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Everything about Differential structure
Mathematical structure
In mathematics, an n-dimensional differential structure on a set M makes M into an n-dimensional differential manifold, which is a topological manifold with some additional mathematical structure that allows for differential calculus on the manifold. If M is already a topological manifold, it is required that the new topology be identical to the existing one. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Differential structureA 5-minute orientation
- Skim a recent paper: Regularity Theory for Non-autonomous Partial Differential Equations Without Uhlenbeck StructureInfluential work since 2022
- Pick up a classic book: Social differentiation and social inequalityThe most-reprinted book on the subject
- Read the landmark paper: Scale and the differential structure of imagesCited 307 times
- Go sideways: Banach manifoldA closely related topic
- Go sideways: Differentiable manifoldA closely related topic
📖 Definitions
Noun A structure defined for a (topological) manifold so that it supports differentiation of functions defined on it.
🏆 Landmark papers (most cited)
Scale and the differential structure of images
Differential Systems with Strongly Indefinite Variational Structure
Differential geometric methods in variable-structure control
Discrete-differential modelling of biofilm structure
Differential Structure, Tangent Structure, and SDG
Higher order differential structure of images
Global Structure of Quaternion Polynomial Differential Equations
Discrete-differential modelling of biofilm structure
🆕 Influential since 2022
Regularity Theory for Non-autonomous Partial Differential Equations Without Uhlenbeck Structure
Airborne Rangefinding With pMUTs Array Using Differential Structure
Dynamical differential covariance recovers directional network structure in multiscale neural systems
Differential–algebraic systems with dissipative Hamiltonian structure
Approach to electrochemical modulating differential extended X-ray absorption fine structure
📚 Books worth reading
Social differentiation and social inequalityJames N. Baron, David B. Grusky · 1996
Foundations of mechanicsRalph Abraham · 1967
Mathematical Techniques For Wave Interaction With Flexible StructuresTrilochan Sahoo · 2012
Moving shape analysis and controlMarwan Moubachir · 2005- 📕Modeling and Control in Vibrational and Structural DynamicsPeng-Fei Yao · 2011
Compressible Navier-Stokes EquationsPavel Plotnikov · 2012
Multi-scale Modelling for Structures and CompositesG. Panasenko · 2005
Shape Optimization By the Homogenization MethodGregoire Allaire · 2001
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Banach manifold In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic…
- Differentiable manifold In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow…
- Submanifold In mathematics, a submanifold of a manifold M {\displaystyle M} is a subset S {\displaystyle S} which itself has the structure of a manifold, and for which…
- Fiber bundle In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally…
- Smooth structure In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a smooth structure allows mathematical…
- Associated bundle In mathematics, the theory of fiber bundles with a structure group G {\displaystyle G} (a topological group) allows an operation of creating an associated…
- (G, X)-manifold In geometry, if X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological…
- Transport of structure In mathematics, particularly in universal algebra and category theory, transport of structure refers to the process whereby a mathematical object acquires…