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Unification of space-time-matter-energy
Sobczyk,Yarman 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.2
A complete description of space-time, matter and energy is given in terms of the conservation of energy-momentum in Einstein’s special the- ory of relativity. We derive explicit equations of motion for two falling bodies, based upon the principle that each body must subtract the mass- equivalent for any change in its kinetic energy that is incurred during the fall. In this theory, we …nd that there are no singularities and consequently no blackholes.
Purc, Anna,Koszarna, Beata,Iachina, Irina,Friese, Daniel H.,Tasior, Mariusz,Sobczyk, Krzysztof,Pę,dziń,ski, Tomasz,Brewer, Jonathan,Gryko, Daniel T. Royal Society of Chemistry 2017 ORGANIC CHEMISTRY FRONTIERS Vol.4 No.5
<▼1><P>Benzofuran has been proven to be the versatile substituent for tuning the optics of diketopyrrolopyrroles.</P></▼1><▼2><P>An in-depth investigation of the reaction of substituted salicylaldehydes with chloroacetonitrile led to the development of new conditions for the synthesis of 2-cyanobenzofurans. The crucial improvement lies in the use of phase-transfer catalysis in the second step, <I>i.e.</I>, intramolecular aldol type condensation. In a two-step process, the reactants were transformed into a library of 3,6-bis(benzofuran-2-yl)diketopyrrolopyrroles. We show that the presence of a methyl group in a position adjacent to the cyano functionality only slightly decreased the yield of diketopyrrolopyrroles (to 30–57%). An analysis of the relationship between the degree of polarization/planarization of aryl-diketopyrrolopyrroles and their one- and two-photon spectroscopic properties is reported. Careful design of the desired dyes and enhanced control of their ability to assume a planar molecular structure resulted in interesting photophysical properties, such as absorption and emission in the so-called biological window. Despite having less promising linear spectroscopic properties, the deplanarized molecules possess pretty strong two-photon absorbing properties. Placing methyl groups at adjacent positions to the linkage between benzofuran and the DPP core caused the formation of yellow-emitting dyes with almost quantitative fluorescence quantum yield, moderate Stokes shift and reasonable two-photon absorption cross-sections.</P></▼2>