Plant topology

The decisions should be taken in an optimal fashion subject to the plant topology and the processing constraints with the objective to maximize the profit, given as the difference of revenues for products and costs for the production. The demands are specified by their amounts and their due dates, where the revenues decrease with increasing lateness of the demand satisfaction. The production costs consist of fixed costs for each batch and for the start-up- and shut-down-procedures of the finishing lines, and variable costs for the product inventory. 

In order to illustrate the approach, a case study is considered. The case study is a multi-stage multiproduct chemical batch plant demonstrator with a plant topology similar to flexible flow shops. Two recipes to produce the end-products are given. The end-products blue (B) and green (G) are produced from three raw materials, yellow (Y), red (R) and white (W). Each batch of the product results from two batches of the raw materials. The production process considered is two batches of material Y and W reacts to produce one batch of B similarly two batches of R and... 

The optimal plant topology as well as the associated design for all equipment and connectivity required. 

The transfer function matrices, F j and s, are generated for the complete flowsheet. This involves computing the frequency response of each component part, and recombining the component parts, as dictated by the plant topology. 

The plant topology as a hierarchy of production resources and devices involved within these production resources ... 

Resource. Production resources are entities involved in production that provide functions to production processes. Resources include both hardware (e.g., robots, conveyors, machines) and software entities (SCADA systems), and are typically organized hierarchically into a plant topology. The properties of production resources are mostly their function capabilities (e.g., welding, transporting, and filing), mechanical information, electrical infOTmation, and control-related information in addition, further technical infonnation can be specified. 

The InstanceHierarchy contains the plant topology, comprising the definition of a specific equipment for an actual project— the instance data. Therefore, all project participants can refer to the instance hierarchy to define the context for their work tasks and results. The instance hierarchy contains all data including attributes, interfaces, role classes, relations, and references. 

The structures of many different plant, insect, and animal spherical viruses have now been determined to high resolution, and in most of them the subunit structures have the same jelly roll topology. However, a very different fold of the subunit was found in bacteriophage MS2, whose structure was determined to 3 A resolution by Karin Valegard in the laboratory of Lars Liljas, Uppsala. 

If the plant engineer is a specialist in anything, it is in his/her own plant or facility. Plant engineers must learn to know their own plants thoroughly, from the geology underlying its foundations and the topology of the rainwater runoff to the distribution of its electricity and the eccentricities of its production machinery. They must ensure the quality of the environment both inside... 

An arbitrary endpoint can also be marked as "root". A tree with a root will be called a planted tree the vertices different from the root are nodes. If no root is marked, the tree is called an unrooted or free tree. From a topological point of view, two trees with the same structure are identical the exact definition of this and some similar, less familiar notions, will be discussed in Sections 34-35. In the sequel, we use the following notations ... 

T number of topologically different planted trees with n nodes. 

Let t x) be the generating function of the topologically different planted trees. 

The series (2) of Sec. 3, too, is a generating function the collection of figures comprises the planted trees which are topologically different. The nodes of the rooted trees play the role of the balls in the figure there is only one category of balls, and thus the series depends only on one variable. Figure 1 indicates how the figures (planted trees) of the same content (number of nodes) are combined in the coefficients. 

Pursuing this correspondence between a C-H graph and the corresponding C-graph we find a new interpretation of the numbers p and R p is the number of topologically different free C-trecs with n vertices, R is the number of planted C-trees with n nodes. In other words ... 

We examine the planted C-H trees with n vertices of degree 4 the number of topologically different trees is of spatially different trees 5 , and of two-dimensionally different trees P. The... 

If the principal node K is an endpoint, the planted tree consists of a , the root and the stem, which connects these two points. There are no vertices of degree 4, there are no principal branches. There are no two noncongruent planted trees of this type, whether we deal with topological, spatial, or planar congruence. Hence... 

According to the nature of the congruence, topological, spatial, or planar, the generating functions of the planted C-H trees are given by... 

Again, we are dealing with planted C-H trees with n vertices of degree 4. We restrict our attention to topologically different ones with exactly a asymmetric points let denote their number. Obviously, the relation... 

Now we turn to arbitrary planted trees with a total of n nodes denotes the number of topologically different trees, the... 

The number of topologically different planted C-trees with n nodes is 1), as we have noted in Sec. 37. It is easy to see that... 

A relationship between the numbers A and corresponds to the similarity of the two equations (2.36) and ( ) [of (2.37) and (1 )]. Choose a topological planted tree counted by with n nodes of the same species. Then label these n nodes individually. The resulting... 

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