Synthetic zeolites and other microporous oxide molecular sieves

Use of synthetic zeolites and other microporous oxides since 1950 has improved insulated windows, automobile air-conditioning, refrigerators, air brakes on trucks, laundry detergents, etc. Their large internal pore volumes, molecular-size pores, regularity of crystal structures, and the diverse framework chemical compositions allow “tailoring” of structure and properties. Thus, highly active and selective catalysts as well as adsorbents and ion exchangers with high capacities and selectivities were developed. In the petroleum refining and petrochemical industries, zeolites have made possible cheaper and lead-free gasoline, higher performance and lower-cost synthetic fibers and plastics, and many improvements in process efficiency and quality and in performance. Zeolites also help protect the environment by improving energy efficiency, reducing automobile exhaust and other emissions, cleaning up hazardous wastes (including the Three Mile Island nuclear power plant and other radioactive wastes), and, as specially tailored desiccants, facilitating the substitution of new refrigerants for the ozone-depleting chlorofluorocarbons banned by the Montreal Protocol.

Randomness and degrees of irregularity.

The fundamental question "Are sequential data random?" arises in myriad contexts, often with severe data length constraints. Furthermore, there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness--e.g., to evaluate the efficacy of therapy in medicine. We address both these issues from a computable framework via a quantification of regularity. ApEn (approximate entropy), defining maximal randomness for sequences of arbitrary length, indicating the applicability to sequences as short as N = 5 points. An infinite sequence formulation of randomness is introduced that retains the operational (and computable) features of the finite case. In the infinite sequence setting, we indicate how the "foundational" definition of independence in probability theory, and the definition of normality in number theory, reduce to limit theorems without rates of convergence, from which we utilize ApEn to address rates of convergence (of a deficit from maximal randomness), refining the aforementioned concepts in a computationally essential manner. Representative applications among many are indicated to assess (i) random number generation output; (ii) well-shuffled arrangements; and (iii) (the quality of) bootstrap replicates.