Integrated generic resource: Mathematical representation ISO 10303-51:2005(E)
© ISO

Cover page
Table of contents
Copyright
Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions and abbreviations

4 Mathematical context
   4.1 Introduction
   4.2 Fundamental concepts and assumptions
   4.3 Mathematical context type definitions
   4.4 Mathematical context entity definitions
5 Mathematical description of distribution
   5.1 Introduction
   5.2 Fundamental concepts and assumptions
   5.3 Mathematical description of distribution type definition
   5.4 Mathematical description of distribution entity definitions

A Short names of entities
B Information object registration
C Computer interpretable listings
D EXPRESS-G diagrams
Index

5 Mathematical description of distribution schema

The following Express declaration begins the mathematical_description_of_distribution_schema and identifies the necessary external references.

EXPRESS specification:

*)
SCHEMA mathematical_description_of_distribution_schema;

REFERENCE FROM mathematical_context_schema    --  ISO 10303-51
  (maths_space_context);

REFERENCE FROM mathematical_functions_schema    --  ISO 10303-50
  (maths_function);

REFERENCE FROM process_property_schema    --  ISO 10303-49
  (action_property,
   resource_property);

REFERENCE FROM product_property_definition_schema    --  ISO 10303-41
  (property_definition,
   general_property_relationship);

REFERENCE FROM support_resource_schema    --  ISO 10303-41
  (identifier,
   label,
   text);
(*

NOTE 1   The schemas referenced above are specified in the following part of ISO 10303:

mathematical_context_schema ISO 10303-51
mathematical_functions_schema ISO 10303-50
process_property_schema ISO 10303-49
product_property_definition_schema ISO 10303-41
support_resource_schema ISO 10303-41

NOTE 2   See Annex D for a graphical representation of this schema.

5.1 Introduction

The mathematical_description_of_distribution_schema specifies a mapping between a property distribution and a mathematical function. The mapping gives semantics to the mathematical function, so that the mathematical function describes or identifies the property distribution.

A property distribution can be with respect to:

EXAMPLE 1   The variation of power output with respect to:

is a property distribution.

EXAMPLE 2   The variation of temperature with respect to:

is a property distribution.

5.2 Fundamental concepts and assumptions

A property distribution is a physical function. The domain of a property distribution function can be: The range of a property distribution function is a physical quantity space.

A property distribution D:X->P, where:

can be described or identified by a mathematical function F:A->B, where A and B are mathematical spaces;

The description or identification depends upon:

The property distribution D is described or identified by the mathematical function F, if and only if: V(D(x)) = F(U(x)), for all x in X.

5.3 mathematical_description_of_distribution_schema type definition

5.3.1 property_distribution_select   EXPRESS-G

The property_distribution_select type is an extensible list of alternate data types. It provides a mechanism to refer to instances of the data types included in the property_distribution_select type or in its extensions.

NOTE  The list of entity data types will be extended in application resources that use the constructs of this resource.

EXPRESS specification:

*)
TYPE property_distribution_select = EXTENSIBLE SELECT
   (action_property,
    general_property_relationship,
    property_definition,
    resource_property);
END_TYPE;
(*

5.4 mathematical_description_of_distribution_schema entity definition

5.4.1 maths_space_context_relationship   EXPRESS-G

A maths_space_context_relationship is a relationship between two instances of maths_space_context.

EXPRESS specification:

*)
ENTITY maths_space_context_relationship;
  id : identifier;
  name : label;
  description : OPTIONAL text;
  relating_context : maths_space_context;
  related_context : maths_space_context;
END_ENTITY;
(*

Attribute definitions:

id: the identifier for the maths_space_context_relationship.

name: the label by which the maths_space_context_relationship is known.

description: the text that characterizes the maths_space_context_relationship. The value of this attribute need not be specified.

relating_context: the instance of maths_space_context that has a relationship with the related_context.

related_context: the instance of maths_space_context that has a relationship with the relating_context.

5.4.2 maths_space_context_relationship_description   EXPRESS-G

A maths_space_context_relationship_description is a specification that a maths_function defines the relationship between two instances of maths_space_context.

Let:

the relating maths_space_context be A:P->S1 ;

the related maths_space_context be B:P->S2;

P be a physical space;

S1 and S2 be two instances of maths_space;

the description of the relationship between the instances of maths_space_context be T:S1->S2 (a maths_function).

An instance of maths_space_context_relationship_description specifies that:

B(p) = T(A(p)) for each p in P.

EXPRESS specification:

*)
ENTITY maths_space_context_relationship_description;
  id : identifier;
  name : label;
  description : OPTIONAL text;
  described_relationship : maths_space_context_relationship;
  describing_relationship : maths_function;
END_ENTITY;
(*

Attribute definitions:

id: the identifier for the maths_space_context_relationship_description.

name: the label by which the maths_space_context_relationship_description is known.

description: the text that characterizes the maths_space_context_relationship_description. The value of this attribute need not be specified.

described_relationship: the maths_space_context_relationship_description that is described by the description.

describing_relationship: the maths_space_context_relationship that is described by the description.

5.4.3 normalized_property_distribution_description   EXPRESS-G

A normalized_property_distribution_description is a specification of how a maths_function describes a property distribution with respect to a reference property distribution.

Let:

An instance of normalized_property_distribution_description specifies that:

D(p) = F(A(p)).D0(p) for each p in P.

EXPRESS specification:

*)
ENTITY normalized_property_distribution_description;
  id : identifier;
  name : label;
  description : OPTIONAL text;
  abstract_function : maths_function;
  domain_context : maths_space_context;
  normalization_basis : property_distribution_select;
  physical_function : property_distribution_select;
END_ENTITY;
(*

Attribute definitions:

id: the identifier for the normalized_property_distribution_description.

name: the label by which the normalized_property_distribution_description is referenced.

description: the text that characterizes the normalized_property_distribution_description. The value of this attribute need not be specified.

abstract_function: the maths_function that describes the physical_function.

domain_context: the maths_space_context that is used to interpret the domain of the abstract_function.

normalization_basis: the reference property distribution that is the basis for the description of the physical_function.

NOTE    The physical_function equals the normalization_basis wherever the abstract_function evaluates to 1.

physical_function: the property distribution that is described by the physical_function.

5.4.4 property_distribution_description   EXPRESS-G

A property_distribution_description is a specificiation of how a maths_function describes a property distribution. Let:

D(p) = U-1(F(A(p))) for each p in P.

NOTE    U-1 is well defined because U is a 1-1 mapping.

EXPRESS specification:

*)
ENTITY property_distribution_description;
  id : identifier;
  name : label;
  description : OPTIONAL text;
  abstract_function : maths_function;
  domain_context : maths_space_context;
  physical_function : property_distribution_select;
  range_context : maths_space_context;
END_ENTITY;
(*

Attribute definitions:

id: the identifier for the property_distribution_description.

name: the label by which the property_distribution_description is known.

description: the text that characterizes the property_distribution_description. The value of this attribute need not be specified.

abstract_function: the maths_function that describes the physical_function.

domain_context: the maths_space_context that is used to interpret the domain of the abstract_function.

physical_function: the property distribution that is described by the abstract_function.

range_context: the maths_space_context that is used to interpret the range of the abstract_function.



*)
END_SCHEMA;  -- mathematical_description_of_distribution_schema
(*


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