Prove that the θ scheme (I − θkD + D −)v n+1 j = (I + (1 − θ)kD + D −)v n j , j = 0, 1,. .. , N, 0 ≤ θ ≤ 1 (1) is unconditionally stable for θ ≥ 1 2. In order to find the necessary conditions for stability, we begin by making the ansatz v n j = 1 √ 2π e iωx j ˆ v n (ω), where the solution is composed of a single Fourier component. Substituting this expression into Equation 1, we obtain the foll...

The oligosaccharide structures of total glycoproteins in suspension-cultured Arabidopsis thaliana MM2d cells are determined. The N-linked sugar chains released by hydrazinolysis were labeled with 2-aminopyridine, and analyzed by a combination of HPLC, matrix-assisted laser desorption/ionization time-of-flight mass spectrometry, and exoglucosidase digestion. The glycan structures determined were...

Faculty of Engineering Yokohama National University, 79–5 Tokiwadai, Hodogaya-ku, Yokohama 240–8501, Japan, Graduate School of Environment and Information Sciences, Yokohama National University, 79–7 Tokiwadai, Hodogaya-ku, Yokohama 240–8501, Japan, and Graduate School of Pharmaceutical Sciences, Kyushu University, 3–1–1 Maidashi, Higashiku, Fukuoka 812–8582, Japan (Received March 15, 2002; Acc...

We explore two predictive tasks: (i) a measure of tag probability, and (ii) identifying a minimum tag set for more meaningful music classification on a 100,000 song dataset joined across complementary databases from the 1 Million Song Dataset (“MSD”). We conclude that a tag set size of around 50 tags is most meaningful and report many of our findings/analysis based on the top 50 tags. Using lin...

The purpose of this term paper is to give an accessible exposition of Fay’s trisecant identity [1]. Fay’s identity is a relation between the theta function and the cross-ratio function associated to a compact Riemann surface [2]. Although the majority of the paper will consist of developing the machinery needed to define these objects, let us briefly say a few words about some familiar objects ...