Let Specie denote the set of prime ideals of a commutative ring with identity R, ordered by inclusion; and call a partially ordered set spectral if it is order isomorphic to Spec R for some R. What are some conditions, necessary or sufficient, for a partially ordered set X to be spectral? The most desirable answer would be the type of result that would allow one to stare at the diagram of a given X and then be able to say whether or not X is spectral. For example, it is known that finite partially ordered sets are spectral (see [2] or [5]).

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Fluid Dynamic Gauging (FDG) has been used to study cake fouling during cross-flow microfiltration of inactive Saccharomyces cerevisiae yeast suspensions through a 5 μm nominal pore size mixed cellulose ester membrane. Cake thickness was measured in-situ and in real-time during fouling, for which an initial growth rate of ca. 0.81 μm•s-1 was observed at TMP = 35 mbar and Re duct = 1000. The thickness increased asymptotically to a terminal value of 130 μm, limited by the FDG process. Although it influences the evolution of the cake thickness, FDG can nevertheless be used to perform strength tests on preformed cakes, by imposing controlled shear stresses to the surface and measuring the thickness following deformation. Cake deformation via incremental increases in shear stress demonstrated that the cake's resilience to tangential fluid shear was inversely proportional to its thickness. It was found that preformed cakes over 250 μm thick were deformed by shear stresses < 10 N•m-2 , indicating very loose cohesion between cells on the cake's surface. The range and accuracy of thickness measurements is subject to the strength of fouling layers and the operating conditions of the apparatus. Measures to enhance the technique's efficacy have been identified and are currently underway.

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