Particulate, discrete and frictional systems such as sand constitute a separate class of materials. In order to derive stress-strain relations for these materials, their key features have to be identified and incorporated into the theoretical formulations. The presence of voids, the ability to undergo continuous and systematic spatial rearrangement of particles, the existence of bounds for the developed ratio of tangent and normal contact forces and the systematic variations of the tangent and normal contact force distributions during general loading, are identified as key features of particulate, discrete and frictional systems. The contact normal and the contact branch length distribution functions describe the spatial arrangement of particles mathematically. The distribution of contact normals exhibit mutually orthogonal principal directions which coincide with the principal stress directions. Most contacts in frictional systems do not develop limiting friction during general loading. Sliding of a few suitably oriented contacts followed by rolling and rigid body rotations and displacements of a large number of particles is the main mechanism causing non-recoverable deformations in frictional systems. As a part of the rearranging process, dominant chains of particles are continuously constructed and destructed, the rates being different at different stages of loading. A change of loading direction is associated with a change of dominant chains of particles resulting in changes in strain magnitudes. Rate insensitive incremental stress-strain relations are derived here using the principle of virtual forces. The key features of frictional systems have been incorporated into the stress-strain relations following the theoretical framework proposed by Rothenburg(1980), for analysing bonded systems of uniform spherical particles. For frictional systems, the load-deformation response at particle contacts is assumed to be non-linear. The deformations resulting from all internal activity are quantified defining equivalent incrementally elastic stiffnesses in the tangent and normal directions at contacts and defining loading and unloading criteria. After each increment of loading, the incremental stiffnesses and contact normal distribution are updated to account for the changes resulting from rearrangement of particles. Laws that describe the spatial rearrangement of particles, changes in the ratio between the tangent and normal contact force distributions and the resistance to deformation resulting from changes in dominant chains of particles are established based on the information from laboratory experiments reported in the literature and numerical experiments of Bathurst(1985). The stress ratio and the state parameter (defined as the ratio of void ratios at the critical-state to the current state, computed for a given mean-normal stress) are identified as key variables that can be used to quantify the extent of particle rearrangements. The proposed formulations are capable of modelling the non-linear stress-strain response which is dependent on the inherent anisotropy, stress induced anisotropy, density of packing, stress level and stress path. To predict the stress-strain response of sand, a total of 24 model parameters have to be evaluated. All the model parameters can be evaluated from five conventional triaxial compression tests. The proposed stress-strain relations have been verified by comparing with laboratory measurements on sand. The data base consists of triaxial tests reported by Negussey(1984), hollow cylinder tests graciously carried out for the author by A. Sayao, and true triaxial and hollow cylinder tests made available for the Cleveland Workshop(1987). / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

This thesis presents a theory of multi-scale, curvature and torsion based shape representation for planar and space curves. The theory presented has been developed to satisfy various criteria considered useful for evaluating shape representation methods in computer vision. The criteria are: invariance, uniqueness, stability, efficiency, ease of implementation and computation of shape properties. The regular representation for planar curves is referred to as the curvature scale space image and the regular representation for space curves is referred to as the torsion scale space image. Two variants of the regular representations, referred to as the renormalized and resampled curvature and torsion scale space images, have also been proposed. A number of experiments have been carried out on the representations which show that they are very stable under severe noise conditions and very useful for tasks which call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation. Planar or space curves are described at varying levels of detail by convolving their parametric representations with Gaussian functions of varying standard deviations. The curvature or torsion of each such curve is then computed using mathematical equations which express curvature and torsion in terms of the convolutions of derivatives of Gaussian functions and parametric representations of the input curves. Curvature or torsion zero-crossing points of those curves are then located and combined to form one of the representations mentioned above. The process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve. This thesis contains a number of theorems about evolution and arc length evolution of planar and space curves along with their proofs. Some of these theorems demonstrate that evolution and arc length evolution do not change the physical interpretation of curves as object boundaries and others are in fact statements on the global properties of planar and space curves during evolution and arc length evolution and their representations. Other theoretical results shed light on the local behavior of planar and space curves just before and just after the formation of a cusp point during evolution and arc length evolution. Together these results provide a sound theoretical foundation for the representation methods proposed in this thesis. / Science, Faculty of / Computer Science, Department of / Graduate

This thesis presents three essays on global yield curve factors and international linkages across yield curves. The essays represent a contribution to our understanding of the effect of globalization on yields, addressing three topics: modeling global and local yield curve factors, modeling global and local yield curve factors in excess bond returns and a joint model of global macroeconomic and yield curve factors. The first essay proposes and develops an empirical model of global and local yield curve factors based on three factors proposed by Nelson and Siegel (1987) dynamized and reinterpreted by Diebold and Li (2006) as level, slope and curvature. The results support the existence of a global yield curve composed of global factors which together with local factors describe the yield curve of the USA, Germany and the UK. Specifically, the global factors explain on average 55% of the variance of yields, and impulse response functions indicate that shocks to global factors are larger and last longer than shocks to local factors. In the second essay, we examine the predictability content of the global and local yield curve factor model to predict excess bond returns one year ahead. We use a rolling window of fifteen years to compare in-sample predictability of our model and two benchmark models: the model proposed by Cochrane and Piazzesi (2005) and the global and local factor model proposed by Dahlquist and Hasseltoft (2011). The results indicate that the global and local yield curve factors from our model predict excess bond returns with an adjusted R² up to 59%. We also find that global factors explain up to 58% of the forecast error variance when predicting excess bond returns. Moreover, our model outperforms both competing models considering the USA, Germany and the UK.The third essay proposes and estimates a joint model of global macroeconomic and yield curve factors, which shows the interaction between global yield curve factors and global macroeconomic factors. Our findings show that the influence of macroeconomic factors on yield curve factors is stronger than the influence of yield curve factors on macroeconomic factors.

The purpose of this thesis is to present a definition and some properties of a curved arc in a plane and to present a definition and some properties of the Jordan curve.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22979号 / 理博第4656号 / 新制||理||1669(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 玉川 安騎男, 教授 小野 薫, 教授 望月 新一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

We give algorithms to compute Coleman integrals on superelliptic curves over unramified extensions of the p-adics, and apply these via Chabauty methods to determine the set of rational points on such curves. We also determine the solution to an explicit instance of the Shafarevich conjecture by finding all elliptic curves with good reduction outside of the first 6 primes, subject to a heuristic. We use a combination of non-abelian Chabauty and the Mordell--Weil sieve to determine the rational points on several quotient modular curves, and therefore classify pairs of elliptic curves over the rationals with 67-, 73-, and 107-isogenies. We give methods to explicitly compute Coleman integrals on modular curves using a canonical lift of Frobenius and canonical local coordinates in each residue disk, and discuss the problem of computing the Weil pairing in finite rings.

No description available.

Flood-control reservoirs experience water level fluctuations that control survival of their biota. I explored diverse but related aspects of water-level management. Three frameworks were indentified for directing rule curve (i.e., daily targets for water levels) changes in flood-control reservoirs managed by the U.S. Army Corps of Engineers (USACE), with differing scopes and requirements. Framework choice depends on the reservoir’s primary authorization and magnitude of the contemplated change. Changes without congressional approval must be based on flood risk. Quantile regression was used to model a maximum water level with a user-specified level of risk. Because actions that request changes to water levels from natural resource professionals should have a sound ecological basis, I analyzed the relationships between water level fluctuations and vegetation in reservoirs. Remote sensing methods were used to calculate a greenness index from vegetation in the reservoir based on 14 years of satellite imagery and water levels.

No description available.

The Harris-Venkatesh conjecture posits a relationship between the action of derived Hecke operators on weight-one modular forms and Stark units. We prove the full Harris-Venkatesh conjecture for all CM dihedral weight-one modular forms. This reproves results of Darmon-Harris-Rotger-Venkatesh, extends their work to the adelic setting, and removes all assumptions on primality and ramification from the imaginary dihedral case of the Harris-Venkatesh conjecture. This is done by introducing the Harris-Venkatesh period on cuspidal one-forms on modular curves, introducing two-variable optimal modular forms, evaluating GL(2) × GL(2) Rankin-Selberg convolutions on optimal forms and newforms, and proving a modulo-ℓᵗ comparison theorem between the Harris-Venkatesh and Rankin-Selberg periods. Furthermore, these methods explicitly describe local factors appearing in the constant of proportionality prescribed by the Harris-Venkatesh conjecture. We also look at the application of our methods to non-dihedral forms.