Following a previous study of the one-loop factorization of the nonsinglet g 2 structure function of the nucleon, we present in this paper the next-to-leading order coefficient functions in the singlet sector. To obtain the result, the partonic processes of virtual Compton scattering off two and three "on-shell" gluons are calculated. A key step in achieving the correct factorization is to separate the correct twist-two contribution. The Burkardt-Cottingham sum rule is nominally satisfied at this order.

We introduce gauge-invariant quark and gluon angular momentum distributions after making a generalization of the angular momentum density operators. From the quark angular momentum distribution, we define the gauge-invariant and leading-twist quark orbital angular momentum distribution L q (x). The latter can be extracted from data on the polarized and unpolarized quark distributions and the off-forward distribution E(x) in the forward limit. We comment upon the evolution equations obeyed by this as well as other orbital distributions considered in the literature.

We study the chromodynamical gauge symmetry in relation to the internal spin structure of the nucleon. We show that ͑1͒ even in the helicity eigenstates the gauge-dependent spin and orbital angular momentum operators do not have gauge-independent matrix element, ͑2͒ the evolution equations for the gluon spin take very different forms in the Feynman and axial gauges, but yield the same leading behavior in the asymptotic limit, and ͑3͒ the complete evolution of the gauge-dependent orbital angular momenta appears intractable in the light-cone gauge. We define a new gluon orbital angular momentum distribution L g (x) which is an experimental observable and has a simple scale evolution. However, its physical interpretation makes sense only in the light-cone gauge just like the gluon helicity distribution ⌬g(x). ͓S0556-2821͑99͒02207-9͔ PACS number͑s͒: 12.38.Aw, 14.20.Dh E ជ a ϭϪٌ ជ A 0a Ϫ ‫ץ‬A ជ ‫ץ‬t Ϫgf abc A ជ b A 0c .

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Considering the possible interpretation of the Ellis-Jaffe sum rule violation that the strange quark in the polarized proton is remarkably polarized in the opposite direction of the proton spin, we investigate its implication in the semi-inclusive Λ production in deep inelastic process with the electron beam unpolarized and proton target polarized longitudinally. As a result, we find that the measurement of the Λ polarization in the process considered can provide clean information about the strange quark spin distribution in the proton.to be published in Phys. Lett. B

Efficient seed germination and establishment are important traits for field and glasshouse crops. Large-scale germination experiments are laborious and prone to observer errors, leading to the necessity for automated methods. We experimented with five crop species, including tomato, pepper, Brassica, barley, and maize, and concluded an approach for large-scale germination scoring. Here, we present the SeedGerm system, which combines cost-effective hardware and open-source software for seed germination experiments, automated seed imaging, and machine-learning based phenotypic analysis. The software can process multiple image series simultaneously and produce reliable analysis of germination-and establishment-related traits, in both comma-separated values (CSV) and processed images (PNG) formats. In this article, we describe the hardware and software design in detail. We also demonstrate that SeedGerm could match specialists' scoring of radicle emergence. Germination curves were produced based on seed-level germination timing and rates rather than a fitted curve. In particular, by scoring germination across a diverse panel of Brassica napus varieties, SeedGerm implicates a gene important in abscisic acid (ABA) signalling in seeds. We compared SeedGerm with existing methods and concluded that it could have wide utilities in large-scale seed phenotyping and testing, for both research and routine seed technology applications.

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