Stationary subdivision

Finally we look at what can be achieved by changing the rules fundamentally, by considering non-stationary subdivision, in which the mask changes from step to step. In particular we consider geometry-sensitive schemes where the mask is itself determined locally and at every step from the geometry of the polygon. 

A.S.Cavaretta, W.Dahmen and C.A.Micchelli Stationary Subdivision. Memoirs of American Mathematical Society 453, 1991 I.Daubechies and J.C.Lagarias Two scale difference equations I. Existence and Global regularity of solutions. SIAM J.Math Anal 22(5) ppl388-1410, 1991... 

N. Dyn and D.Levin Stationary and Non-stationary subdivision schemes. pp209-216 in Mathematical methods in Computer Aided Geometric Design (eds Lyche and Schumaker), 1992... 

B. Jiittler, U.Schwaneke Analysis and Design of Hermite subdivision schemes. The Visual Computer 18, pp326-342, 2002 M.F.Hassan, I.P.Ivrissimtzis, N.A.Dodgson and M.A.Sabin An interpolating 4-point C2 ternary stationary subdivision scheme. CAGD 19(1), ppl-18, 2002... 

C.Beccari, G.Gasciola and L.Romani An interpolating 4-point C2 ternary non-stationary subdivision scheme with tension control. CAGD 23(4), pp210-219, 2007... 

S.Daniel and P.Shunmugaraj An approximating C2 non-stationary subdivision scheme. CAGD 26(7), pp810-821, 2009 N.Dyn, M.S.Floater and K.Hormann Four-point curve subdivision based on iterated chordal and centripetal parameterizations. CAGD 26(3), pp279-286, 2009... 

Gel-permeation chromatography (GPC) is a subdivision of size-exclusion chromatography (SEC), in which macromolecular species are separated from one another based on their size. As its name implies, GPC employs a gel (usually cross-linked polystyrene) as the stationary phase, with detection through either Ught-scattering or refractive index. 

Another important criterion is to determine whether the nodular transformation in the liver is complete or incomplete. This morphological characteristic can be found both in progressive and stationary cirrhoses. In complete cirrhosis, the parenchyma is completely partitioned by connective tissue septa. The collapse of fibres (due to portocentral bridging necroses) results in the development of portocentral septa (= passive septa). Due to the spreading of the inflammation to the periportal parenchyma, septa develop and branch out from the portal fields (= active septa). Generally, they lead to capillarization of the sinusoidal walls as well. (s. fig. 35.7) Incomplete cirrhosis only displays the formation of short septa (= subsepta), so that there are areas of incomplete (partial) subdivision of the parenchyma. 

The body of this book describes five major questions which we are now able to answer about an arbitrary uniform, stationary, symmetric subdivision scheme. In each case there are additional issues which are conveniently addressed in the same chapter. 

N. Dyn, D.Levin and A.Luzzato Non-stationary interpolatory subdivision schemes reproducing spaces of exponential polynomials. Found Comput Math, ppl97-206, 2003... 

The mobile phase is always liquid. The stationary phase is liquid or solid. Table 1 shows in detail this classification. There are two modifications of LSC normal phase (NP) and reversed-phase (RP), depending on the relative polarity of the two phases. The same is valid for LLC, but this subdivision is rarely... 

Thin-layer chromatography is a subdivision of liquid chromatography, in which the mobile phase is a liquid and the stationary phase is situated as a thin layer on the surface of a flat plate. TLC is sometimes grouped with paper chromatography under the term planar liquid chromatography because of the flat geometry of the paper or layer stationary phases. 

Catalytic reactors are continuous reactors more often than not. The main subdivision types include fluidized or fixed bed. Fixed bed types may be either tubular, bed, or multitray types. Fluidized bed types further break down into stationary or moving (recirculating) bed types and tubular (transfer tube) types. The catalyst is generally in powdered suspension and may be removed either in batches or continuously withdrawn and regenerated. In transfer tube types, the catalyst stays in suspension with the fluid flow through the tubes. 

Particulate material is ubiquitously distributed, partly because there are many sources. The concentration, particle size, and chemical characteristics of particulate material vary widely in both space and time. Distinctions are commonly drawn between occupational and environmental (or perhaps, more appropriately, nonoccupational) settings, with the latter subdivided into the outdoor (or ambient) versus indoor environment. For the ambient environment, a distinction is customarily made between stationary point sources (e.g., a factory or refinery) and mobile sources (e.g., automobiles and trucks). Roadways are line sources. The occupational environment also has subdivisions that can vary markedly in their particulate matter content, depending on the particular processes being carried out in different work areas. The document Air Quality Criteria for Particulate Material (23) is an excellent summary of information on sources and characteristics of particulate matter, with special reference to the United States. 

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