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In differential calculus, the domain-straightening theorem states that, given a vector field X {\displaystyle X} on a manifold, there exist local coordinates
Straightening theorem for vector fields
Straightening_theorem_for_vector_fields
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by
Frobenius theorem (differential topology)
Frobenius_theorem_(differential_topology)
Mapping from p forms to p-1 forms
i.e., X = ∂ 1 {\displaystyle X=\partial _{1}} . (See Straightening theorem for vector fields) By linearity of the interior product, exterior derivative
Interior_product
Doughnut-shaped surface of revolution
as for a cylinder of length 2πR and radius r, obtained from cutting the tube along the plane of a small circle, and unrolling it by straightening out
Torus
Distance along a curve
be if we straightened it out. It can be formalized mathematically for smooth curves using vector calculus and differential geometry, or for curves that
Arc_length
Conjecture in linear algebra
of bases, named after Gian-Carlo Rota. It states that, if X is either a vector space of dimension n or more generally a matroid of rank n, with n disjoint
Rota's_basis_conjecture
Topological space that locally resembles Euclidean space
as length, angles, areas (or volumes), curvature and divergence of vector fields. All differentiable manifolds (of constant dimension) can be given the
Manifold
Technique for the generative modeling of a continuous probability distribution
This is beneficial, because we can integrate along such a vector field with very few steps. For example, if an ODE ϕ t ˙ ( x ) = v t ( ϕ t ( x ) ) {\displaystyle
Diffusion_model
Way to create new manifolds out of disk bundles
manifold to a certain stable vector bundle. A crucial theorem for the development of surgery theory is the so-called Plumbing Theorem (Browder, 1972, II.1.3)
Plumbing_(mathematics)
Boundary condition for generalized functions
estimate for C 1 ( Ω ¯ ) {\textstyle C^{1}({\bar {\Omega }})} -functions is first proven for a locally flat boundary using the divergence theorem. By transformation
Trace_operator
Type of differential equation
choice varies from PDE to PDE. To understand it for any given equation, existence and uniqueness theorems are usually important organizational principles
Partial_differential_equation
Generalization of a category
basic category theory and some of the advanced notions and theorems have their analogues for quasi-categories. An elaborate treatise of the theory of quasi-categories
Quasi-category
Field of mathematics using techniques from combinatorics and commutative algebra
commutative algebra techniques. A signature theorem in combinatorial commutative algebra is the characterization of h-vectors of simplicial polytopes conjectured
Combinatorial commutative algebra
Combinatorial_commutative_algebra
Coordinates to capture characteristics of rotating frames of reference
Because the obstruction from the Frobenius theorem can be understood in terms of the failure of the vector fields p → 2 , p → 3 {\displaystyle {\vec {p}}_{2}
Born_coordinates
a certain stability of filtration by an ideal. ASL Acronym for algebra with straightening law. associated An associated prime of a module M over a ring
Glossary of commutative algebra
Glossary_of_commutative_algebra
Shape with three inward-curved sides
minimally rigid planar graphs, and in methods for placing guards in connection with the art gallery theorem. The shelling antimatroid of a planar point
Pseudotriangle
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STRAIGHTENING THEOREM-FOR-VECTOR-FIELDS
STRAIGHTENING THEOREM-FOR-VECTOR-FIELDS
STRAIGHTENING THEOREM-FOR-VECTOR-FIELDS
STRAIGHTENING THEOREM-FOR-VECTOR-FIELDS
STRAIGHTENING THEOREM-FOR-VECTOR-FIELDS
STRAIGHTENING THEOREM-FOR-VECTOR-FIELDS
STRAIGHTENING THEOREM-FOR-VECTOR-FIELDS
STRAIGHTENING THEOREM-FOR-VECTOR-FIELDS
STRAIGHTENING THEOREM-FOR-VECTOR-FIELDS
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