Global regularity for a family of 3D models of the axisymmetric Navier-Stokes equations

We consider a family of 3D models for the axi-symmetric incompressible Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier-Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the original Navier-Stokes equations, which demonstrates the potential stabilizing effect of convection

Essays on the U.S. Treasury Debt Market and Asset-Pricing

The three essays in this dissertation examine questions in the U.S. Treasury bond market and an asset-pricing anomaly in the stock market. They are unified by the theme relating quantities of assets with asset prices. These essays challenge the notion that because financial markets are highly liquid, quantities of (demand or supply) do not matter for predicting asset prices. Chapter 1 examines the time-varying impact of the US Treasury debt supply on bond risk premiums. I find that the elasticity of bond risk premium with respect to supply depends on the correlation between stock and bond returns. An increase in the supply of Treasury bonds raises the required bond risk premiums, but the effect is stronger as stock and bond returns become more positively correlated. I interpret this evidence within the context of a preferred-habitat asset pricing model where the arbitrageurs are the marginal investor for all bond maturities. Arbitrageurs demand higher compensation for maturity risk when the stock-bond correlation is positive as bonds are poor hedges for stocks. On the other hand, when the correlation turns more negative, an increased bond supply induces low or even negative risk premiums. The findings have practical implications for understanding the impact of the impending Federal Reserve's unwinding of its $4.5 trillion bond portfolio. Chapter 2 documents new empirical stylized facts about the postwar U.S. Treasury debt management policy. In particular, I document the puzzling fact that the US Treasury has tended to historically issue more long-term debt when the term spread is greatest. I propose a simple model that captures the practical incentives and constraints faced by the Treasury debt manager. The debt manager seeks to minimize borrowing costs while managing rollover risks. I calibrate the model to generate a measure of time-varying roll-over risks faced by the U.S. Treasury. Chapter 3 investigates the earnings announcement premium puzzle in Finland. Between 1999-2002 and 2006-2009, I find that stocks with earnings announcement earn excess returns over non-announcement stock in the 2 week window before the announcements that quickly dissipates post-announcement. Moreover, I find that the premium is significantly higher and persistent through a 30 day window around the financial statement releases. I find no premium around the interim earnings report and in fact accumulative losses. I also assess the relationship between announcement premium and trading volume. Using an administrative transaction-level data set, I find some supportive evidence for the attention-grabbing hypothesis. I find a positive correlation between the announcement premium and the net-buying trading volume among individual investors, especially around the financial statements.PHDEconomicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146013/1/houfei_1.pd

Almost global solutions of 1D nonlinear Klein-Gordon equations with small weakly decaying initial data

It has been known that if the initial data decay sufficiently fast at space infinity, then 1D Klein-Gordon equations with quadratic nonlinearity admit classical solutions up to time $e^{C/\epsilon^2}$ while $e^{C/\epsilon^2}$ is also the upper bound of the lifespan, where $C>0$ is some suitable constant and $\epsilon>0$ is the size of the initial data. In this paper, we will focus on the 1D nonlinear Klein-Gordon equations with weakly decaying initial data. It is shown that if the $H^s$-Sobolev norm with $(1+|x|)^{1/2+}$ weight of the initial data is small, then the almost global solutions exist; if the initial $H^s$-Sobolev norm with $(1+|x|)^{1/2}$ weight is small, then for any $M>0$, the solutions exist on $[0,\epsilon^{-M}]$. Our proof is based on the dispersive estimate with a suitable $Z$-norm and a delicate analysis on the phase function

An Updated Numerical Analysis of eV Seesaw with Four Generations

We consider the so-called "eV seesaw" scenario, with right-handed Majorana mass $M_R$ at eV order, extended to four lepton generations. The fourth generation gives a heavy pseudo-Dirac neutral lepton, which largely decouples from other generations and is relatively stable. The framework naturally gives 3 active and 3 sterile neutrinos. We update a previous numerical analysis of a 3+3 study of the LSND anomaly, taking into account the more recent results from the MiniBooNE experiment. In particular, we study the implications for the third mixing angle $\mathrm{sin}^2\theta_{13}$, as well as CP violation. We find that current data do not seriously constrain more than one sterile neutrinos.Comment: References updated, and a Note Adde

A Model Program to Maximize Intellectual Development for Taiwanese Daycare/Preschool Children Ages 0-3

The purpose of this project was to design and develop a model program to maximize intellectual development for Taiwanese daycare/ preschool children ages 0-3. To accomplish this purpose, a review of current literature regarding intellectual development of preschool age children and related early childhood education was conducted. Additionally, related information from selected daycare/ preschool centers was obtained and analyzed