Allylic strain refers to the steric and electronic interactions that occur in allylic systems, where substituents are located on adjacent carbon atoms in a double bond configuration or where there is a single carbon-carbon bond adjacent to a double bond. This strain arises mainly from the positioning of substituents at the allylic positions, which can lead to increased steric hindrance and torsional strain.

Trigram search is a technique used in text processing and information retrieval to improve the efficiency and accuracy of searching for substrings or phrases within larger bodies of text. It involves breaking down words or text into groups of three consecutive characters, known as trigrams. ### How Trigram Search Works 1. **Tokenization**: The text is first split into individual words or tokens. 2. **Trigram Generation**: Each word is then processed to extract all possible trigrams.

TriG is a serialization format for RDF (Resource Description Framework) data. It is an extension of the Turtle (Terse RDF Triple Language) syntax, designed to facilitate the representation of RDF graphs with named graphs. Named graphs allow for the representation of RDF data sets where the data can be identified by a graph name (often a URI), making it easier to manage and reason about the data in complex applications.

Supercomputing in China has evolved to become one of the most advanced and influential sectors in the global computing landscape. The country has made significant investments in supercomputing technology, infrastructure, and talent development. Here are some key aspects of supercomputing in China: 1. **Leading Supercomputers**: China has been home to several of the world's fastest supercomputers.

A "weather rock" is a humorous and simple tool often used to indicate weather conditions. It is essentially a rock that is accompanied by a set of guidelines or a legend that explains how to interpret the weather based on the condition of the rock. For example: - If the rock is wet, it's raining. - If the rock is white, it's snowing. - If the rock is moving, it's windy. - If the rock is hard to see, it's foggy.

Yuri Nesterenko is a prominent mathematician known for his contributions to number theory, particularly in the areas of Diophantine equations and algebraic number theory. He has made significant advancements in understanding the distribution of rational points on algebraic varieties and has worked on various problems related to arithmetic geometry. Nesterenko is also known for his work in transcendental number theory and has produced important results concerning the normal forms of certain algebraic varieties.

Free convolution is a concept in the field of free probability theory, which is an area of mathematics that studies non-commutative random variables in a way that is analogous to classical probability theory. Free probability was introduced by Dan Voiculescu in the 1990s and has since become an important area of research, especially in the study of random matrices and operator algebras.

The truncated great dodecahedron is a convex Archimedean solid. It is derived from the great dodecahedron, which is one of the duals of the regular dodecahedron.

The Truncated Newton method, also known as the Newton-CG (Change of Variable) method, is an optimization algorithm that combines aspects of the Newton method with techniques from conjugate gradient methods. It is particularly useful for optimizing large-scale problems where the direct computation and storage of the Hessian matrix (the matrix of second derivatives) is impractical.

Prelog strain refers to a type of strain observed in certain polymers that exhibit a characteristic behavior under stress. Particularly, it is defined in the context of the mechanical properties of polymers, where it is related to their ability to deform elastically or plastically. The term is often used in relation to the study of polymer mechanics and the response of materials to external forces.

A tube socket is an electrical component designed to hold vacuum tubes (also known as electron tubes or thermionic valves) in place within a circuit. These sockets provide a secure and reliable connection between the tube's pins and the circuit board or chassis. Tube sockets come in various configurations to accommodate different types of vacuum tubes. They typically feature multiple holes or sockets for the tube's pins, allowing for easy insertion and removal of the tube without soldering or desoldering.

Turtle syntax refers to a specific way of representing data using Resource Description Framework (RDF) in a compact and human-readable text format. RDF is a standard model for data interchange on the web, and Turtle (Terse RDF Triple Language) is one of the serialization formats used to express RDF data. In Turtle syntax, data is expressed in terms of "triples," which consist of three parts: 1. **Subject**: The resource or entity being described.

A two-dimensional gas refers to a theoretical model in which gas particles are confined to move in two dimensions, effectively creating a system where all motion occurs on a flat surface (like a plane) rather than in three-dimensional space. This model is often used in statistical mechanics and condensed matter physics to explore and understand the properties of systems that can be approximated as having only two degrees of freedom in spatial motion.

A singular point of an algebraic variety is a point where the variety is not well-behaved in terms of its geometric structure. More formally, a point \( P \) on an algebraic variety \( V \) defined by a set of polynomial equations is termed a singular point if the local behavior of the variety at that point exhibits some form of "singularity," meaning that it fails to meet certain smoothness conditions.

Sōichi Kakeya is a Japanese mathematician known for his work in the fields of geometry and analysis. He is particularly recognized for contributions related to the Kakeya needle problem, which involves determining the minimum area required to rotate a needle of a certain length. The problem has deep implications in various areas of mathematics, including measure theory and the study of fractals.

A "solved game" is a term used in game theory and computer science to refer to a game for which the outcome can be accurately predicted from any position, assuming both players play optimally. In other words, for a solved game, we know the best strategies for all players involved and what the result will be (whether it's a win, loss, or draw) from any possible state of the game.

A ceiling projector is a type of video projector that is mounted on the ceiling of a room to display images or videos onto a screen or wall. This positioning can be beneficial for various applications, including home theaters, classrooms, conference rooms, and public presentations. Ceiling projectors are typically designed for permanent installation and can provide a clean, unobtrusive look, minimizing floor clutter.

The term "sound speed gradient" generally refers to the variation of sound speed with respect to a particular variable, such as depth in a medium or distance from a source. This concept is particularly relevant in fields such as acoustics, oceanography, and meteorology. In the context of oceanography, for example, the sound speed gradient describes how the speed of sound changes with depth in the ocean. Several factors influence this, including temperature, salinity, and pressure.