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In this paper, we explore the exponential map and its inverse, the logarithm map, for the group SIM(n) of similarity transformations in ℝn which are the composition of a rotation, a translation and a uniform scaling. We give a formula for the exponential map and we prove that it is surjective. We give an explicit formula for the case of n = 3 and show how to efficiently compute the logarithmic map...
Recent progress in gold nanoparticle (Au NP) based systems in cancer imaging and therapeutic has motivated development of a liposome-based system to enhance delivery of smaller NPs to cells. Our studies have shown that liposomal delivery resulted in an enhancement in the cellular uptake of the small Au NPs. Real-time intracellular tracking of the AuNP-liposomes revealed an average speed of 12.48 ±...
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