In mathematics, particularly in differential geometry, the concept of tangent space is fundamental to understanding the local properties of differentiable manifolds. ### Definition The **tangent space** at a point on a manifold is a vector space that consists of the tangent vectors at that point. Intuitively, you can think of it as the space of all possible directions in which you can tangentially pass through a given point on the manifold. ### Formal Construction 1.

A **prime power** is a number that can be expressed in the form \( p^k \), where \( p \) is a prime number and \( k \) is a positive integer. In other words, a prime power is a number that results from raising a prime number to an integer exponent greater than zero.

Machine guidance refers to the use of technology and systems to assist operators in controlling and navigating machinery and equipment. This concept is commonly applied in various industries, including construction, agriculture, and manufacturing. The goal of machine guidance is to enhance operational accuracy, efficiency, safety, and productivity. ### Key Components of Machine Guidance: 1. **Sensors and GPS Technology**: Machine guidance systems often use sensors to gather real-time data about the environment, along with GPS technology to provide precise location information.

As of my last knowledge update in October 2021, "Discoveries" by Federico Bellini does not correspond to a widely recognized work or concept in literature, art, or any other field. It's possible that it could be a recent release, a lesser-known work, or perhaps a self-published piece that gained traction after my last update.

Advanced Functional Materials is a multidisciplinary scientific journal that focuses on research in the field of materials science. It publishes high-quality articles covering a wide range of topics related to functional materials, which are materials designed to have specific properties and functionalities for various applications. These can include, but are not limited to, materials used in electronics, photonics, energy storage, nanotechnology, biomaterials, and environmental applications.

A Weyl transformation, also known as a Weyl scaling, is a type of transformation in which the metric of a space is rescaled by a smooth, positive function. It is commonly used in the context of differential geometry, theoretical physics, and especially in the study of conformal field theories and general relativity.

Applied Physics A is a peer-reviewed scientific journal that focuses on research in applied physics and related fields. It covers a wide range of topics, including materials science, optics, condensed matter physics, and nanotechnology, among others. The journal aims to provide a platform for the dissemination of innovative research that bridges the gap between theoretical physics and practical applications. It typically publishes original research articles, reviews, and sometimes letters to the editor.

An **integer literal** is a notation for representing a fixed value of an integer in programming languages. It's a way to specify integer constants directly within the code. Integer literals can appear in different forms depending on the language and the notation being used. The basic forms of integer literals include: 1. **Decimal literals**: These are numbers expressed in base 10. For example, `42` and `-7` are decimal integer literals.

The Meredith graph is a specific type of graph in the field of graph theory. It is defined as a bipartite graph and is notable because it is a regular graph with 12 vertices, where each vertex has a degree of 3. The graph consists of two sets of vertices, each containing 6 vertices, and it can be described by specific connections between these two sets.

A "quantum computer operating system". Or in English, control system + quantum error correction.

uknqt.ukri.org/wp-content/uploads/2021/10/UKNQTP-Strategic-Intent-2020.pdf page 24 mentions UKNQTP investment and gives an overview of some layers.

Nikolai Bakhvalov may refer to a specific person or name, but without more context, it's hard to provide a precise answer. There may be multiple individuals with that name across various fields such as academia, sports, or the arts.

Symplectic topology is a branch of differential topology and geometry that studies symplectic manifolds and their properties. A symplectic manifold is a smooth, even-dimensional manifold equipped with a closed, non-degenerate 2-form, called the symplectic form. This symplectic form captures essential geometric and topological information about the manifold.

Nikolai Yefimov is not a widely recognized figure in mainstream culture, history, or current events as of my last update in October 2023. It’s possible that he could refer to a lesser-known individual, a fictional character, or someone who has gained recognition after that date.

"Discoveries" by Fernand Rigaux is a work that presents an overview of various significant discoveries across different fields, such as science, technology, and exploration. Rigaux, through this work, aims to highlight the impact these discoveries have had on human civilization and our understanding of the world. Although details about the book’s content and themes may vary, the general premise revolves around celebrating innovation and the curiosity that drives humanity to explore and discover new truths.

The Serre–Swan theorem is a fundamental result in algebraic topology and differential geometry that establishes a profound connection between vector bundles and sheaves of modules.

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.

"Discoveries" by Francesco Manca is a book that explores the themes of innovation, exploration, and the scientific method. It typically combines history, philosophy, and science to discuss significant discoveries and their impact on human knowledge and society.