The detection limit is one of the most important performance parameters for bioanalytical techniques. Here we present a generic method to estimate the detection limit of biomolecular assays based on a step-by-step analysis of the assay procedure. Enzyme-linked immunosorbent assay (ELISA) is used here as an example; however, much of the information presented in this article may be applied to other types of biomolecular assays and analytical techniques. A clear understanding of what affects the detection limit can help researchers to evaluate different bio-analytical techniques properly, and to design better strategies to optimize and achieve the best analytical performance.

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The growth kinetics and mechanism of a gold nanoparticle synthesis using water as a single phase solvent and oleylamine as both reducing agent and monolayer protection agent were studied. FT-IR and 1H NMR spectroscopic analysis revealed a conversion of oleylamine ligands to oleylamides when gold(III) was reduced to gold(I) and gold atoms. During the reaction, it was found by UV-Vis absorption spectroscopy and transmission electron microscopic study that oleylamine ligands formed large complex aggregates with gold salt instantly upon mixing these two agents together. At an elevated temperature of 80 degrees C, the complex decomposed first into very small particles and then the small particles recombined together into larger and thermally stable particles with an average core size around 9-10 nm. The oleylamide ligands formed a protecting monolayer around the nanoparticles through a hydrogen bonding network between the amide groups. The recombination of small particles into larger ones was found to follow a logistic model, as confirmed by a nonlinear regression fitting of the UV-Vis absorption data of the reaction solution with the mathematical model.

Elements of a finite field, GF ð2 m Þ, are represented as elements in a ring in which multiplication is more time efficient. This leads to faster multipliers with a modest increase in the number of XOR and AND gates needed to construct the multiplier. Such multipliers are used in error control coding and cryptography. We consider rings modulo trinomials and 4-term polynomials. In each case, we show that our multiplier is faster than multipliers over elements in a finite field defined by irreducible pentanomials. These results are especially significant in the field of elliptic curve cryptography, where pentanomials are used to define finite fields. Finally, an efficient systolic implementation of a multiplier for elements in a ring defined by x n þ x þ 1 is presented.

Nanoparticle growth in solution is a rather complicated process governed by many thermodynamic and kinetics factors. A better understanding of nanoparticle growth kinetics is of primary importance leading to a better control on the nanoparticle size and size distribution. In this work we conducted both experimental and theoretical study on the kinetics of Brust-Schiffrin reaction for the synthesis of gold nanoparticles. Using an excessive amount of thiol ligands, the nanoparticle growth was stopped at different intermediate stages. Our study revealed and confirmed that the reproducibility of Brust-Schiffrin reaction for the synthesis of gold nanoparticles with diameters around 2 nm is rather poor due to the intrinsic complexity of this two-phase reaction. The analysis results of each intermediate product by TEM showed that nanoparticles grew very rapidly at the early stage of reaction and reached a maximum value of 2.6 nm at reaction time of around 10 minutes. Further increase of reaction time led to a decrease of nanoparticle size. In addition to the experimental study, we proposed a kinetic model for nanoparticle growth in solution by assuming that the nanoparticle core expands through incremental addition of gold atoms to the existing nanoparticle nuclei. This model not only gave a relatively good fitting to the experimental data, but also provided further insight into the nucleation and core expansion stage of the nanoparticle growth, which had not been revealed in previous modeling studies.