A **differential structure** is a mathematical concept that allows for the definition of differentiable functions on a set. In the context of differential geometry and topology, a differential structure can be understood through the following key points: 1. **Topological Space:** A differential structure is typically defined on a topological space, which provides the foundational set of points and the notion of open sets.

Cobordism is a concept from the field of topology, particularly in algebraic topology, that studies the relationships between manifolds. In simple terms, cobordism provides a way to classify manifolds based on their boundaries and their relationships to each other.

In the context of mathematics, particularly in algebraic geometry and algebraic topology, the term "inverse bundle" is not widely recognized as a standard term. However, it could potentially refer to a few concepts depending on the context. 1. **Vector Bundles and Duals**: In the theory of vector bundles, one often talks about the dual bundle (or dual vector bundle) associated with a given vector bundle.

The Kervaire semi-characteristic is a topological invariant associated with smooth manifolds, particularly in the context of cobordism theory and differential topology. It serves as a generalization of the Euler characteristic for manifolds that may not necessarily be compact or without boundary.

Obstruction theory is a branch of algebraic topology that deals with the conditions under which a certain kind of mathematical object, usually a topological space or a geometrical structure, can be extended or approximated. It provides tools to study when a certain problem can or cannot be solved by considering the "obstructions" that prevent it from being extendable. One of the main frameworks of obstruction theory is through the use of cohomology theories.

The unit tangent bundle is a fundamental concept in differential geometry and is used in the study of manifolds, particularly in the context of differential geometry and geodesic flows. Given a smooth manifold \( M \), the unit tangent bundle, denoted as \( U(TM) \), consists of all unit tangent vectors at every point in \( M \).

In mathematics, particularly in the context of combinatorial optimization and graph theory, "plumbing" refers to a technique used to connect different mathematical objects or structures in a way that allows for the study of their properties as a whole. It is often applied in the context of manifolds and topology, where complex shapes can be constructed from simpler pieces by "plumbing" them together.

Diffraction in time typically refers to the phenomenon where waves spread out and bend around obstacles or through openings, but instead of focusing on spatial dimensions, it considers how these waves behave over time.

Thom's second isotopy lemma is a result in the field of topology, particularly in the study of manifolds and their embeddings. This lemma is concerned with how certain isotopies (continuous deformations) of maps can be handled in the presence of singularities.

Differentiation of integrals refers to a concept in calculus where one takes the derivative of an integral with respect to its limits or the variable of integration. This idea is formalized by the Fundamental Theorem of Calculus, which establishes a relationship between differentiation and integration.

As of my last update, "Discoveries" by Joseph Rheden does not appear to be a widely recognized book or work in literature, science, or any other field. It's possible that it might be a lesser-known or newly released work, or it could be a self-published piece that hasn't garnered significant attention.

The Inverse Function Rule is a concept in calculus that relates the derivatives of a function and its inverse.

Diffraction gratings are optical devices used to separate light into its constituent wavelengths or colors. They consist of a surface that has a large number of closely spaced lines or grooves, which can be either reflective or transmissive. When light encounters the grating, it interacts with these structures, leading to constructive and destructive interference effects based on the wavelength of the light.

"Discoveries" is an album by José Manteca, a notable musician known for his work in Afro-Cuban jazz and contemporary Latin music. The album showcases Manteca's skill as a composer and musician, typically incorporating rich rhythms, vibrant melodies, and a fusion of various musical influences. His work often reflects a deep appreciation for Afro-Cuban traditions while also exploring modern jazz and multicultural sounds.

"Discoveries" by János Kelemen is likely a reference to a work by the Hungarian author, though specific details about a publication by this name are not widely recognized in mainstream literature as of my last update in October 2023. János Kelemen may have contributed to various fields, including science or literature, but without additional context, it's challenging to pinpoint a specific work titled "Discoveries.

As of my last knowledge update in October 2023, there are no widely recognized works or significant figures specifically known as "Discoveries by Juan Lacruz." It’s possible that this could refer to a lesser-known work, project, or emerging author that has gained attention after my last update.

Fraunhofer diffraction describes the diffraction patterns observed when light passes through a small aperture or around an obstacle, and it is analyzed at a far distance from the aperture or object. Under these conditions, the incoming wavefront can be approximated as planar waves. The mathematical formulation of the Fraunhofer diffraction pattern can be expressed in terms of the Fourier transform of the aperture function.

A Greninger chart, also known as a Greninger diagram, is a type of graphical representation used primarily in the fields of engineering and project management. It helps in visualizing the relationship between different elements of a project, such as tasks, resources, and timelines. The chart typically focuses on the allocation of resources over time, allowing for better understanding and management of project dynamics.

Kikuchi lines are a phenomenon observed in electron diffraction patterns, particularly in materials science and crystallography when analyzing the structures of crystalline materials using techniques such as electron backscatter diffraction (EBSD) or transmission electron microscopy (TEM). They appear as bands or lines in the diffraction pattern and are an important feature for understanding the crystalline structure and orientation of the material being studied. These lines result from the inelastic scattering of electrons and the interaction of the electron beam with the periodic lattice structure of the crystal.

The Kirchhoff integral theorem is a fundamental result in mathematical physics, particularly in the field of wave propagation and acoustics. It provides a way to express the values of a wave field (such as sound or electromagnetic waves) in terms of its values over a surface enclosing a volume. The theorem is particularly useful for solving problems involving wave equations.