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Keywords
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.
Commercial materials with polyvinylpolypyrrolidone and polymeric amberlites (XAD7HP, XAD16) are commonly used for the adsorptive downstream processing of polyphenols from renewable resources. In this study, beta-zeolite-based adsorbent systems were examined, and their properties were compared to organic resins. Batch adsorption experiments were conducted with synthetic solutions of major polyphenols. Adsorption isotherms and desorption characteristics of individual adsorbent were determined based on these results. Maximum adsorption capacities were calculated using the Langmuir model. For example, the zeolites had capacities up to 203.2 mg/g for ferulic acid. To extend these results to a complex system, additional experiments were performed on rapeseed meal and wheat seed extracts as representative renewable resources. HPLC analysis showed that with 7.5% w/v, which is regarded as the optimum amount of zeolites, zeolites A and B could bind 100% of the major polyphenols as well as release polyphenols at high yields. Additionally, regeneration experiments were performed with isopropyl alcohol at 99°C to evaluate how zeolites regenerate under mild conditions. The results showed only a negligible loss of adsorption capacity and no loss of desorption capacity. In summary, it was concluded that beta-zeolites were promising adsorbents for developing new processes to isolate polyphenols from renewable resources.