Tate cohomology is a concept in algebraic topology and algebraic geometry that generalizes classical cohomology theories. It is particularly useful in the context of studying topological spaces that have group actions or in the context of number theory and arithmetic geometry.

In homological algebra, a mapping cone is a construction that allows us to define a new complex from a given morphism of chain complexes. It plays a significant role in various contexts, such as in the study of derived categories and in the formulation of the Long Exact Sequence in homology.

Matrix factorization in algebra refers to the process of decomposing a matrix into a product of two or more matrices. This can reveal underlying structures in the data represented by the original matrix, simplify computations, and enable various applications in fields such as statistics, machine learning, and computer graphics. ### Types of Matrix Factorization 1.

Semiorthogonal decomposition is a concept in mathematics, particularly in the fields of functional analysis and category theory. It refers to a method of breaking down a complex structure into simpler components that satisfy certain orthogonality conditions. In a more specific context, particularly in algebraic geometry and derived categories, semiorthogonal decomposition allows the decomposition of a category—typically a derived category of coherent sheaves—into simpler subcategories that have a well-defined relationship with each other.

The Snake Lemma is a fundamental result in homological algebra, particularly in the study of abelian categories and exact sequences. It describes a way to construct a long exact sequence of homology groups from a commutative diagram involving two short exact sequences.

The Universal Coefficient Theorem is a fundamental result in algebraic topology, particularly in the context of homology and cohomology theories. It provides a way to relate the homology of a topological space to its homology with coefficients in an arbitrary abelian group.

As of my last knowledge update in October 2021, there is no widely recognized figure by the name of Jennie Lasby Tessmann. It's possible she could be a private individual, a local figure, or someone who has gained prominence after that date. If you have any more specific context or details about her, I could help you better.

Betty Holberton (born Betty Jennings in 1917) was an American computer programmer and one of the original programmers of the ENIAC (Electronic Numerical Integrator and Computer), one of the first general-purpose electronic digital computers. Along with other women who worked on ENIAC, Holberton played a crucial role in the development of early computer programming and was instrumental in pioneering techniques that are still used in programming today.

Elizabeth Langdon Williams is not a widely recognized public figure or concept, so it’s possible that she may refer to a lesser-known individual, or perhaps you’re referring to a specific context such as an author, artist, academic, or other professional.

Hydraulic jumps are sudden changes in the flow regime of water that occur in open channel flow, such as in rectangular channels. They are characterized by a transition from supercritical flow (where the flow velocity is greater than the wave speed) to subcritical flow (where the flow velocity is less than the wave speed). This phenomenon is crucial in fluid mechanics and hydraulic engineering, as it affects the energy, momentum, and flow depth of the system.

Heron's Fountain is a classical hydraulic machine attributed to the ancient Greek engineer Hero of Alexandria. It is an example of a closed hydraulic system that demonstrates principles of fluid mechanics and pneumatic pressure. The fountain operates without any external power source and relies solely on gravity and air pressure. The design consists of a container filled with water, usually with three main parts: 1. **Upper Chamber**: This is where water is stored and can be filled.

"Ram guard" can refer to different things depending on the context. Here are a few possibilities: 1. **Automotive Accessory**: In some contexts, "Ram Guard" may refer to a protective accessory or cover designed for vehicles, specifically those made by RAM Trucks. These accessories can include items that protect the truck's body, grille, or other parts from damage.

Parflange F37 is a method of creating pipe connections that utilizes a unique flange design for joining pipes in a secure and leak-free manner. This system is often used in applications involving high-pressure and high-temperature environments. The Parflange F37 system typically involves the use of specially designed fittings that allow for the reliable connection of pipes made from various materials, such as stainless steel or carbon steel.

The Fano plane is a finite projective plane consisting of 7 points and 7 lines, with the property that each line contains exactly 3 points and each point lies on exactly 3 lines. It is the smallest projective plane and serves as a simple example in the study of combinatorial geometry and finite geometries.

In geometry, a "flag" typically refers to a specific configuration of points and subspaces in a vector space or a geometric object. More formally, a flag consists of a nested sequence of subspaces.

In projective geometry, an ovoid is a specific type of geometric structure that can be thought of as a type of surface. More formally, an ovoid is defined as a closed, convex set in a projective space such that every line intersects the ovoid in at most two points. This makes ovoids analogous to ellipsoids in Euclidean geometry.

The **Tantrasamgraha** is a significant text in the tradition of Shaiva Tantra. Attributed to the 10th-century philosopher and saint **Abhinavagupta**, the Tantrasamgraha serves as a concise summary and synthesis of various Tantric teachings and practices associated with Shaivism.

Epilogism is not a widely recognized term in modern usage, but it might refer to a few concepts depending on the context in which it's used. In general, the prefix "epi-" suggests something related to an "epilogue," which is a concluding section of a literary work that provides closure or additional commentary on the main content.

Explicature is a term used in linguistics, particularly in the field of pragmatics, to refer to the aspects of meaning that arise from the contextual interpretation of an utterance. It involves the process of elaborating the literal meaning of a sentence to include contextually relevant information that is not explicitly stated but is inferred by the listener. In transactional communication, explicature helps to clarify the speaker's intended meaning based on the context in which the utterance is made.

Braess's paradox is a concept in traffic flow and game theory that suggests that adding extra capacity to a network can sometimes lead to a decrease in overall efficiency. The paradox is named after the mathematician Dietrich Braess, who formulated it in 1968. In essence, Braess's paradox occurs when individual users of a network (such as drivers on a road network) behave in their own self-interest, and their decisions lead to a less efficient outcome for the entire system.