Back to foundations

But in practical calculations, we never have the complete set at our disposal. We always need to limit it to a certain finite number of functions, and it does not represent any complete set. Depending on our computational resources, we limit the number of functions. We usually try to squeeze the best results from our time and money. How do we do it We apply our physical intuition to the problem, believing that it will pay off. First of all, intuition suggests the use of functions for some atom which is present in the molecule, and not those of the harmonic oscillator, or the hydrogen or uranium atom, which are absent from our molecule. And here we meet another problem. Which atom, because we have Na, C and O in Na2C03. It appears that 

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That was part of the dream to which I woke the morning I was to write this welcome to readers. I connected the dream with the way my friend David Gingell came to learn about van der Waals forces 30 years ago. He began immediately by computing with previously written programs, then improved these programs to ask better questions, and finally worked back to foundations otherwise inaccessible to a zoologist. 

The discovery that usehil chemicals could be made from coal tar provided the foundation upon which the modem chemical industry is built. Industrial chemistry expanded rapidly in the late nineteenth century in German laboratories and factories where coal-tar chemicals were refined and used in synthesis of dyes and pharmaceuticals. But coal-tar production has an eadier origin, dating back to the discovery by William Murdock in 1792 that heating coal in the absence of air generated a gas suitable for lighting. Murdock commercialized this technology, and by 1812 the streets of London were illuminated with coal gas (1). 

The origins of lean manufacturing are often ascribed to the creation of the Toyota Production System (TPS) by the Toyota Motor Corporation. However, the history of lean manufacturing can be traced back to industrial developments which occurred more than 150 years before TPS. The foundation for modern manufacturing was laid by Eli Whitney in 1798 while Whitney is best known for his invention of the cotton gin, it is his invention of interchangeable parts and uniform production which revolutionized mass production (www.EliWhitney.org). 

However, this statement deserves to be examined much more closely. The absolute certainty of an overkill heating process is diminished considerably when the product is not heated or not given sufficient heat to sterilize the container. In addition, there is inevitable manipulation involved before the container is sealed. This uncertainty has resulted in a discussion of the acceptable element of risk in an aseptic process. Unfortunately, this risk cannot be measured directly and various guess factors have been vectored into the discussion, all without scientific foundation. Going back to fundamentals, it is necessary to remind oneself that there are no degrees of sterility—a product is either sterile or it is not. 

Scientific and engineering investigations into the properties and behavior of particulate solids date back to the early work of Coulomb, who in 1776 developed a theory on soil pressure and resistance, thus laying sound foundations for important engineering... 

Thus in turbulent flow, the dispersion coefficient is independent of the diffusion coefficient, but in laminar flow, the dispersion coefficient depends inversely on the diffusion coefficient. This counterintuitive inverse dependence, the result of axial convection coupled with radial diffusion, is the foundation of the Goulay equation describing peak spreading in chromatography. We now return from this dispersion tangent back to diffusion and in particular, to mass transfer. 

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