A computation of modular forms of weight one and small level

We report on a computation of holomorphic cuspidal modular forms of weight one and small level (currently level at most 1500) and classification of them according to the projective image of their attached Artin representations. The data we have gathered, such as Fourier expansions and projective images of Hecke newforms and dimensions of space of forms, is available in both Magma and Sage readable formats on a webpage created in support of this project

Effect of long-time, elevated-temperature exposures to vacuum and lithium on the properties of a tantalum alloy, T-111

The effect of long-term, elevated-temperature vacuum and lithium exposures on the mechanical properties of T-111 (Ta-8W-2Hf) is determined. Exposure conditions were for 1000 hours at 980 or 1315 C, 5000 hours at 1315 C, and a duplex temperature exposure of 1000 hours at 980 C plus 4000 hours at 1040 C. The exposures resulted in reduced tensile and creep strengths of the T-111 in the 900 to 1100 C temperature range where a dynamic strain-age-strengthening mechanism is operative in this alloy. This strength reduction was attributed to the depletion of oxygen from solid solution in this alloy

On the canonical degrees of curves in varieties of general type

A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from above by some expression $a\chi(C)+b$, where $a$ and $b$ are positive constants, with the possible exceptions corresponding to curves lying in a strict closed subset (depending on $a$ and $b$). A theorem of Miyaoka proves this for smooth curves in minimal surfaces, with $a>3/2$. A conjecture of Vojta claims in essence that any constant $a>1$ is possible provided one restricts oneself to curves of bounded gonality. We show by explicit examples coming from the theory of Shimura varieties that in general, the constant $a$ has to be at least equal to the dimension of the ambient variety. We also prove the desired inequality in the case of compact Shimura varieties.Comment: 10 pages, to appear in Geometric and Functional Analysi

On certain finiteness questions in the arithmetic of modular forms

We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3: restructered parts of the article; v4: minor corrections and change

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Schemes in Lean

We tell the story of how schemes were formalized in three different ways in the Lean theorem prover

Development of a food frequency questionnaire to estimate habitual dietary intake in Japanese children

<p>Abstract</p> <p>Background</p> <p>Food frequency questionnaires (FFQ) are used for epidemiological studies. Because of the wide variations in dietary habits within different populations, a FFQ must be developed to suit the specific group. To date, no FFQ has been developed for Japanese children. In this study, we developed a FFQ to assess the regular dietary intake of Japanese children. The FFQ included questions regarding both individual food items and mixed dishes.</p> <p>Methods</p> <p>Children (3-11 years of age, n = 621) were recruited as subjects. Their parents or guardians completed a weighed dietary record (WDR) for each subject in one day. We defined FOOD to be not only as a single food item but also as a mixed dish. The dieticians conceptually grouped similar FOODs as FOOD types. We used a contribution analysis and a multiple regression analysis to select FOOD types.</p> <p>Results</p> <p>We obtained a total of 586 children's dietary data (297 boys and 289 girls). In addition, we obtained 1,043 FOODs. Dieticians grouped into similar FOODs, yielding 275 FOOD types. A total of 115 FOOD types were chosen using a contribution analysis and a multiple regression analysis, then we excluded overlapping items. FOOD types that were eaten by fewer than 15 subjects were excluded; 74 FOOD types remained. We also added liver-based dishes that provided a high amount of retinol. A total of 75 FOOD types were finally determined for the FFQ. The frequency response formats were classified into four type categories: seven, eight, nine and eleven, according to the general intake frequency of each FOOD type. Information on portion size was obtained from the photographs of each listed FOOD type in real scale size, which was the average amount of the children's portion sizes.</p> <p>Conclusions</p> <p>Using both a contribution analysis and a multiple regression analysis, we developed a 75-food item questionnaire from the study involving 586 children. The next step will involve the verification of FFQ reproducibility and validity.</p