MODEL syntax

There are two notations for formal models. One is the diagrammatic form which appears in model views. This is a restricted subset of a standard entity-relationship (E-R) model syntax. The other is a textual form, the syntax for which is discussed in 3.5. 

MATLAB is object-oriented. Linear time-invariant (LTI) models are handled as objects. Functions use these objects as arguments. In classical control, LTI objects include transfer functions in polynomial form or in pole-zero form. The LTI-oriented syntax allows us to better organize our problem solving we no longer have to work with individual polynomials that we can only identify as numerators and denominators. 

The subject of these notes might be described as "abstract flowcharts" - the study of mathematical models for programs and flowcharts, and of the interrelation between the syntax of programs (what can be said about their behavior from their very format) and the semantics (interpretations and the functions computed under varying interpretations) and the application of formal proof systems to verify properties of programs. 

II. PROGRAM SCHEMES - BASIC DEFINITIONS AND CONCEPTS A. SYNTAX - IHE MODEL... 

Now we have defined the syntax of our model - how a scheme is formally put together - we must define the semantics - how a function is computed under an interpretation. Interpretations are defined as for ordinary program schemes or for recursion schemes - the defined functions are not interpreted. 

Following the above observations, the process model can be formulated by TA. For formal definitions of the syntax and semantics of TA, see [15]. TA are used to model the individual resources by resource automata and to describe timing constraints by place automata. The former are used to start and to finish tasks which are uniquely assigned to resources, the latter establish timing constraints of places. 

Stereotypes can be used on an individual model element as an alternative syntax to apply a framework (similar to Section 9.6.2, Template as Generic Types and Classes). The shorthand rules are as follows. 

The Object Constraint Language (OCL), a standard part of UML 1.1, is a specification language used in conjunction with UML models. It is an expression-based, side-effect-free language that eschews mathematical symbols (V, 3, and so on) for textual equivalents (forAII, exists). It uses a syntax more usual in object-oriented languages V x T, p(x) becomes T->forAII (x x.p). 

OCL uses a Smalltalk-based block syntax to allow you to define some kinds of functions conveniently and inline, but it does not provide corresponding type rules for this based on generic types. For our discussion here, we treat blocks as first-class functions and use the syntax (T1 X T2 X T3 -> T ) for such a function. This is purely a syntactic convenience functions can be modeled as objects. Any function f (a,b) c can be described as an object with a single method eval (a, b) c. Thus,... 

Catalysis uses model frameworks for extensibility stereotypes are only one special (and limited) syntax for applying a framework. 

This part discusses the syntax of models with device tolerance and how to use the models in a simulation. This part does not discuss how to easily create models within Capture. After you have understood the syntax for the models and how to run the simulations, you may wish to look at Part 7 to see how to create new models to specify the tolerance you need. 

Each vendor of SPICE simulation software has added features such as Monte Carlo analysis, schematic entry, and post simulation waveform processing, as well as extensive model libraries. In most cases, the manufacturers have modified the algorithms for controlling convergence and have added new parameters or syntax for component models. As a result, each electronic design automaton (EDA) tool vendor has the basic Berkeley SPICE 2 features and a unique set of capabilities and performance enhancements. 

Users can create their own models, but most of the time they will depend on the model libraries provided by a vendor. The library models that do not use pure Berkeley SPICE 2G.6 syntax are unique to that particular simulator. While the SPICE syntaxes of each product are similar, they are not exactly compatible both distinct and subtle differences exist. However, in many cases, most models in vendors libraries have been provided by the component manufacturers. These models are available for free on the Internet. 

For kinetic modeling in PHREEQC two keywords are necessary KINETICS n (n = number of SOLUTION, for which the kinetics shall be calculated) and RATES. For both keywords, a rate name has to be entered, e g. calcite when the dissolution of calcite shall be kinetically modeled. The general syntax within the keyword KINETICS is as shown in Table 25. 

The major requirement to simulate an ODE-based model using Matlab (or most other packages) is to supply a code that computes the time derivatives of the state variables - the right-hand side of Equations (3.27). An example of a function that computes the time derivatives for this model using Matlab syntax is given below.2... 

The syntax of K identifies the elements of any subclass modeling element (e.g., K dioai-cusproportionation)- These are elements (inputs) (enabling-conditions) (ab-initio-operator) (output). Each of these is defined by simpler entities, as shown above. (The decomposition of (ab-initio-operator) was given in the previous section.)... 

A variable events is defined whose value in each round is the current set of events at the user interface. Everything that is input in one round at one access point is regarded as one value. Hence events never contains more than one input per access point. Similarly, only values from the correct domains, as far as these domains are known statically, will appear in events. Hence such syntax checks are not modeled explicitly in the requirements. 

As defined in Subsect. 2.1.2, a document is an aggregation of data and acts as a carrier of product data in a certain work context. One possibility to represent models of document contents is the use of the extensible Markup Language (XML) [1060] and its Document Type Definitions (DTDs), as suggested by Bayer and Marquardt [19]. Within a DTD, the structure of a specific document type can be described. Figure 2.9 shows the (incomplete) DTD of a specification sheet for vessels. Here, the different data items like temperature or construction material are indicated to specify the piece of equipment. However, the expressiveness of such document type definitions is rather restricted. A DTD specifies only the syntax of the document content but not its semantics. One possibility to enrich the DTD with meaning is to relate the single DTD elements to the classes and attributes of a product data model. This is exemplarily shown Fig. 2.9, where relations between some DTD elements and the corresponding classes of the product data model CLiP (cf. Subsect. 2.2.3) are indicated. 

The abstract syntax of collaboration diagrams is defined by the graph schema shown in Fig. 5.67, which will be explained later. A formal definition of the abstract syntax, again, enables the modeling environment to guarantee (syntactical) correctness and completeness with respect to context-free as well as context-sensitive conditions, such as tjrpe conformity of actual and formal parameters to facilitate the generation of executable code. 

Concerning the implementation aspects of FireS, we will concentrate on modeling the dynamic behavior. The graph schema shown in Fig. 5.67 defines the abstract syntax for the collaboration diagrams used in phase 4. It is an extension of the formerly introduced graph schema of Fig. 5.60, which serves as meta model for defining the static data model in phase 3. 

Common features among the three different classes of models and their implementation within the S-Plus environment come into light during the analysis of the examples in particular, the syntax for defining the fixed and random effects in the models, as well as methods for extracting estimates from fitted objects. All data sets discussed in this chapter are fictitious that is, they are generated by simulation. The reader is encouraged to experiment with the code provided in Appendix 4.1 to explore alternative scenarios. 

Closely related to the latter is declarative programming that describes states rather than how to achieve them. Additionally, the syntax is modeled after the way humans describe a state and thus is more declarative than other languages. 

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