The inclusion relation between Sobolev and modulation spaces

The inclusion relations between the $L^p$-Sobolev spaces and the modulation spaces is determined explicitly. As an application, mapping properties of unimodular Fourier multiplier $e^{i|D|^\alpha}$ between $L^p$-Sobolev spaces and modulation spaces are discussed.Comment: 21 page

Application of continuous light in a plant factory system 4. Physiological changes and concept of injury induction in plant leaves under continuous light

Physiological changes and concept of injury induction occurring under continuous light are comprehensively reviewed. Continuous light usually reduces photosynthetic rate, which may relate to changes in transpiration and leaf necrosis caused by reactive oxygen species. Other factors apart from photosynthesis may also affect leaf injuries occurring under continuous light. Continuous light sometimes increases carbohydrate and some secondary metabolite contents