Static Invariants

Static invariants are detailed in Section 2.5 precise action specification is discussed in Section 3.4. 

Not all combinations of attributes values are legal. Section 2.5 introduces static invariants as a way of describing integrity constraints on the values of attributes, shows some common uses of such invariants, and outlines how these invariants appear in the business domain as well as in code. 

The limitation of snapshots is that they show particular sample situations we want to describe the effect an action has in all possible situations. We can do that by writing postconditions—informal statements or formal expressions that define the effect of an action, using—the same navigation style as invariants in Section 2.5, Static Invariants. For example ... 

A static invariant is implicitly anded to the precondition and the postcondition of every action within a defined range of actions. In the simplest case, the range of an invariant... 

A static invariant is expected to hold before and after the actions in its range. Sometimes, an effect is required to be true of all the actions in its range. For example, suppose we want to count every operation invocation on our calendar. An effect invariant defines an effect that is invariant across all actions in its range and is implicitly anded to the postconditions... 

We saw in Section 3.5, Actions with Invariants, that invariants are implicitly conjoined with action specifications. Static invariants factor those constraints that apply to every state, and effect invariants capture rules about every state change. Both of them simplify action specs by making them fess redundant. 

Specifically, parameterized attributes are constrained by static invariants. In contrast, any operation is defined by its pre- and postcondition (see Section 3.1.2, Pie- and Postconditions Specify Actions) a read-only operation would have a postcondition that defined the returned value in terms of the inputs and current state. 

Static invariant Whatever happens, this must be tme afterward. 

You can write in the bottom section of the box an invariant that applies to all the external actions. A static invariant would be anded with all their pre- and postconditions an effect invariant would be anded with all postconditions. This approach is useful for expressing some rule that is always observed when nothing is going on inside the collaboration but that is not observed by the collaborators between themselves. An open collaboration typically cannot list external actions explicitly, because they are usually unknown. Instead, you can use an effect invariant to constrain every external action to conform to specific rules. For example, the external effect invariant in Figure 4.18 states. 

Existing batch-mode systems Often, late-night COBOL batch jobs encode critical sets of business rules. Mary of these mles can be captured as time-dependent static invariants on the type model (the batch job cuts in to make sure that no objects will be in violation of these invariants, come sunrise) or as effect invariants, of the form Whenever this thing has changed, that other thing must be triggered. ... 

The intent is to flush out useful constraints. You encounter this pattern when building a static type model (as part of a business model or component spec) it helps you to capture static invariants. 

A static invariant is a condition that should always be true, at least between the executions of any action that forms part of the same model. As a Boolean, it is composed of comparisons between pairs of objects. They might be < or = comparisons between numbers or other scalars or more-complex comparisons defined over more-substantial types or identity comparisons (whether one object is the same object as another). 

Many time-triggered actions are better specified as static invariants initially inv System — there must never be any expired reservation in the system, or, inv Reservation — cannot ever be expired... 

Catalysis static invariants (this constraint between these attributes is always hue) and dynamic invariants (any action that causes such-and-such must also cause so-and-so) let us succinctly capture most business rules. 

RPA, and CPHF. Time-dependent Hartree-Fock (TDFIF) is the Flartree-Fock approximation for the time-dependent Schrodinger equation. CPFIF stands for coupled perturbed Flartree-Fock. The random-phase approximation (RPA) is also an equivalent formulation. There have also been time-dependent MCSCF formulations using the time-dependent gauge invariant approach (TDGI) that is equivalent to multiconfiguration RPA. All of the time-dependent methods go to the static calculation results in the v = 0 limit. 

The second method of improving the power factor of an installation is to provide static capacitor banks. These can be installed as a single block at the point of supply busbar, as a set of switchable banks or as individual units connected to specific loads. For an installation where no synchronous machines are installed for other purposes (i.e. as prime movers or generators) then static capacitor banks are almost invariably the most cost-effective way of improving the power factor. 

The models of Chapter 9 contain at least one empirical parameter. This parameter is used to account for complex flow fields that are not deterministic, time-invariant, and calculable. We are specifically concerned with packed-bed reactors, turbulent-flow reactors, and static mixers (also known as motionless mixers). We begin with packed-bed reactors because they are ubiquitous within the petrochemical industry and because their mathematical treatment closely parallels that of the laminar flow reactors in Chapter 8. 

As mentioned above, the backbone of the controller is the identified LTI part of Wiener model and the inverse of static nonlinear part just plays the role of converting the original output and reference of process to their linear counterpart. By doing so, the designed controller will try to make the linear counterpart of output follow that of reference. What should be advanced is, therefore, to obtain the linear input/output data-based prediction model, which is obtained by subspace identification. Let us consider the following state space model that can describe a general linear time invariant system ... 

A well-substantiated correlation for air-water systems taken from the trickle bed literature (Morsi and Charpentier, 1981) was used for the volumetric mass transfer coefficients in the / , and (Rewap)i terms in the model. The hi term was taken from a correlation of Kirillov et al. (1983), while the liquid hold-up term a, in Eqs. (70), (71), (74), (77), and (79) were estimated from a hold-up model of Specchia and Baldi (1977). All of these correlations require the pressure drop per unit bed length. The correlation of Rao and Drinkenburg (1985) was employed for this purpose. Liquid static hold-up was assumed invariate and a literature value was used. Gas hold-up was obtained by difference using the bed porosity. 

Whereas the static probability distribution was invariant under time reversal, Eq. (153), the actual steady-state probability satisfies... 

Other synonyms for steady state are time-invariant, static, or stationary. These terms refer to a process in which the values of the dependent variables remain constant with respect to time. Unsteady state processes are also called nonsteady state, transient, or dynamic and represent the situation when the process-dependent variables change with time. A typical example of an unsteady state process is the operation of a batch distillation column, which would exhibit a time-varying product composition. A transient model reduces to a steady state model when d/dt = 0. Most optimization problems treated in this book are based on steady state models. Optimization problems involving dynamic models usually pertain to optimal control or real-time optimization problems (see Chapter 16)... 

Chapter 2, Static Models Object Attributes and Invariants, describes how attributes abstract variations in the implementation of object state. Chapter 3, Behavior Models Object Types and Operations, describes how operation specifications describe externally visible behavior of an object, independently of algorithmic and representation decisions. 

The static part deals with the information we have about the state of an object at ary given moment. At a given level of time granularity, we describe static attributes, relationships, and constraints between objects. Chapter 2, Static Models Object Attributes and Invariants, is about modeling static aspects using abstract attributes. 

The static model of an object s internal state and of information exchanged in the operation requests, using attributes, associations, and invariants... 

Because collaborations explicitly separate external from internal actions, you can now define invariants—static as well as effect invariants—that range over different sets of actions. There are two useful cases ranging only over external actions (internal ones are excluded and need not maintain these invariants) and ranging over all actions, both internal and external. 

Invariant To impose a static constraint on every action s postcondition makes specs more succinct and natural. 

Facts and rules Statements involving the names—definitions of them (such as constant or type or class definitions) and constraints (such as invariants, pre- and postconditions, and cardinalities of associations). Facts can be stated pictorially—in the forms of all the static type models, action diagrams, and state charts that we have been discussing—or in text. 

The general rules are the same as those discussed in Chapter 6, Abstraction, Refinement, and Testing. In this case, the static models are the same the only thing we have to worry about is that invariant in the Requirement. 

You should end up with a model showing the types of main interest. They should have static associations and attributes, and they should have action links showing how they interact. The model consists of diagrams, invariants, and a dictionary (see Chapter 5, Effective Documentation). You should be able to describe any significant business event or activity entirely in terms of the model. 

There are useful mles of thumb for finding objects, attributes, and actions. Looking through existing documents (business requirements, user manuals, and so on), map nouns to object types, verbs to actions, static relationships to associations, rules to static and dynamic invariants, and variations to subtypes or other refinements. 

After a reasonable (although still imperfect) model is drafted, hold workshops for the experts to review it. Take these in stages static model first then actions then invariants and use case specs. Use snapshots to communicate the intent of the model. 

Mary invariants can be constructed when there is a loop2 in the static type model two different ways of coming at items of the same type. For example, a Library s books can be lent only to its own members. We could write... 

---