The double tangent bundle is a mathematical construction in differential geometry that generalizes the notion of tangent bundles. To understand the double tangent bundle, we first need to comprehend what a tangent bundle is. ### Tangent Bundle For a smooth manifold \( M \), the tangent bundle \( TM \) is a vector bundle that consists of all tangent vectors at every point on the manifold.

TED is a global conference series that focuses on spreading ideas through short, powerful talks. The name TED stands for Technology, Entertainment, and Design, which were the original focus areas of the conference when it began in 1984. Since then, TED has expanded to cover a wide range of topics, including science, business, global issues, education, and personal development.

Brobdingnag is a fictional land featured in Jonathan Swift's satirical novel "Gulliver's Travels," published in 1726. In the story, Brobdingnag is the homeland of giants, where everything is significantly larger than in the real world. The protagonist, Lemuel Gulliver, visits Brobdingnag after leaving Lilliput, a land inhabited by tiny people.

Władysław Matwin is not widely recognized in general public discourse, so it is possible that he may refer to a lesser-known individual in a specific context, such as a local figure, a professional in a specialized field, or even a fictional character.

The 17th century was a significant period for mathematics in Portugal, marked by contributions from several notable mathematicians. One of the most prominent figures of the time was **Pedro Nunes** (1502–1578), who, although his most influential work predates the 17th century, laid foundational ideas that were important for the development of navigation and mathematics in Portugal.

Osip Somov is primarily known as a Russian and Soviet botanist and plant geographer, who made significant contributions to the understanding of plant distribution and vegetation types, particularly in the context of the Soviet Union's diverse ecosystems. His work often involved studying the relationships between plants and their environments, which has implications for ecology, conservation, and botany.

Sergei Stepanov is a Russian mathematician known primarily for his work in the field of mathematics and computer science. His research has included contributions to areas such as graph theory, algorithm design, and combinatorial optimization. He has been involved in various mathematical projects and has published scholarly articles that explore complex mathematical concepts and their applications.

Vyacheslav Feodoritov is not a widely recognized figure in mainstream media or academic literature as of my last update in October 2023. If you're referring to a specific individual, it’s possible that he may be known in a particular niche, field, or region. Without additional context, it's difficult to provide accurate information.

Yury Yershov is a name that might refer to different individuals, but without additional context, it is challenging to provide a specific answer.

The Maurer–Cartan form is a fundamental concept in the theory of Lie groups and differential geometry, particularly in the study of Lie group representations and the geometry of principal bundles. Given a Lie group \( G \), the Maurer–Cartan form is a differential 1-form on the Lie group that captures information about the group structure in terms of its tangent space.

Unsurprisingly the term "computer" became a synonym for this from the 1960s onwards!

Of course, this only made sense when Apple was more of an underdog to IBM, and Ciro Santilli greatly admires their defiance of the norm.

As of 2020 however, Apple is kind of on the top of the mobile world, and Think different simply makes no sense anymore, notably because it relies on closed source offline software used by millions.

it's Popular Now It Sucks comes to mind.

This is a trap every company that prides itself on it's "alternative culture" sets for itself. If they succeed, they could become the norm.

The Kervaire invariant is a concept in algebraic topology, specifically in the study of bordism theory and the classification of high-dimensional manifolds. It is named after the mathematician Michel Kervaire, who introduced it in the context of differentiable manifolds. More formally, the Kervaire invariant is a specific invariant associated with a smooth manifold, particularly focusing on the topology of the manifold's tangent bundle.

Static spacetime is a concept in general relativity that refers to a type of spacetime geometry that is both time-independent (static) and has a specific symmetry. More formally, a static spacetime is one where the gravitational field does not change over time and exhibits certain symmetries, particularly time translation symmetry and spatial symmetry. Key characteristics of static spacetimes include: 1. **Time Independence**: The metric tensor, which describes the geometry of spacetime, does not vary with time.

As of my last knowledge update in October 2021, Thomas Timusk is a prominent physicist known for his contributions to the field of condensed matter physics. He has worked on topics such as superconductivity, magnetism, and other critical phenomena in materials. His research has often focused on the use of experimental techniques to study the properties of materials at low temperatures.

W. G. Unruh is a prominent theoretical physicist known for his work in several areas of physics, including general relativity, quantum field theory, and cosmology. One of his most significant contributions is the formulation of what is now known as the Unruh effect. This phenomenon predicts that an observer accelerating through a vacuum will observe thermal radiation (akin to blackbody radiation), even though an inertial observer in that same vacuum would perceive it as empty space.

Russell W. Porter was an American astronomer and a significant figure in the field of optics and telescope design, particularly known for his pioneering work in amateur astronomy. He is best known for his contributions to the design and construction of high-quality telescopes, particularly the "Porter Garden Telescope," which served as a model for many amateur telescopes in the 20th century.