THREE HUNDRED YEARS OF THE ST. PETERSBURG PARADOX

The St. Petersburg Paradox was first presented by Nicholas Bernoulli in 1713. It is related to a gambling game whose mathematical expected payoff is infinite, but no reasonable person would pay more than $25 to play it. In the history, a number of ideas in different areas have been developed to solve this paradox, and this report will mainly focus on mathematical perspective of this paradox. Different ideas and papers will be reviewed, including both classical ones of 18th and 19th century and some latest developments. Each model will be evaluated by simulation using Mathematica.

ELECTROCATALYTIC PROCESSING OF RENEWABLE BIOMASS-DERIVED COMPOUNDS FOR PRODUCTION OF CHEMICALS, FUELS AND ELECTRICITY

The dual problems of sustaining the fast growth of human society and preserving the environment for future generations urge us to shift our focus from exploiting fossil oils to researching and developing more affordable, reliable and clean energy sources. Human beings had a long history that depended on meeting our energy demands with plant biomass, and the modern biorefinery technologies realize the effective conversion of biomass to production of transportation fuels, bulk and fine chemicals so to alleviate our reliance on fossil fuel resources of declining supply. With the aim of replacing as much non-renewable carbon from fossil oils with renewable carbon from biomass as possible, innovative R&D activities must strive to enhance the current biorefinery process and secure our energy future. Much of my Ph.D. research effort is centered on the study of electrocatalytic conversion of biomass-derived compounds to produce value-added chemicals, biofuels and electrical energy on model electrocatalysts in AEM/PEM-based continuous flow electrolysis cell and fuel cell reactors. High electricity generation performance was obtained when glycerol or crude glycerol was employed as fuels in AEMFCs. The study on selective electrocatalytic oxidation of glycerol shows an electrode potential-regulated product distribution where tartronate and mesoxalate can be selectively produced with electrode potential switch. This finding then led to the development of AEMFCs with selective production of valuable tartronate or mesoxalate with high selectivity and yield and cogeneration of electricity. Reaction mechanisms of electrocatalytic oxidation of ethylene glycol and 1,2-propanediol were further elucidated by means of an on-line sample collection technique and DFT modeling. Besides electro-oxidation of biorenewable alcohols to chemicals and electricity, electrocatalytic reduction of keto acids (e.g. levulinic acid) was also studied for upgrading biomass-based feedstock to biofuels while achieving renewable electricity storage. Meanwhile, ORR that is often coupled in AEMFCs on the cathode was investigated on non-PGM electrocatalyst with comparable activity to commercial Pt/C. The electro-biorefinery process could be coupled with traditional biorefinery operation and will play a significant role in our energy and chemical landscape.