Diagram map

The simplest form of ternary RCM, as exemplified for the ideal normal-paraffin system of pentane-hexane-heptane, is illustrated in Fig. 13-58 7, using a right-triangle diagram. Maps for all other non-azeotropic ternary mixtures are qiiahtatively similar. Each of the infinite number of possible residue curves originates at the pentane vertex, travels toward and then away from the hexane vertex, and terminates at the heptane vertex. 

In chemistry, a Pourbaix diagram, also known as a potential/pH diagram, maps out the possible stable (equilibrium) phases of an aqueous electrochemical system. Predominant ion boundaries are represented by lines. As such, a Pourbaix diagram can be read much like a standard phase diagram with... 

Single-component phase diagram -> Map showing the most stable phase of a substance at... 

The many corrosion equilibria involving iron can be conveniently summarized in an equilibrium or Pourbaix diagram (15). These diagrams map regions of stability for various ionic and solid species as functions of pH and on the basis of equilibrium potentials. A simplified equilibrium diagram is shown in Figure 2. At sufficiently negative potential, iron is thermodynamically stable, and corrosion cannot occur. The domain of stability of water is defined by the dashed lines a and b below a,... 

We remark that for a fixed trisp A, the diagrams of objects of any fixed category over A, together with diagram maps form a category. 

It is now time to formalize an important property of homotopy colimits their flexibility with respect to homotopy type. It turns out that if the topological spaces in a diagram are replaced by homotopy equivalent ones in a coherent way (as a diagram map), then the homotopy type of the homotopy colimit... 

Remark 15.13. It may be worthwhile to explicitly mention the following special case when all the spaces v) in the diagram are contractible, then we have a diagram map from V to the point diagram defined in Example 15.9(0). It follows by Theorem 15.12 that the homotopy colimit of our diagram is homotopy equivalent to the base trisp, with the homotopy equivalence given by Pfc. 

Proof of nerve lemma. Let T> be the nerve diagram of tl, and let D be the trivial diagram over BdA/"(W), i.e., all associated spaces are points. Consider the unique diagram map X -.V V. Since all maps X cr) for a Af(U) are homotopy equivalences, we can conclude by the homotopy lemma that also the map hocolimX hocolimP — hocolimH is a homotopy equivalence. 

Strahler, Alan. Introducing Physical Geography. 5th ed. Hoboken, N.J. John Wiley Sons, 2010. An excellent textbook with very useful diagrams, maps, and color photos that cover many aspects of hydrology and stream flow. 

Figure 2.6 Bed behavior diagram. Mapping of bed behavior regimes for different operation conditions. (Henein, 1980.)...

The planet flirted with freezing over a few times, tipping into an ice-covered snowball at least twice, but both times it recovered and warmed up again. Earth has not left the liquid island on the phase diagram map for billions of years. 

Graphs are often used in chemistry because on a simple level they provide an instant visual representation of data. Visual learners make up tbe majority of tbe population and they absorb and recall information most effectively by seeing. Visual learners relate best to written information, notes, diagrams, maps and graphs. However, graphs are not just visual representations of the physical world - they are powerful tools that can be used to establish numerical relationships, determine physical quantities and make predictions. 

Refer to Figure 6.3, Basic Six Sigma Process Model Aligned to SMS diagram mapped to a successful safety management system. 

The hydrogen ion concentration - expressed by pH - is an important parameter for calculating electrochemical equilibrium potentials. The Pourbaix diagram maps in a clear way the influence of the pH value on complicated electrochemical equilibria. The diagram form, which is named after the Belgian corrosion researcher Marcel Pourbaix, was developed in the 1940s. 

The phase diagram tells us only what phases can exist in equilibrimn. The final micro-structure is controlled by the rate of transformation. A sketch of a typical isothermal time-temperature-transformation (often called a T-T-T diagram) map for the austenitic to ferritic transformation is shown in Figure 14.3. 

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