Zariski's lemma is a result in algebraic geometry that is named after the mathematician Oscar Zariski. It provides a condition for the vanishing of a polynomial function on an algebraic variety.

Higher-dimensional Einstein gravity refers to the generalization of Einstein's theory of general relativity to spaces with more than four dimensions. In Einstein's original formulation, gravity is described as the curvature of spacetime, which is modeled by a four-dimensional pseudo-Riemannian manifold. In the case of higher-dimensional Einstein gravity, one extends this framework to \(d\)-dimensional spacetimes, where \(d > 4\).

Higher order coherence refers to the statistical properties of light (or other fields) that go beyond the second-order autocorrelation, which is typically used to describe intensity fluctuations of classical and quantum light sources. In classical optics, coherence is often described using first-order and second-order coherence measures. 1. **First-order coherence** relates to the phase relation between light waves and is typically expressed through the complex degree of coherence. It is crucial for phenomena such as interference.

High-Power Impulse Magnetron Sputtering (HiPIMS) is an advanced thin-film deposition technique that enhances the traditional magnetron sputtering process by using high-power pulses instead of continuous power. This technology is utilized to create thin films with enhanced properties, which can be utilized in a variety of applications, including coatings for tools, electronics, optics, and more.

High rail refers to a vehicle that is capable of operating on both road and rail tracks. These vehicles are often used for maintenance and inspection of railway lines and infrastructure. High rail vehicles have special equipment, such as retractable rail wheels, that can be lowered onto the tracks for railway operations and raised for conventional road travel. High rail technology allows for efficient movement between road and rail without the need for changing vehicles, making it easier for maintenance crews to access various parts of the railway network.

Hilbert's twentieth problem is one of the 23 problems presented by the German mathematician David Hilbert in 1900. The problem specifically deals with the field of mathematics known as algebraic number theory and has to do with the decidability of certain kinds of equations. The statement of Hilbert's twentieth problem asks whether there is an algorithm to determine whether a given Diophantine equation has a solution in integers.

The history of artificial life (ALife) encompasses a multidisciplinary field that studies life processes through the synthesis and simulation of living systems in artificial environments. It covers several areas including biology, computer science, robotics, and philosophy. Here's a brief overview of its development: ### Early Concepts and Foundations - **1920s-1950s**: Early thoughts on artificial life can be traced back to ideas in literature and philosophy about the nature of life.

A **holonomic function** is a function that satisfies a linear ordinary differential equation with polynomial coefficients.

The history of laptops is a fascinating journey that reflects advances in technology, design, and user needs. Here's an overview of key milestones in the evolution of laptops: ### 1960s - 1970s: Early Concepts - **1968**: The concept of a portable computer was first introduced by Alan Kay at Xerox PARC, who envisioned a "Dynabook" that would be a personal computer for children.

A Hodge structure is a concept in algebraic geometry and differential geometry that is used to study the relationships between algebraic and topological properties of complex manifolds. It provides a bridge between the geometric structure of a manifold and its algebraic properties. A Hodge structure on a vector space \( V \) over the complex numbers can be described as a decomposition of the space into subspaces that reflect the complex geometry of the underlying manifold.

Hölder summation is a concept in mathematical analysis related to the convergence of series and is particularly tied to the idea of summability methods. It is named after the German mathematician Otto Hölder, who developed theories around function spaces and converging series. Hölder summation provides a way to assign a value to a divergent series by transforming it under certain conditions.

Holmgren's wool test is a diagnostic test used to assess color vision deficiency, particularly in relation to red-green color blindness. It was developed by the Swedish ophthalmologist Alarik Holmgren in the late 19th century. In the test, the subject is presented with a set of colored wool strands, typically in various shades of green and red, and is asked to sort them into piles based on color.

Homogeneous coordinates are a system of coordinates used in projective geometry, which provides a way to represent points in a projective space. In computer graphics, robotics, and computer vision, homogeneous coordinates are commonly used to simplify various mathematical operations, particularly when dealing with transformations such as translation, rotation, scaling, and perspective projections.

"Homo Ludens" is a concept developed by the Dutch historian and cultural theorist Johan Huizinga in his 1938 book of the same name. The term translates to "man the player" or "playing man" and emphasizes the importance of play in human culture and society. Huizinga argues that play is a fundamental aspect of human existence, influencing culture, social interactions, art, and even the development of civilization itself.

Homothety, also known as dilation or similarity transformation, is a geometric transformation that alters the size of a figure while maintaining its shape and relative proportions. It can be described as a scaling transformation around a specific point, known as the center of homothety. In formal terms, a homothety can be defined by the following characteristics: 1. **Center of Homothety**: This is a fixed point in the plane from which the scaling occurs.

The Horace Hearne Institute for Historical and Cultural Studies is an academic research organization based in the United States. It is typically focused on promoting research and scholarship in the fields of history, culture, and related disciplines. The institute aims to support and disseminate studies that contribute to a deeper understanding of historical events and cultural developments. Its activities may include hosting lectures, publishing research, and fostering collaborations among scholars.

The Hosoya index, also known as the Hosoya polynomial or the Hosoya number, is a graph-theoretic invariant used to measure the structural complexity of a molecular graph, which represents a chemical compound. Named after Hiroshi Hosoya, the index is particularly useful in the field of cheminformatics and quantitative structure-activity relationship (QSAR) studies. The Hosoya index is defined as the total number of matchings (or perfect matchings) in a graph.

"How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension" is a seminal work by the mathematician and statistician Benoit Mandelbrot, published in 1967. In this work, Mandelbrot explores the concept of self-similarity in natural shapes and discusses the implications of measuring irregularities in coastlines using fractal geometry.

Hua's lemma is a result in number theory, particularly in the area of additive number theory, often associated with the work of the Chinese mathematician Hua Luogeng. It generally pertains to the distribution of integers and can be used in problems related to additive representations or counting problems. The lemma can be formulated in terms of a sum over integers, usually involving counting the number of ways an integer can be expressed as a sum of a fixed number of integers from a specific set.