mathematics, in the topology of 3-manifolds, the loop theorem is a generalization of Dehn's lemma. The loop theorem was first proven by Christos Papakyriakopoulos...

the surface. The classical theorem of Stokes can be stated in one sentence: The line integral of a vector field over a loop is equal to the surface integral...

parallel elements. The loop theorem is a generalization of Dehn's lemma and should more properly be called the "disk theorem". It was first proven by...

Structure Theorem" in the early 1970s. This version of the theorem replaces all the original program's control flow with a single global while loop that simulates...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

In quantum electrodynamics, Furry's theorem states that if a Feynman diagram consists of a closed loop of fermion lines with an odd number of vertices...

using his "tower construction". He also generalized the theorem to the loop theorem and sphere theorem. Papakyriakopoulos proved Dehn's lemma using a tower...

the Peano axioms) in his incompleteness theorem. Gödel showed that mathematics and logic contain strange loops: propositions that not only refer to mathematical...

Papakyriakopoulos is best known for his proofs of Dehn's lemma, the loop theorem, and the sphere theorem, three foundational results for the study of 3-manifolds...

Klein bottle that is not π1-injective. However, if S is two-sided, the loop theorem implies Kneser's lemma, that if S is incompressible, then it is π1-injective...

body Handlebody Incompressible surface Dehn's lemma Loop theorem (aka the Disk theorem) Sphere theorem Haken manifold JSJ decomposition Branched surface...

In computer science, a loop invariant is a property of a program loop that is true before (and after) each iteration. It is a logical assertion, sometimes...

Theorem. Assume two stable systems S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} are connected in a feedback loop, then the closed loop system...

In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic). Such a diagram can be obtained from a connected...

Kutta-Joukowski theorem, the loop must be chosen outside this boundary layer. (For example, the circulation calculated using the loop corresponding to...

homotopy groups, where Ω denotes the loop functor and Σ denotes the reduced suspension functor. The suspension theorem then states that the induced map on...

The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

rectifiable simple loop in U ¯ {\textstyle {\overline {U}}} . The Cauchy integral theorem leads to Cauchy's integral formula and the residue theorem. If one assumes...

specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow...

The fluctuation–dissipation theorem (FDT) or fluctuation–dissipation relation (FDR) is a powerful tool in statistical physics for predicting the behavior...

loop, extend to infinity or start/end at solid boundaries. Fluid elements initially free of vorticity remain free of vorticity. Helmholtz's theorems have...

"glancing blow" solution, to evade inconsistencies arising from causality loops. In the revised scenario, the ball from the future emerges at a different...

In topology, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides...

mathematics, Morera's theorem, named after Giacinto Morera, gives a criterion for proving that a function is holomorphic. Morera's theorem states that a continuous...

conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere, which is the hypersphere that...

In graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph...

Lie group is a Lie group. This is known as the closed subgroup theorem or Cartan's theorem. The quotient of a Lie group by a closed normal subgroup is a...

better. In Ada, the above loop construct (loop-while-repeat) can be represented using a standard infinite loop (loop - end loop) that has an exit when clause...

limitations": ...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram...

In group theory, a branch of mathematics, the Nielsen–Schreier theorem states that every subgroup of a free group is itself free. It is named after Jakob...