Let j be the modular invariant. For the primes p ≤ 23 the q-expansion coefficients of U(j− 744) are multiplicative as it was a Hecke eigenformmodulo a power of p which increases withm. This was conjectured by Atkin on the basis of extensive numerical experiments, and is proved in this paper. The cases p = 5, 7 and 11 are under special consideration in this paper.

It has been known for more than a century that sieve plates in the phloem in plants contain callose, a β-1,3-glucan. However, the genes responsible for callose deposition in this subcellular location have not been identified. In this paper we examine callose deposition patterns in T-DNA insertion mutants (cs7) of the Callose Synthase 7 (CalS7) gene. We demonstrated here that the CalS7 gene is e...

The sieve element occlusion (SEO) gene family originally was delimited to genes encoding structural components of forisomes, which are specialized crystalloid phloem proteins found solely in the Fabaceae. More recently, SEO genes discovered in various non-Fabaceae plants were proposed to encode the common phloem proteins (P-proteins) that plug sieve plates after wounding. We carried out a compr...

This note is a detailed explanation of Shanks–Atkin NUCOMP— composition and reduction carried out “simultaneously”—for all quadratic fields, that is, including real quadratic fields. That explanation incidentally deals with various “exercises” left for confirmation by the reader in standard texts. Extensive testing in both the numerical and function field cases by Michael J Jacobson, Jr, report...

Summary Analysis of HIV-1 virions from participants infected in a randomized controlled preventive HIV-1 vaccine efficacy trial can help elucidate mechanisms of partial protection. By comparing the genetic sequence of viruses from vaccine and placebo recipients to the sequence of the vaccine itself, a technique called 'sieve analysis', one can identify functional specificities of vaccine-induce...

In this paper we introduce a simpli"ed implementation of the 1D recursive median sieve. The sieve is a multiscale data analysis method based on iterative application of recursive median "lters of increasing window length. We show that this system can be implemented by applying only 3-point median operations, due to the introduction of do not care vertices to the positive Boolean function corres...

We describe a hardware device for supporting the sieving step in integer factoring algorithms like the quadratic sieve or the number field sieve. In analogy to Bernstein’s proposal for speeding up the linear algebra step, we rely on a mesh of very simple processing units. Manufacturing the device at moderate cost with current hardware technology on standard wafers with 200 mm or 300 mm diameter...

This study introduced the application of high-throughput sequencing techniques to the investigation of microbial diversity in the field of plant quarantine. It examined the microbial diversity of wheat imported into China, and established a bioinformatics database of wheat pathogens based on high-throughput sequencing results. This study analyzed the nuclear ribosomal internal transcribed space...

The modern sieve method began from Brun’s fundamental work in 1915. This remained the dominant work until 1941 when Ju. V. Linnik expanded on the sieve method. In 1947, A. Selberg advanced the sieve method by using his upper bound sieve. His sieve weights, are fundamentally different from Brun’s thus he brought a structural change into the sieve method. The linear sieve was developed by Rosser ...