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Showing 181–210 of 1709 reference entries

InformationFinite graphs and trees

Graphs represent pairwise connections; trees impose acyclicity.

DefinitionInformationData-structure interfaces and operation costs

An interface defines operations; an implementation determines costs.

MethodInformationLoop invariants and total correctness

An invariant establishes correctness only with its proof obligations.

MethodInformationComparison sorting lower bound

Distinct-key comparisons need enough branches to distinguish orders.

Mathematical statementInformationBreadth-first and depth-first traversal

Graph searches visit reachable vertices using different orders.

MethodInformationShortest-path algorithm conditions

Edge weights determine which shortest-path method applies.

MethodInformationTuring machines and effective computation

Finite instructions can act on an unbounded writable tape.

DefinitionInformationRelations and tabular data

A relation is a set of tuples from declared domains.

DefinitionPhysicsCentre-of-mass dynamics

External force controls the mass-weighted centre's acceleration.

ModelPhysicsRigid-body inertia tensor

A tensor relates rotation to angular momentum.

ModelPhysicsEuler equations for a rigid body

Body-axis angular acceleration includes rotation of the axes.

ModelPhysics · Mathematics & logicEuler–Lagrange equations

Stationary action supplies coordinate equations of motion.

Mathematical statementPhysics · Mathematics & logicHamilton's canonical equations

Canonical coordinates and momenta evolve from the Hamiltonian.

Mathematical statementPhysicsFluid mass continuity

Density change balances mass flux through a region.

ModelPhysicsBernoulli's streamline relation

An ideal steady flow balances pressure, motion and height.

ModelPhysicsIncompressible Navier–Stokes equation

Fluid inertia balances pressure, viscosity and gravity.

ModelPhysicsReynolds number

Compare inertial and viscous scales of a flow.

ModelPhysicsDriven damped oscillator

A linear restoring force, damping and periodic drive determine response.

ModelPhysicsIdeal-string wave equation

A local differential equation determines small string disturbances.

ModelPhysics · Mathematics & logicWave superposition and interference

Linear disturbances add; their relative phase determines reinforcement.

ModelPhysicsFixed-end string modes

Boundary conditions select standing-wave frequencies.

ModelPhysicsSnell's refraction relation

Angles at an interface depend on refractive indices.

ModelPhysicsThin-lens image equation

A paraxial lens relates object and image distances.

ModelPhysicsSingle-slit diffraction minima

An aperture's finite width selects dark far-field directions.

ModelPhysicsLinear polarization and Malus's law

An ideal analyzer transmits the field component along its axis.

ModelPhysicsElectromagnetic potentials

Scalar and vector potentials encode electric and magnetic fields.

ModelPhysicsCapacitance

A linear two-conductor arrangement stores separated charge.

DefinitionPhysicsSelf-inductance

Changing current changes linked magnetic flux and induced emf.

ModelPhysicsElectromagnetic energy balance

The rate of field-energy change balances outward energy flow and power transferred to charges.

ModelPhysicsKirchhoff circuit balances

Lumped circuit models balance node currents and loop voltages.

Model
DefinitionSource checked

Relations and tabular data

Information

A relation is a set of tuples from declared domains.

Key knowledge

An n-ary relation R⊆D₁×⋯×Dₙ is a set of tuples. A table can represent this model: rows are tuples and columns draw values from their declared domains.

Conditions and scope

  • Set semantics disregard duplicate rows and row order.
  • This mathematical model alone does not specify SQL nulls, bag semantics, database constraints or transaction behavior.
Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. CS2800 2016, Lecture 30: RelationsCornell UniversityCourse notescs.cornell.eduRead source

Evidence and review

Relations as subsets of Cartesian products; database rows as tuples and columns as domains.

2026-10-10 · Cartesian-product relation and basic database-table correspondence.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–2 of 2 relationships

Scientific relationships · 2 / 2

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Uses definition
    Relationship sources · 1

    Linked statements

    • An n-ary relation R⊆D₁×⋯×Dₙ is a set of tuples. A table can represent this model: rows are tuples and columns draw values from their declared domains.
  2. Related to
    Relationship sources · 1

    Linked statements

    • A relation is a set of tuples over a schema. Selection keeps rows satisfying a predicate, projection selects attributes and removes duplicates under set semantics, and join combines tuples satisfying a stated condition. SQL normally has bag semantics and three-valued NULL logic, so algebraic rewrites must retain duplicate, NULL and ordering assumptions. An algebraic equivalence describes results, not a fixed execution cost.

    Schemas and tuples supply the underlying data model.

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