off-diagonal elements in the slepton mass matrix must be suppressed at the 10-3 level to avoid experimental bounds from lepton avor changing processes. This dissertation shows that an enlarged R-parity can alleviate the lepton avor problem. An analysis of all sensitive parameters was performed in the mass range below 1 TeV, and we find that slepton maximal mixing is possible without violating bounds from the lepton avor changing processes: μ [arrow right] eγ; μ [arrow right] e conversion, and μ [arrow right] 3e. Topic three is the collider phenomenology of quirky dark matter. In this model, quirks are particles that are gauged under the electroweak group, as well as a \dark" color SU (2) group. The hadronization scale of this color group is well below the quirk masses. As a result, the dark color strings never break. Quirk and anti-quirk pairs can be produced at the LHC. Once produced, they immediately form a bound state of high angular momentum. The quirk pair rapidly shed angular momentum by emitting soft radiation before they annihilate into observable signals. This dissertation presents the decay branching ratios of quirkonia where quirks obtain their masses through electroweak symmetry breaking. This dissertation includes previously published and unpublished co-authored material. / Committee in charge: Dr. Davison Soper: Chair; Dr. Graham Kribs: Advisor; Dr. Ray Frey: Member; Dr. Michael Kellman: Outside Member

xv, 219 p. : ill. (some col.) / Chemists have long recognized the potential of the BN bond to mimic CC double bonds in aromatic systems. Phenyl and indole are two of the most important arenes in natural systems, as well as medicine, applied chemistry, and materials science. Despite the potential of BN arenes as phenyl and indole mimics in biomolecules, few isoelectronic and isostructural BN biomolecules have been synthesized. Substitution of BN for C=C imparts tunability to aromatic systems, giving new and potentially valuable properties to the resulting molecules. Our group has sought to expand the utility of BN arenes by developing the synthetic arsenal available to chemists seeking to incorporate the BN bond into biological and other organic molecules of importance. The scope of this dissertation is twofold: (1) development of the first "fused" BN indole, including a survey of its reactivity towards electrophiles, synthesis of the parent N -H compound with complete characterization, and a comparison to natural indole and (2) expansion of the synthetic methodologies for constructing 1,2-dihydro-1,2-azaborine derivatives, including complete structural characterization of a family of "pre-aromatic" and aromatic compounds and a protection-free synthesis of azaborines. The contributions outlined in this dissertation expand both the fundamental understanding of BN isosterism in aromatic molecules and the synthetic toolbox for chemists seeking to incorporate BN arenes into biological and other organic motifs. This dissertation includes previously published and unpublished coauthored material. / Committee in charge: Professor Kenneth M. Doxsee, Chair; Professor Shih-Yuan Liu, Advisor; Professor Victoria J. DeRose, Member; Professor Michael M. Haley, Member; Professor Janis Weeks, Outside Member