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京都大学 / 0048 / 新制・課程博士 / 博士(薬科学) / 甲第20312号 / 薬科博第81号 / 新制||薬科||9(附属図書館) / 京都大学大学院薬学研究科医薬創成情報科学専攻 / (主査)教授 大野 浩章, 教授 高須 清誠, 教授 竹本 佳司 / 学位規則第4条第1項該当 / Doctor of Pharmaceutical Sciences / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20885号 / 理博第4337号 / 新制||理||1623(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 望月 拓郎, 教授 中島 啓, 教授 小野 薫 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

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We develop the mathematical theory of the open/closed correspondence, proposed by Mayr in physics as a class of dualities between open strings on Calabi-Yau 3-folds and closed strings on Calabi-Yau 4-folds. Given an open geometry on a toric Calabi-Yau 3-orbifold relative to a framed Aganagic-Vafa outer brane, we construct a closed geometry on a toric Calabi-Yau 4-orbifold and establish the correspondence between the two geometries on the following levels across both the A- and B-sides of mirror symmetry: numerical Gromov-Witten invariants; generating functions of Gromov-Witten invariants; B-model hypergeometric functions and Givental-style mirror theorems; Picard-Fuchs systems and solutions; integral cycles on Hori-Vafa mirrors and periods; mixed Hodge structures.

Landau-Ginzburg mirror symmetry takes place in the context of affine singularities in CN. Given such a singularity defined by a quasihomogeneous polynomial W and an appropriate group of symmetries G, one can construct the FJRW theory (see [3]). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch [1]. The conjecture is that the A-model of W and G should match the B-model of a dual singularity and dual group (which we denote by WT and GT). The B-model construction is based on the Milnor ring, or local algebra, of the singularity. We verify this conjecture for a wide class of singularities on the level of Frobenius algebras, generalizing work of Krawitz [10]. We also review the relevant parts of the constructions.

America invests large amounts of money in K-12 education to develop its human capital. As such, K-12 student success is vital to the human capital development and future of America's children and adolescents. There is significant concern for the K-12 students who are predictably at risk of not graduating from high school (e.g., low-income, ethnic minority, and first generation college students) let alone qualifying for and enrolling in postsecondary education. Over the past four decades student success has primarily been explained by sociological research on status attainment as well as social capital and cultural capital. However, very little research addresses the relationship between this sociological research and motivation theory from the field of psychology. Specifically, student success research generally neglects describing how social capital and cultural capital become contextually and motivationally relevant for K-12 students. This study explored the pathway of success for students from the following backgrounds: low-income, first generation in college, active members of the Church of Jesus Christ of Latter-day Saints (LDS), Hispanic, graduated from a Utah high school in 2009 and who were admitted to Brigham Young University the same year as new freshmen. Case study methods were employed initially in phase one of the analysis using a grounded theory or emic paradigm, allowing data and patterns to emerge. In phase two of the analysis, using a post-positivist or etic paradigm data were contrasted with existing research. The findings revealed a new model that explains the conditions of student motivation. While the findings support existing research on the influences of social capital and cultural capital on student success, all students in this study experienced a triggering relationship that caused them to contextualize and assign value to various forms of capital in the past and present and leveraged them towards student success. This contextualization also served as a motivation for students to be successful and to pursue additional forms of capital to assist them on their pathway to success. The implications of this triggering relationship theory can assist parents, educators, and many others who facilitate the human capital development of children and adolescents.

The goal of this thesis is to investigate a conjecture about Mirror Symmetry for Landau Ginzburg (LG) models with non-abelian gauge groups. The conjecture predicts that the LG A-model for a polynomial-group pair $(W,G)$ is equivalent to the LG B-model for the dual pair $(W^*, G^*)$. In particular, the A-model and B-model include the construction of a Frobenius algebra. The LG mirror symmetry conjecture predicts that the A-model Frobenius algebra for $(W,G)$ will be isomorphic to the B-model Frobenius algebra for the dual pair $(W^*,G^*)$. Part of the conjecture includes a rule describing how to construct the dual pair. Until now, no examples of this phenomenon have been verified. In this thesis we will verify the conjecture for the polynomial $W(x_1,x_2,x_3,x_4) = x_1^4+x_2^4+x_3^4+x_4^4$ with a maximal admissible non-abelian group. I present a supplementary guide along with a worked example to compute the state spaces of each of the A and B models with non-abelian groups. This includes formalizing G-actions to take invariants, computing each state space, formalizing the product on each state space, and as the main result, showing there indeed exists an isomorphism of Graded Frobenius Algebras between the LG A-model and dual LG B-model.

Theatre in its most crude, poignant, and honest form exists as the unapologetic mirror of our world. It houses the piercing reflections of mankind's hope, fear, self-doubt, passion, joy, despair, brilliance, destitution, and desire. It becomes the image of all that man hopes to be, yearns to achieve, and knows he has destroyed. Theatrical performance is without equal in its ability to conjure visible truth from the reflection man sees everyday and hopelessly fails to recognize. Ultimately, theatre demands that man see himself without the masks of excuse, ignorance, or makeup. It is the vision of this journey to honor theatre's mask-less demand. Through the development of a multi-scene theatrical performance; the collection and analysis of relevant research material; and the cultivation of a comprehensive journal outlining the processes, the challenges, and the revelations that will travel the same road--from the cluttered moments of conception to the still air of an empty room after an exhausting final bow--only a mirror will remain. Each component--production, research, and journal--will function as equally essential elements. They will illuminate the evolution of fully realized theatre and detail the composition of a common theatrical message: Truth is both the seed of desperation and discovery.

Nanoscale p-channel transistors under negative gate bias at an elevated temperature show threshold voltage degradation after a short period of stress time. In addition, nanoscale (45 nm) n-channel transistors using high-k (HfO2) dielectrics to reduce gate leakage power for advanced microprocessors exhibit fast transient charge trapping effect leading to threshold voltage instability and mobility reduction. A simulation methodology to quantify the circuit level degradation subjected to negative bias temperature instability (NBTI) and fast transient charge trapping effect has been developed in this thesis work. Different current mirror and two-stage operation amplifier structures are studied to evaluate the impact of NBTI on CMOS analog circuit performances for nanoscale applications. Fundamental digital circuit such as an eleven-stage ring oscillator has also been evaluated to examine the fast transient charge transient effect of HfO2 high-k transistors on the propagation delay of ring oscillator performance. The preliminary results show that the negative bias temperature instability reduces the bandwidth of CMOS operating amplifiers, but increases the amplifier's voltage gain at mid-frequency range. The transient charge trapping effect increases the propagation delay of ring oscillator. The evaluation methodology developed in this thesis could be extended to study other CMOS device and circuit reliability issues subjected to electrical and temperature stresses.