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East Molokai Volcano is a shield volcano located on the island of Molokai in Hawaii. It is one of the two primary volcanic structures on the island, the other being West Molokai Volcano. East Molokai Volcano is characterized by its broad, gently sloping profile, typical of shield volcanoes, and is primarily composed of basaltic lava flows. This volcano is believed to have formed over a period of millions of years through numerous eruptions that created a large and wide configuration.

Collinder 228 is an open star cluster located in the constellation of Cassiopeia. It was cataloged by the Swedish astronomer Per Collinder in 1931 as part of his investigation of open clusters. Open clusters are groups of stars that are gravitationally bound and formed from the same molecular cloud, typically containing a few dozen to a few thousand stars. Collinder 228 is relatively young and is notable for its stars being relatively hot and bright.

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.

Conley's fundamental theorem of dynamical systems, often referred to as Conley's theorem, addresses the behavior of dynamical systems, particularly focusing on asymptotic behavior and the presence of invariant sets. The theorem is part of the broader study of dynamical systems and lays the groundwork for understanding the structure of trajectories of these systems.

In topology, the connected sum is an important operation that allows us to combine two manifolds into a single manifold. The most common context for this operation is in the realm of surfaces and higher-dimensional manifolds.

A critical value is a point in a statistical distribution that helps to determine the threshold for making decisions about null and alternative hypotheses in hypothesis testing. It essentially divides the distribution into regions where you would accept or reject the null hypothesis. Here's how it generally works: 1. **Hypothesis Testing**: In hypothesis testing, you typically have a null hypothesis (H0) that represents a default position, and an alternative hypothesis (H1) that represents a new claim you want to test.

The degree of a continuous mapping refers to a topological invariant that describes the number of times a continuous function covers its target space. This concept is most commonly applied in the context of mappings between spheres or between manifolds.

Donaldson's theorem is a significant result in differential geometry, particularly in the area of symplectic geometry and the study of 4-manifolds. It was introduced by the mathematician Simon Donaldson in the 1980s and provides conditions under which certain types of smooth manifolds can be classified.

In mathematics, particularly in the field of topology and differential geometry, a "double manifold" typically refers to a space formed by taking two copies of a manifold and gluing them together along a common boundary or a particular subset. However, the term "double manifold" can also refer to other specific constructions depending on the context.

The term "meter water equivalent" (MWE) refers to the volume of water that would have the same energy content as a given amount of energy in another form, typically in the context of geothermal energy or heat transfer. In simpler terms, it's a way of expressing energy in terms of the equivalent distance that a column of water would rise if it were subjected to the same energy.

Aviation and health are interconnected fields that examine the impact of aviation on health and well-being, as well as the health-related aspects of the aviation industry itself. Here are some key areas where these two fields intersect: ### 1. **Aviation Medicine:** - **Definition:** A branch of medicine that focuses on the health and medical issues of air travel and the aviation industry, especially those affecting pilots, crew members, and passengers.

Transport accidental deaths refer to fatalities that occur as a result of accidents involving various forms of transportation. This includes a wide range of incidents, such as: 1. **Road Traffic Accidents**: Deaths from collisions between vehicles, pedestrians, cyclists, and other forms of transportation (e.g., buses, motorcycles, cars). 2. **Aviation Accidents**: Fatalities resulting from airline crashes or other aircraft-related incidents.

A "jet bundle" is a mathematical structure used in differential geometry and theoretical physics, particularly in the context of analyzing smooth manifolds and their mappings. The term often appears in discussions related to the geometry of differential equations and field theory. In more detail: 1. **Jet Spaces**: A jet space is a formal way to study the behavior of functions and their derivatives at a point.

The Kervaire manifold, specifically the Kervaire manifold of dimension \( 2n+1 \) for \( n \geq 1 \), is a type of differentiable manifold that arises in the study of smooth structures on high-dimensional spheres and exotic \( \mathbb{R}^n \). It is named after mathematician Michel Kervaire.

A **line bundle** is a fundamental concept in the fields of algebraic geometry and differential geometry. To understand what a line bundle is, let's break it down into the essential components: 1. **Vector Bundle**: A vector bundle is a topological construction that consists of a base space (often a manifold) and a vector space attached to each point of that base space.

A **neat submanifold** is a concept from differential topology, particularly in the study of manifolds and their embeddings. A submanifold \( N \) of a manifold \( M \) is called a **neat submanifold** if it is embedded in such a way that the intersection of the submanifold with the boundary of the manifold behaves well.

An orbifold is a generalization of a manifold that allows for certain types of singularities. More formally, an orbifold can be defined as a space that looks locally like a manifold but may have points where the structure of the space is modified by a finite group acting on it.

A **parallelizable manifold** is a differentiable manifold that has a global frame of vector fields. This means there exists a set of smooth vector fields that span the tangent space at every point of the manifold, and these vector fields can be chosen to vary smoothly. In more formal terms, a manifold \( M \) is said to be parallelizable if there exists a smooth bundle of vector fields \( \{V_1, V_2, ...

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.

A polyvector field is a mathematical concept that arises in the context of differential geometry and algebraic topology, specifically in the study of multivector fields on manifolds. It generalizes the notion of vector fields by allowing for the consideration of multivectors, which can be thought of as elements of the exterior algebra.