Classical Morphology of Plants as an Elementary Instance of Classical Invariant Theory

It has long been known that structural chemistry shows an intriguing correspondence with Classical Invariant Theory (CIT). Under this view, an algebraic binary form of the degree n corresponds to a chemical atom with valence n and each physical molecule or ion has an invariant-theoretic counterpart. This theory was developed using the Aronhold symbolical approach and the symbolical processes of convolution/transvection in CIT was characterized as a potential “accurate morphological method”. However, CIT has not been applied to the formal morphology of living organisms. Based on the morphological interpretation of binary form, as well as the process of convolution/transvection, the First and Second Fundamental Theorems of CIT and the Nullforms of CIT, we show how CIT can be applied to the structure of plants, especially when conceptualized as a series of plant metamers (phytomers). We also show that the weight of the covariant/invariant that describes a morphological structure is a criterion of simplicity and, therefore, we argue that this allows us to formulate a parsimonious method of formal morphology. We demonstrate that the “theory of axilar bud” is the simplest treatment of the grass seedling/embryo. Our interpretations also represent Troll's bauplan of the angiosperms, the principle of variable proportions, morphological misfits, the basic types of stem segmentation, and Goethe's principle of metamorphosis in terms of CIT. Binary forms of different degrees might describe any repeated module of plant organisms. As bacteria, invertebrates, and higher vertebrates are all generally shared a metameric morphology, wider implications of the proposed symmetry between CIT and formal morphology of plants are apparent

Phototrophic biofilms and their potential applications

Phototrophic biofilms occur on surfaces exposed to light in a range of terrestrial and aquatic environments. Oxygenic phototrophs like diatoms, green algae, and cyanobacteria are the major primary producers that generate energy and reduce carbon dioxide, providing the system with organic substrates and oxygen. Photosynthesis fuels processes and conversions in the total biofilm community, including the metabolism of heterotrophic organisms. A matrix of polymeric substances secreted by phototrophs and heterotrophs enhances the attachment of the biofilm community. This review discusses the actual and potential applications of phototrophic biofilms in wastewater treatment, bioremediation, fish-feed production, biohydrogen production, and soil improvement

Z-scan studies in fluorescein-doped boric acid glass

The non-linear response of fluorescein-doped boric acid glass was probed using the Z-scan technique. A striking contrast was observed in its non-linear transmission characteristics at different argon-ion laser wavelengths. The non-linear transmission characteristics exhibit strong saturation behaviour at 457.9 nm whilst at 476.5 nm and 488.0 nm the response is dominated by intense excited state absorption. The experimental observations are explained using the four-level saturable absorber model. The excited state absorption cross-section, saturation intensity, light induced absorption and refraction changes have been determined along with the sign of the non-linearity at various argon laser wavelengths. The optical limiting characteristics of fluorescein at 476.5 nm and 457.9 nm are also reported. The behaviour of the sample was in agreement with the Z-scan observations