In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant-step operation and f -representations, and makes it possible to relate the infrastructure to the (Arakelov) divisor class group of the global field. In the case of global function fields, we present results that establish ...

We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes’ transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which Dp-branes may be polarized into a noncommutative geometry by ...

A short critical review of the state-of-the-art and emerging trends on mathematical modeling heterogeneous photocatalytic solar reactors, applied for degradation contaminants (EC) in water, is presented. The discusses key aspects about EC reaction kinetics, artificial radiation emission models, absorption-scattering models evaluation radiant field large-scale photoreactors, based radiation-assi...

In this research, photocatalytic degradation method has been introduced to clean up Spent Caustic of Olefin units of petrochemical industries (neutralized Spent Caustic by means of sulfuric acid) in the next step, adaptable method and effective parameters in the process performance have been investigated. Chemical oxygen demand (COD) was measured by the commercial zinc oxide that synthesized wi...

The novel complex photocatalytic material was prepared by coating TiO₂ nanoparticles on tourmaline using the sol-gel method, and used in the degradation of the herbicide 2,4-D. The results indicated that coating TiO₂ with tourmaline enhanced the photocatalytic activity significantly. Based on the research of a simplified model for the average light intensity in the photoreactor, the influence o...

Photocatalysis for organic synthesis has experienced an exponential growth in the past 10 years. However, the variety of experimental procedures that have been reported to perform photon-based catalyst excitation has hampered the establishment of general protocols to convert visible light into chemical energy. To address this issue, we have designed an integrated photoreactor for enhanced photo...

The use of microflow reactors enabled dramatic improvements in the apparent rates photochemical reactions. However, scaling-up photomicroreactors remains a challenge due to difficulties distributing light and flow all units photomicroreactors. In this work, mass photon transfer limitations an easily scalable micro-structured reactor, aerosol photoreactor, was studied. reactor concept, each drop...

A series of 4,4'-dimethoxybenzophenone mediated intra- and intermolecular photodecarboxylation reactions involving phthalimides have been examined under microflow conditions. Conversion rates, isolated yields and chemoselectivities were compared to analogous reactions in a batch photoreactor. In all cases investigated, the microreactions gave superior results thus proving the superiority of mic...