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Algorithm Knowledge Graph Ontology

This version:
https://mardi4nfdi.de/mathalgodb/0.1
Revision:
0.1
Authors:
Aurela Shehu (https://orcid.org/0000-0002-1994-0612), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
Björn Schembera (https://orcid.org/0000-0003-2860-6621), Universität Stuttgart (https://ror.org/04vnq7t77, https://isni.org/isni/0000000419369713)
Burkhard Schmidt (https://orcid.org/0000-0002-9658-499X), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
Christian Himpe (https://orcid.org/0000-0003-2194-6754)
Christine Biedinger (https://orcid.org/0009-0002-5082-8386), Fraunhofer Institute for Industrial Mathematics ITWM (https://ror.org/019hjw009)
Frank Wübbeling (https://orcid.org/0000-0002-2375-2008)
Hendrik Kleikamp (https://orcid.org/0000-0003-1264-5941)
Jochen Fiedler (https://orcid.org/0000-0002-9176-780X), Fraunhofer Institute for Industrial Mathematics ITWM (https://ror.org/019hjw009)
Marco Reidelbach (https://orcid.org/0000-0002-1919-1834), Zuse Institute Berlin (https://ror.org/02eva5865, https://isni.org/isni/000000011010926X)
René Fritze (https://orcid.org/0000-0002-9548-2238)
Stephan Rave (https://orcid.org/0000-0003-0439-7212)
Thomas Koprucki (https://orcid.org/0000-0001-6235-9412), Weierstrass Institute Berlin for Applied Analysis and Stochastics (https://ror.org/00h1x4t21, https://isni.org/isni/000000010066936X)
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License:
https://creativecommons.org/licenses/by/4.0
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Cite as:
MaRDI Task Area 2 - Scientific Computing @ University of Münster. MathAlgoDB - Algorithm Knowledge Graph - Ontology (Version 0.1). MaRDI (Mathematical Research Data Initiative), 2022. https://mardi4nfdi.de/mathalgodb/0.1
Provenance of this page
Draft

Abstract

This vocabulary and grammar defines which types of objects are admissible to the MathAlgoDB - the algorithm knowledge graph - and by which properties they can relate. All in all five classes, "problem", "algorithm", "benchmark", "software", "publication", are defined, as well as a minimal but intuitively intelligible number of properties. As opposed to the more liberal WikiData, MathAlgoDB relies on the strict adherence to the ontology to provide a reliable machine-readable database of (numerical) algorithm knowledge.

Introduction back to ToC

This is a place holder text for the introduction. The introduction should briefly describe the ontology, its motivation, state of the art and goals.

Namespace declarations

Table 1: Namespaces used in the document
mathalgodb<https://mardi4nfdi.de/mathalgodb/0.1#>
qudt<http://qudt.org/schema/qudt>
vaem<http://www.linkedmodel.org/schema/vaem>
owl<http://www.w3.org/2002/07/owl>
xsd<http://www.w3.org/2001/XMLSchema>
swrl<http://www.w3.org/2003/11/swrl>
swrlb<http://www.w3.org/2003/11/swrlb>
skos<http://www.w3.org/2004/02/skos/core>
rdfs<http://www.w3.org/2000/01/rdf-schema>
mathmoddb<https://mardi4nfdi.de/mathmoddb>
swrla<http://swrl.stanford.edu/ontologies/3.3/swrla.owl>
rdf<http://www.w3.org/1999/02/22-rdf-syntax-ns>
terms<http://purl.org/dc/terms>
xml<http://www.w3.org/XML/1998/namespace>
dcterms<http://purl.org/dc/terms>
opla-sd<http://ontologydesignpatterns.org/opla-sd>
bibo<http://purl.org/ontology/bibo>
vann<http://purl.org/vocab/vann>
prov<http://www.w3.org/ns/prov>
foaf<http://xmlns.com/foaf/0.1>
dc<http://purl.org/spar/datacite>

MathModDB Ontology: Overview back to ToC

This ontology has the following classes and properties.

Classes

Object Properties

Data Properties

MathModDB Ontology: Description back to ToC

This is a placeholder text for the description of your ontology. The description should include an explanation and a diagram explaining how the classes are related, examples of usage, etc.

Cross-reference for MathModDB Ontology classes, object properties and data properties back to ToC

This section provides details for each class and property defined by MathModDB Ontology.

Classes

Algorithmc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#algorithm

The main building blocks of the graph are algorithms. Here you can take a look at all algorithms documented in the graph.
is in domain of
has component op, has subclass op, is analyzed in op, is applied in op, is component of op, is implemented by op, is invented in op, is related to op, is studied in op, is subclass of op, is surveyed in op, precludes op, recommends op, requires op, solves op
is in range of
analyzes op, applies op, has component op, has subclass op, implements op, invents op, is component of op, is related to op, is solved by op, is subclass of op, precluded by op, recommended by op, required by op, studies op, surveys op
is disjoint with
Benchmark c, Algorithmic Task c, Publication c, Software c, Identifiable c, Algorithmic Task c, Algorithmic Task c, Publication c, Realization c

Algorithmic Taskc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#problem

When interested in algorithms solving a certain problem at hand, we here provide an overview of all problems defined in the graph.
An engineering challenge that includes a mathematical part
is in domain of
contains formulation op, equivalent to op, instantiates op, is solved by op, specializedBy op, specializes op
is in range of
contained as formulation in task op, equivalent to op, is instance of op, solves op, specializedBy op, specializes op
is disjoint with
Algorithm c, Benchmark c, Publication c, Software c, Algorithm c, Identifiable c, Algorithm c, Publication c, Realization c

All MathAlgoDB objectsc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#all_objects

is equivalent to
Algorithm c or Benchmark c or Algorithmic Task c or Publication c or Software c
Algorithm c or Benchmark c or Algorithmic Task c or Publication c or Software c or Computational Task c or Mathematical Formulation c or Mathematical Model c or Publication c or Quantity c or Quantity Kind c or Research Field c or Research Problem c or Task c
is in domain of
has category dp

Benchmarkc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#benchmark

For testing, evaluating and comparing numerical algorithms, so called benchmark problems are often useful.
is in domain of
is instance of op, is tested by op
is in range of
instantiates op, tests op
is disjoint with
Algorithm c, Algorithmic Task c, Publication c, Software c

Computational Taskc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#ComputationalTask

A specific computational tasks associated with a mathematical model. Typically, various tasks differ from each other by the choice of given quantities (input), unknown quantities (output), parameters or constants as well as boundary conditions, inital conditions and/or final conditions.
has super-classes
Task c
is in domain of
applies model op, approximated by task op, approximates task op, contained in task op, contains input op, contains objective op, contains output op, contains parameter op, contains task op, discretized by task op, discretizes task op, equivalent to op, generalized by task op, generalizes task op, linearized by task op, linearizes task op, similar to task op
is in range of
applied by task op, approximated by task op, approximates task op, contained as input in op, contained as objective in op, contained as output in op, contained as parameter in op, contained in task op, contains task op, discretized by task op, discretizes task op, equivalent to op, generalized by task op, generalizes task op, linearized by task op, linearizes task op, similar to task op
is disjoint with
Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c

Identifiablec back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#identifiable

is equivalent to
Benchmark c or Publication c or Software c
is in domain of
has identifier dp
is disjoint with
Algorithm c, Algorithmic Task c

Mathematical Formulationc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#MathematicalFormulation

Typically, a mathematical formulation is based on equations (general construct indicating equality of quantities) or on inequalities (non-equal relations between quantities), or a logic quantifier
is in domain of
Formulation Property dp, approximated by formulation op, approximates formulation op, contained as assumption in op, contained as boundary condition in op, contained as constraint condition in op, contained as coupling condition in op, contained as final condition in op, contained as formulation in op, contained as formulation in task op, contained as initial condition in op, contains quantity op, defines op, defining formulation dp, discretized by formulation op, discretizes formulation op, generalized by formulation op, generalizes formulation op, has Formulation Order dp, has Formulation Property dp, in defining formulation dp, linearized by formulation op, linearizes formulation op, nondimensionalized by formulation op, nondimensionalizes formulation op, precluded by op, recommended by op, required by op, similar to formulation op
is in range of
approximated by formulation op, approximates formulation op, contained in formulation op, contains assumption op, contains boundary condition op, contains constraint condition op, contains coupling condition op, contains final condition op, contains formulation op, contains formulation op, contains initial condition op, defined by op, discretized by formulation op, discretizes formulation op, generalized by formulation op, generalizes formulation op, linearized by formulation op, linearizes formulation op, nondimensionalized by formulation op, nondimensionalizes formulation op, precludes op, recommends op, requires op, similar to formulation op
is disjoint with
Computational Task c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c, Task c

Mathematical Modelc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#MathematicalModel

A mathematical model for describing a part of the reality by means of abstraction and simplifying assumptions. The aim of modeling is to make a particular part or feature of the world easier to simulate, interpret and/or optimize based on existing knowledge.
is in domain of
applied by task op, approximated by model op, approximates model op, contained in model op, contains model op, discretized by model op, discretizes model op, generalized by model op, generalizes model op, linearized by model op, linearizes model op, models op, similar to model op
is in range of
applies model op, approximated by model op, approximates model op, contained in model op, contains model op, discretized by model op, discretizes model op, generalized by model op, generalizes model op, linearized by model op, linearizes model op, modeled by op, similar to model op
is disjoint with
Computational Task c, Mathematical Formulation c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c, Task c

Publicationc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#publication

To find theoretical or numerical results on the performance of algorithms, take a look at the related publications in this list.
is in domain of
analyzes op, applies op, documents op, invents op, studies op, surveys op, uses op
is in range of
is analyzed in op, is applied in op, is documented in op, is invented in op, is studied in op, is surveyed in op, is used in op
is disjoint with
Algorithm c, Benchmark c, Algorithmic Task c, Software c, Algorithm c, Algorithmic Task c, Realization c

Publicationc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#Publication

A scientific publication
is in domain of
documents op, invents op, studies op, surveys op, uses op
is in range of
documented in op, invented in op, studied in op, surveyed in op, used in op
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Quantity c, Quantity Kind c, Research Field c, Research Problem c, Task c

Quantityc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#Quantity

A quantity is a property of a system that can be measured or obtained from calculation/simulation. Can be a scalar, a vector, a matrix or a higher-order tensor. The overarching, abstract quantity in the QuantityKind class should be referenced if possible/applicable.
is in domain of
approximated by quantity op, approximates quantity op, generalized by quantity op, linearized by quantity op, linearizes quantity op
is in range of
approximated by quantity op, approximates quantity op, generalizes quantity op, linearized by quantity op, linearizes quantity op
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity Kind c, Research Field c, Research Problem c, Task c

Quantity Kindc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#QuantityKind

The kind of quantity, e.g. the abstract, generalized concept of a quantity. Typically, it could be chosen from an established, controlled vocabulary of quantityKinds, such as QUDT, IEC, .... Note that the kind of a quantity cannot be generalized by another (kind of a) quantity.
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Research Field c, Research Problem c, Task c

Realizationc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#realization

Union of all MathAlgoDB-Classes that *may* have a unique identifier.
is equivalent to
Benchmark c or Software c
is in domain of
is documented in op, is used in op
is in range of
documents op, uses op
is disjoint with
Algorithm c, Algorithmic Task c, Publication c

Research Fieldc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#ResearchField

A field of research (or academic discipline), e.g. Arts & Humanities, Life Sciences & Biomedicine, Physical & Natural Sciences or Engineering.
is in domain of
contains problem op, generalized by field op, generalizes field op, similar to field op
is in range of
contained in field op, generalized by field op, generalizes field op, similar to field op
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Problem c, Task c

Research Problemc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#ResearchProblem

A research problem (or research question) to be investigated, typically from a scientific or engineering application, i.e. a specific issue or gap in existing knowledge that you aim to address in your research.
is in domain of
contained in field op, generalized by problem op, generalizes problem op, modeled by op, similar to problem op
is in range of
contains problem op, generalized by problem op, generalizes problem op, models op, similar to problem op
is disjoint with
Computational Task c, Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Task c

Softwarec back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#software

This table contains software packages that implement some of the algorithms from the graph.
is in domain of
implements op, tests op
is in range of
is implemented by op, is tested by op
is disjoint with
Algorithm c, Benchmark c, Algorithmic Task c, Publication c

Taskc back to ToC or Class ToC

IRI: https://mardi4nfdi.de/mathmoddb#Task

A specific task associated with a mathematical model. The subclasses of this superclass should reflect their differences, e.g. a computational task or a task of doing a mathematical analysis (the latter is not yet implemented).
has sub-classes
Computational Task c
is disjoint with
Mathematical Formulation c, Mathematical Model c, Publication c, Quantity c, Quantity Kind c, Research Field c, Research Problem c

Object Properties

analyzesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#analyzes

has domain
Publication c
has range
Algorithm c
is inverse of
is analyzed in op

applied byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#appliedBy

has sub-properties
applied by task op

applied by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#appliedByTask

has super-properties
applied by op
has domain
Mathematical Model c
has range
Computational Task c
is inverse of
applies model op

appliesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#applies

has domain
Publication c
has range
Algorithm c
is inverse of
is applied in op

appliesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#applies

has sub-properties
applies model op

applies modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#appliesModel

has super-properties
applies op
has domain
Computational Task c
has range
Mathematical Model c
is inverse of
applied by task op

approximated byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedBy

has characteristics: transitive

has sub-properties
approximated by formulation op, approximated by model op, approximated by quantity op, approximated by task op
is inverse of
approximates op

approximated by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByFormulation

has characteristics: transitive

has super-properties
approximated by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
approximates formulation op

approximated by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByModel

has characteristics: transitive

has super-properties
approximated by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
approximates model op

approximated by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByQuantity

has characteristics: transitive

has super-properties
approximated by op
has domain
Quantity c
has range
Quantity c
is inverse of
approximates quantity op

approximated by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatedByTask

has characteristics: transitive

has super-properties
approximated by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
approximates task op

approximatesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximates

has characteristics: transitive

has sub-properties
approximates formulation op, approximates model op, approximates quantity op, approximates task op
is inverse of
approximated by op

approximates formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesFormulation

has characteristics: transitive

has super-properties
approximates op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
approximated by formulation op

approximates modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesModel

has characteristics: transitive

has super-properties
approximates op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
approximated by model op

approximates quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesQuantity

has characteristics: transitive

has super-properties
approximates op
has domain
Quantity c
has range
Quantity c
is inverse of
approximated by quantity op

approximates taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#approximatesTask

has characteristics: transitive

has super-properties
approximates op
has domain
Computational Task c
has range
Computational Task c
is inverse of
approximated by task op

contained as assumption inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsAssumptionIn

Assumptions in a mathematical model|task|formulation are the conditions that must be met for the mathematical model|task|formulation to be valid.

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains assumption op

contained as boundary condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsBoundaryConditionIn

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains boundary condition op

contained as constant inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsConstantIn

This property serves to indicate that a certain quantity is considered as a constant in a computational task.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c or Mathematical Formulation c
is inverse of
contains constant op

contained as constraint condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsConstraintConditionIn

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains constraint condition op

contained as coupling condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsCouplingConditionIn

has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains coupling condition op

contained as final condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsFinalConditionIn

has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains final condition op

contained as formulation inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsFormulationIn

use this property to denote that a formulation is contained in a (single or coupled) model or formulation or task, e.g., a Darcy formulation is contained in a Darcy-Stokes model or formulation or a related task

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains formulation op

contained as formulation in taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsFormulationInTask

has domain
Mathematical Formulation c
has range
Algorithmic Task c
is inverse of
contains formulation op

contained as initial condition inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsInitialConditionIn

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Formulation c
has range
Computational Task c or Mathematical Formulation c or Mathematical Model c
is inverse of
contains initial condition op

contained as input inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsInputIn

Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains input op

contained as objective inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsObjectiveIn

This property serves to indicate that a certain quantity is to be minimized or maximized in a mathematical optimization task.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains objective op

contained as output inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsOutputIn

Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains output op

contained as parameter inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedAsParameterIn

Note that (base) quantities may be assigned as input or output or parameter in the context of a (specific!) mathematical task but not in the context of a (general!) model or equation.
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Computational Task c
is inverse of
contains parameter op

contained in fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInField

has super-properties
contained in op
has domain
Research Problem c
has range
Research Field c
is inverse of
contains problem op

contained in formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInFormulation

use this property to denote that a quantity is contained in a formulation e.g. masses are contained in a Newton Equation
has super-properties
contained in op
has domain
Quantity c or Quantity Kind c
has range
Mathematical Formulation c
is inverse of
contains quantity op

contained in modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInModel

use this property to denote that a single model is included in a coupled model, e.g. a Darcy model and a Stokes model are included in a Darcy Stokes model

has characteristics: transitive

has super-properties
contained in op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
contains model op

contained in taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containedInTask

This indicates that a computational sub-task is contained in a higher task.
has super-properties
contained in op
has domain
Computational Task c
has range
Computational Task c
is inverse of
contains task op

contains assumptionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsAssumption

Assumptions in a mathematical model|task|formulation are the conditions that must be met for the mathematical model|task|formulation to be valid.

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as assumption in op

contains boundary conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsBoundaryCondition

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions.[1] A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as boundary condition in op

contains constantop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsConstant

This property serves to indicate that a certain quantity is considered as a constant in a computational task.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c
has range
Quantity c or Quantity Kind c
is inverse of
contained as constant in op

contains constraint conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsConstraintCondition

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as constraint condition in op

contains coupling conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsCouplingCondition

Conditions needed to model the interaction of two or more systems that are interacting with each other
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as coupling condition in op

contains final conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsFinalCondition

Similar to initial conditions. Sometimes used in the context of optimal control.
has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as final condition in op

contains formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#containsFormulation

has domain
Algorithmic Task c
has range
Mathematical Formulation c
is inverse of
contained as formulation in task op

contains formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsFormulation

use this property to denote that a (single or coupled) model or formulation includes a mathematical formulation, e.g. a Darcy Stokes model/formulation includes a Darcy formulation and a Stokes formulation

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as formulation in op

contains initial conditionop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsInitialCondition

In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value,  is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0).

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c
has range
Mathematical Formulation c
is inverse of
contained as initial condition in op

contains inputop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsInput

Indicates that a (base) quantity is considered as input in the context of a (specific!) computational task.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as input in op

contains modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsModel

use this property to denote that a coupled model includes single models, e.g. a Darcy Stokes model includes a Darcy model and a Stokes model

has characteristics: transitive

has super-properties
contains op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
contained in model op

contains objectiveop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsObjective

This property serves to indicate that a certain quantity is to be minimized or maximized in a computational optimization task. An objective function, a target function, a loss function or cost function (minimization), a utility function or fitness function (maximization), or, in certain fields, an energy function or energy functional.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as objective in op

contains outputop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsOutput

Indicates that a (base) quantity is considered as output in the context of a (specific!) computational task.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as output in op

contains parameterop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsParameter

Auxiliary variable or arbitrary constant that characterizes a system or specifies a mathematical function among a family of functions. This property serves to indicate that a certain quantity is considered as a parameter in a computational task.
has super-properties
contains op
has domain
Computational Task c
has range
Quantity c or Quantity Kind c
is inverse of
contained as parameter in op

contains problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsProblem

has super-properties
contains op
has domain
Research Field c
has range
Research Problem c
is inverse of
contained in field op

contains quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsQuantity

use this property to denote that a mathematical formulation contains a quantity, e.g., a Newton Equation contains masses
has super-properties
contains op
has domain
Mathematical Formulation c
has range
Quantity c or Quantity Kind c
is inverse of
contained in formulation op

contains taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#containsTask

This indicates that a computational task contains a subtask.

has characteristics: transitive

has super-properties
contains op
has domain
Computational Task c
has range
Computational Task c
is inverse of
contained in task op

defined byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#definedBy

has domain
Quantity c or Quantity Kind c
has range
Mathematical Formulation c
is inverse of
defines op

definesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#defines

has domain
Mathematical Formulation c
has range
Quantity c or Quantity Kind c
is inverse of
defined by op

discretized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedBy

Discrete models are the discrete analogues of continuous models. In discrete modelling, processes are described by discrete data, i.e., data that could potentially take on only a countable set of values, such as the integers, and which are not infinitely divisible. Thus, discrete modeling yields a computer representable and computable versions of continuous mathematical models,
has sub-properties
discretized by formulation op, discretized by model op, discretized by task op
is inverse of
discretizes op

discretized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedByFormulation

Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions. Here, they serve as a connecting node to the AlgoData ontology (TA2 of MaRDI) which mainly deals with software, algorithms and benchmarks.
has super-properties
discretized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
discretizes formulation op

discretized by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedByModel

Discretizing is the process of obtaining discrete models that are the analogues of continuous models. Thus, discretization yields a computer representable and computable versions. Here, they serve as a connecting node to the AlgoData ontology (TA2 of MaRDI) which mainly deals with software, algorithms and benchmarks.
has super-properties
discretized by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
discretizes model op

discretized by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizedByTask

has super-properties
discretized by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
discretizes task op

discretizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizes

Discretizing is the process of obtaining discrete models/formulations that are the analogues of continuous models/formulations. Thus, discretization yields a computer representable and computable versions.
has sub-properties
discretizes formulation op, discretizes model op, discretizes task op
is inverse of
discretized by op

discretizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizesFormulation

Discretizing is the process of obtaining discrete formulations that are the analogues of continuous formulations. Thus, discretization yields a computer representable and computable versions.
has super-properties
discretizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
discretized by formulation op

discretizes modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizesModel

Discretizing is the process of obtaining discrete models that are the analogues of continuous models, thus making them computer representable and hopefully(!) computer solvable. Note, however, that certain models are already discretized from the outset.
has super-properties
discretizes op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
discretized by model op

discretizes taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#discretizesTask

has super-properties
discretizes op
has domain
Computational Task c
has range
Computational Task c
is inverse of
discretized by task op

documented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#documentedIn

A property to express that an entity (problem, model, ...) is documented in a specific Publication
has range
Publication c
is inverse of
documents op

documentsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#documents

has domain
Publication c
has range
Realization c
is inverse of
is documented in op

documentsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#documents

A property that expresses a Publication is documenting some entity (problem, model, ...)
has domain
Publication c
is inverse of
documented in op

equivalent toop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#equivalentTo

has domain
Algorithmic Task c
has range
Computational Task c
is inverse of
equivalent to op

equivalent toop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#equivalentTo

has domain
Computational Task c
has range
Algorithmic Task c
is inverse of
equivalent to op

generalized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedBy

has characteristics: transitive

has sub-properties
generalized by field op, generalized by formulation op, generalized by model op, generalized by problem op, generalized by quantity op, generalized by task op
is inverse of
generalizes op

generalized by fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByField

has characteristics: transitive

has super-properties
generalized by op
has domain
Research Field c
has range
Research Field c
is inverse of
generalizes field op

generalized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByFormulation

has characteristics: transitive

has super-properties
generalized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
generalizes formulation op

generalized by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByModel

has characteristics: transitive

has super-properties
generalized by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
generalizes model op

generalized by problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByProblem

has characteristics: transitive

has super-properties
generalized by op
has domain
Research Problem c
has range
Research Problem c
is inverse of
generalizes problem op

generalized by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByQuantity

has characteristics: transitive

has super-properties
generalized by op
has domain
Quantity c
has range
Quantity c or Quantity Kind c
is inverse of
generalizes quantity op

generalized by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizedByTask

has characteristics: transitive

has super-properties
generalized by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
generalizes task op

generalizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizes

has characteristics: transitive

has sub-properties
generalizes field op, generalizes formulation op, generalizes model op, generalizes problem op, generalizes quantity op, generalizes task op
is inverse of
generalized by op

generalizes fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesField

has characteristics: transitive

has super-properties
generalizes op
has domain
Research Field c
has range
Research Field c
is inverse of
generalized by field op

generalizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesFormulation

has characteristics: transitive

has super-properties
generalizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
generalized by formulation op

generalizes modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesModel

has characteristics: transitive

has super-properties
generalizes op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
generalized by model op

generalizes problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesProblem

has characteristics: transitive

has super-properties
generalizes op
has domain
Research Problem c
has range
Research Problem c
is inverse of
generalized by problem op

generalizes quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesQuantity

has characteristics: transitive

has super-properties
generalizes op
has domain
Quantity c or Quantity Kind c
has range
Quantity c
is inverse of
generalized by quantity op

generalizes taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#generalizesTask

has characteristics: transitive

has super-properties
generalizes op
has domain
Computational Task c
has range
Computational Task c
is inverse of
generalized by task op

has componentop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#hasComponent

has characteristics: transitive

has domain
Algorithm c
has range
Algorithm c
is inverse of
is component of op

has subclassop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#hasSubclass

has characteristics: transitive

has domain
Algorithm c
has range
Algorithm c
is inverse of
is subclass of op

implementsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#implements

has domain
Software c
has range
Algorithm c
is inverse of
is implemented by op

instantiatesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#instantiates

has domain
Algorithmic Task c
has range
Benchmark c
is inverse of
is instance of op

invented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#inventedIn

A property that states that some entity (problem, model, ...) was invented in a specific Publication
has range
Publication c
is inverse of
invents op

inventsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#invents

has domain
Publication c
has range
Algorithm c
is inverse of
is invented in op

inventsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#invents

A property that states that a Publication invented some entity (problem, model, ...)
has domain
Publication c
is inverse of
invented in op

is analyzed inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#analyzedIn

has domain
Algorithm c
has range
Publication c
is inverse of
analyzes op

is applied inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#appliedIn

has domain
Algorithm c
has range
Publication c
is inverse of
applies op

is component ofop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#componentOf

has characteristics: transitive

has domain
Algorithm c
has range
Algorithm c
is inverse of
has component op

is documented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#documentedIn

has domain
Realization c
has range
Publication c
is inverse of
documents op

is implemented byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#implementedBy

has domain
Algorithm c
has range
Software c
is inverse of
implements op

is instance ofop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#instanceOf

has domain
Benchmark c
has range
Algorithmic Task c
is inverse of
instantiates op

is invented inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#inventedIn

has domain
Algorithm c
has range
Publication c
is inverse of
invents op

is related toop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#relatedTo

has characteristics: symmetric, transitive

has domain
Algorithm c
has range
Algorithm c

is solved byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#solvedBy

has domain
Algorithmic Task c
has range
Algorithm c
is inverse of
solves op

is studied inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#studiedIn

has domain
Algorithm c
has range
Publication c
is inverse of
studies op

is subclass ofop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#subclassOf

has characteristics: transitive

has domain
Algorithm c
has range
Algorithm c
is inverse of
has subclass op

is surveyed inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#reviewedIn

has domain
Algorithm c
has range
Publication c
is inverse of
surveys op

is tested byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#testedBy

has domain
Benchmark c
has range
Software c
is inverse of
tests op

is used inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#usedIn

has domain
Realization c
has range
Publication c
is inverse of
uses op

linearized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedBy

has sub-properties
linearized by formulation op, linearized by model op, linearized by quantity op, linearized by task op
is inverse of
linearizes op

linearized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByFormulation

A property that states that a formulation is linearized (exact or approximate) by another formulation.
has super-properties
linearized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
linearizes formulation op

linearized by modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByModel

A property that states that a model is linearized (exact or approximate) by another model.
has super-properties
linearized by op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
linearizes model op

linearized by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByQuantity

A property that states that a quantity is linearized (exact or approximate) by another quantity.
has super-properties
linearized by op
has domain
Quantity c
has range
Quantity c
is inverse of
linearizes quantity op

linearized by taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizedByTask

A property that states that a task is linearized (exact or approximate) by another task.
has super-properties
linearized by op
has domain
Computational Task c
has range
Computational Task c
is inverse of
linearizes task op

linearizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizes

Linearization of a formulation, model, quantity or task.
has sub-properties
linearizes formulation op, linearizes model op, linearizes quantity op, linearizes task op
is inverse of
linearized by op

linearizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesFormulation

A property that states that a formulation linearizes (exact or approximate) another formulation.
has super-properties
linearizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
linearized by formulation op

linearizes modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesModel

A property that states that a model linearizes (exact or approximate) another model.
has super-properties
linearizes op
has domain
Mathematical Model c
has range
Mathematical Model c
is inverse of
linearized by model op

linearizes quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesQuantity

A property that states that a quantity linearizes (exact or approximate) another quantity.
has super-properties
linearizes op
has domain
Quantity c
has range
Quantity c
is inverse of
linearized by quantity op

linearizes taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#linearizesTask

A property that states that a task linearizes (exact or approximate) another task.
has super-properties
linearizes op
has domain
Computational Task c
has range
Computational Task c
is inverse of
linearized by task op

modeled byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#modeledBy

Mathematical modeling describes a part of the reality, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features.
has domain
Research Problem c
has range
Mathematical Model c
is inverse of
models op

modelsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#models

Mathematical modeling describes a part of the reality, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features.
has domain
Mathematical Model c
has range
Research Problem c
is inverse of
modeled by op

nondimensionalized byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizedBy

has characteristics: inverse functional

has sub-properties
nondimensionalized by formulation op, nondimensionalized by quantity op
is inverse of
nondimensionalizes op

nondimensionalized by formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizedByFormulation

A property that states that a formulation is nondimensionalized (partially or complete) by another formulation.
has super-properties
nondimensionalized by op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
nondimensionalizes formulation op

nondimensionalized by quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizedByQuantity

A property that states that a quantity is nondimensionalized (partially or complete) by another quantity.
has super-properties
nondimensionalized by op
has domain
Quantity c or Quantity Kind c
has range
Quantity c or Quantity Kind c
is inverse of
nondimensionalizes quantity op

nondimensionalizesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizes

Partial or full removal of physical dimensions from a quantity or a formulation.

has characteristics: functional

has sub-properties
nondimensionalizes formulation op, nondimensionalizes quantity op
is inverse of
nondimensionalized by op

nondimensionalizes formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionalizesFormulation

A property that states that a formulation nondimensionalizes (partially or complete) another formulation.
has super-properties
nondimensionalizes op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c
is inverse of
nondimensionalized by formulation op

nondimensionalizes quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#nondimensionaliesQuantity

A property that states that a quantity nondimensionalizes (partially or complete) another quantity.
has super-properties
nondimensionalizes op
has domain
Quantity c or Quantity Kind c
has range
Quantity c or Quantity Kind c
is inverse of
nondimensionalized by quantity op

precluded byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#precludedBy

has domain
Mathematical Formulation c
has range
Algorithm c
is inverse of
precludes op

precludesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#precludes

has domain
Algorithm c
has range
Mathematical Formulation c
is inverse of
precluded by op

recommended byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#recommendedBy

has domain
Mathematical Formulation c
has range
Algorithm c
is inverse of
recommends op

recommendsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#recommends

has domain
Algorithm c
has range
Mathematical Formulation c
is inverse of
recommended by op

required byop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#requiredBy

has domain
Mathematical Formulation c
has range
Algorithm c
is inverse of
requires op

requiresop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#requires

has domain
Algorithm c
has range
Mathematical Formulation c
is inverse of
required by op

similar toop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarTo

use this property only if the two things are similar but the one is not the generalization of the other one

has characteristics: symmetric, transitive

has sub-properties
similar to field op, similar to formulation op, similar to model op, similar to problem op, similar to quantity op, similar to task op

similar to fieldop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToField

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Research Field c
has range
Research Field c

similar to formulationop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToFormulation

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Mathematical Formulation c
has range
Mathematical Formulation c

similar to modelop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToModel

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Mathematical Model c
has range
Mathematical Model c

similar to problemop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToProblem

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Research Problem c
has range
Research Problem c

similar to quantityop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToQuantity

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Quantity c or Quantity Kind c
has range
Quantity c or Quantity Kind c

similar to taskop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#similarToTask

has characteristics: symmetric, transitive

has super-properties
similar to op
has domain
Computational Task c
has range
Computational Task c

solvesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#solves

has domain
Algorithm c
has range
Algorithmic Task c
is inverse of
is solved by op

specializedByop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#specializedBy

has characteristics: transitive

has domain
Algorithmic Task c
has range
Algorithmic Task c
is inverse of
specializes op

specializesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#specializes

has characteristics: transitive

has domain
Algorithmic Task c
has range
Algorithmic Task c
is inverse of
specializedBy op

studied inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#studiedIn

This property states that an entity (problem, model, ...) is studied in a specific Publication
has range
Publication c
is inverse of
studies op

studiesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#studies

has domain
Publication c
has range
Algorithm c
is inverse of
is studied in op

studiesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#studies

This property states that a Publication studies an entity (problem, model, ...)
has domain
Publication c
is inverse of
studied in op

surveyed inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#surveyedIn

This property states that an entity (problem, model, application, ...) is surveyed in a specific Publication. Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
has range
Publication c
is inverse of
surveys op

surveysop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#reviews

has domain
Publication c
has range
Algorithm c
is inverse of
is surveyed in op

surveysop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#surveys

This property states that a Publication surveys some entity (problem, model, application...). Surveys are e.g. a review article, a handbook, an encyclopedia, monographs, a documentation, technical report ... .
has domain
Publication c
is inverse of
surveyed in op

testsop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#tests

has domain
Software c
has range
Benchmark c
is inverse of
is tested by op

used inop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#usedIn

A property that states that an entity (problem, model, ...) is used in a Publication
has range
Publication c
is inverse of
uses op

usesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#uses

has domain
Publication c
has range
Realization c
is inverse of
is used in op

usesop back to ToC or Object Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#uses

A property that states that a Publication uses a specific entity (problem, model, ...)
has domain
Publication c
is inverse of
used in op

Data Properties

defining formulationdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#definingFormulation

Equations, inequalities, expressions, logic quantifiers, ... in Latex or MathML, e.g. $F = ma$, $v \llt c$, $\forall n \in N$, ...
has super-properties
Formulation Property dp
has domain
Mathematical Formulation c
has range
la te x or math m l

Formulation Propertydp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#formulationProperty

has sub-properties
defining formulation dp, has Formulation Order dp, has Formulation Property dp, in defining formulation dp
has domain
Mathematical Formulation c

has categorydp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathalgodb/0.1#category

has domain
All MathAlgoDB objects c
has range
string

has Formulation Orderdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#hasFormulationOrder

The Order of a mathematical formulation
has super-properties
Formulation Property dp
has domain
Mathematical Formulation c
has range
integer

has Formulation Propertydp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#hasFormulationProperty

has super-properties
Formulation Property dp
has domain
Mathematical Formulation c
has range
string

has identifierdp back to ToC or Data Property ToC

IRI: http://purl.org/spar/datacite/hasIdentifier

has domain
Identifiable c
has range
string

in defining formulationdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#inDefiningFormulation

Symbol / Term of formulation and corresponding quantity in comma-separated list, e.g. ($\mathbf{F}$,qudt:Force) and/or ($m$,dbpedia:Mass) and/or ($\mathbf{a}$,wikidata:Q11376)
has super-properties
Formulation Property dp
has domain
Mathematical Formulation c
has range
string or la te x or math m l

is convexdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isConvex

Boolean. True if convex, false if not convex
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is deterministicdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isDeterministic

Boolean. True, if the model is deterministic; false, if the model is probabilistic (stochastic)
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is dimensionlessdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isDimensionless

has domain
Mathematical Formulation c or Mathematical Model c or Quantity c or Quantity Kind c
has range
boolean

is dynamicdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isDynamic

Boolean. True, if dynamic; false, if static
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is lineardp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isLinear

Boolean. True, if linear; false, if non-linear
has domain
Computational Task c or Mathematical Formulation c or Mathematical Model c or Quantity c
has range
boolean

is space-continuousdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isSpaceContinuous

Boolean. True, if continuous in space; false, if discrete in space
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is stiffdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isStiff

Boolean. True, if dynamic; false, if stiff
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

is time-continuousdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#isTimeContinuous

Boolean. True, if continuous in time; false, if discrete in time
has domain
Mathematical Formulation c or Mathematical Model c
has range
boolean

Matrix Propertiesdp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#MatrixProperties

has domain
Quantity c or Quantity Kind c
has range
{ "NegativeDefinite" , "NegativeSemiDefinite" , "PositiveDefinite" , "PositiveSemiDefinite" }

Matrix Structuredp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#MatrixStructure

has domain
Quantity c or Quantity Kind c
has range
{ "Block" , "CentroSymmetric" , "Circulant" , "Diagonal" , "Hessenberg" , "SkewSymmetric" , "Symmetric" , "Toeplitz" , "TriDiagonal" }

Quantity Typedp back to ToC or Data Property ToC

IRI: https://mardi4nfdi.de/mathmoddb#quantityType

has domain
Quantity c or Quantity Kind c
has range
{ "Higher Order Tensor" , "Matrix" , "Scalar" , "Vector" }

Legend back to ToC

c: Classes
op: Object Properties
dp: Data Properties

References back to ToC

Add your references here. It is recommended to have them as a list.

Acknowledgments back to ToC

The authors would like to thank Silvio Peroni for developing LODE, a Live OWL Documentation Environment, which is used for representing the Cross Referencing Section of this document and Daniel Garijo for developing Widoco, the program used to create the template used in this documentation.