The 1980s was a transformative decade in the world of computing, marked by significant technological advancements, the introduction of personal computers (PCs), and the growth of software and networking. Here are some key highlights from that era: 1. **Rise of Personal Computers**: The 1980s saw a surge in the popularity and availability of personal computers.

The 1990s was a transformative decade in computing, marked by significant technological advancements, the rise of the internet, and the commercialization of personal computing. Here are some key highlights from that era: 1. **Personal Computers (PCs)**: The 1990s saw the widespread adoption of personal computers in homes and businesses. Companies like IBM, Dell, and Compaq were key players.

In group theory, the term "core" can refer to a specific concept related to the notion of a normal subgroup. The core of a subgroup \( H \) of a group \( G \), often denoted as \( \text{Core}_G(H) \), is defined as the largest normal subgroup of \( G \) that is contained within \( H \).

The 20th century witnessed remarkable developments in computer technology, leading to advancements that have profoundly shaped modern society. Here’s an overview of key introductions and milestones related to computers during that period: ### Early Computing Devices (1940s) - **Mechanical Computers**: Before the electronic computer revolution, mechanical devices, such as the Analytical Engine proposed by Charles Babbage in the 19th century and later adaptions, were designed but not fully realized during that time.

The history of computing hardware from the 1960s to the present is marked by significant technological advancements and paradigmatic shifts. Here’s an overview of the major developments during this period: ### 1960s: Mainframes and Minicomputers - **Mainframes:** The decade saw the prominence of large mainframe computers, used primarily by governments and large corporations for business, scientific, and engineering tasks.

De Sitter invariant special relativity refers to a theoretical framework that extends the principles of special relativity to include de Sitter space, which is a model of spacetime that includes a positive cosmological constant. This framework can be seen as an extension of the usual flat Minkowski spacetime of special relativity, incorporating the geometric properties associated with de Sitter space, which has a constant positive curvature.

In mathematics, "1990s" often refers to the decade that spans from 1990 to 1999. This does not have a specific mathematical meaning, but the 1990s were notable for several developments in various fields of mathematics. During this decade, significant progress was made in areas such as: 1. **Computer Science and Mathematics**: The rise of computational mathematics and numerical methods became more prominent, with advancements in algorithms, complexity theory, and optimization.

The 20th century was a prolific period for mathematics, marked by significant advancements and the contributions of numerous influential mathematicians. Here are some key figures and developments from that era: 1. **David Hilbert**: Known for his work in various fields including algebra, number theory, and mathematical logic, Hilbert is famous for his formulation of Hilbert's problems in 1900, which set the agenda for much of 20th-century mathematics.

The term "Soviet physicists" refers to scientists who specialized in the field of physics and worked in the Soviet Union from its establishment in 1922 until its dissolution in 1991. During this period, the Soviet Union was home to many influential physicists who made significant contributions to various areas of physics, including theoretical and experimental physics, astrophysics, condensed matter physics, and nuclear physics.

The term "Yugoslav physicists" typically refers to physicists from the former Yugoslavia, a multi-ethnic state in Southeast Europe that existed from 1918 until its dissolution in the early 1990s. Yugoslavia produced several notable physicists who made significant contributions to various fields of physics, including theoretical, experimental, and applied physics. Some prominent Yugoslav physicists include: 1. **Milan R.

The 20th century saw remarkable advancements in physics, largely driven by the work of many influential American physicists. Here are some key figures and their contributions: 1. **Albert Einstein** (1879-1955) - Although German-born, Einstein became a key figure in American physics after moving to the U.S. in 1933. His theories of Special and General Relativity fundamentally changed our understanding of space, time, and gravity.

The 20th century saw significant contributions from Dutch physicists to various fields of physics. Here are some notable figures and their achievements: 1. **Hendrik Lorentz (1853–1928)** - Lorentz made groundbreaking contributions to the understanding of electromagnetism and is best known for the Lorentz transformations, which are fundamental to Einstein's theory of special relativity. He was awarded the Nobel Prize in Physics in 1902. 2. **Albert A.

The 20th century saw significant contributions from Israeli physicists in various fields of physics. Here are a few notable figures: 1. **Raphael Mechoulam** - Known for his groundbreaking work in the field of cannabinoid research, Mechoulam is often referred to as the "father of cannabis research." His discoveries have implications in both physics (in terms of the properties of cannabinoids) and medicine.

The 20th century was a remarkable period for Japanese physics, marked by significant contributions from various physicists who made notable advancements in different areas of the field. Here are some prominent Japanese physicists from that era: 1. **Hideki Yukawa (1907–1981)**: Yukawa is best known for his prediction of the existence of the meson, a particle that mediates the strong nuclear force.

The 20th century saw significant contributions from Australian physicists in various fields, including quantum mechanics, nuclear physics, and astrophysics. Here are some notable figures: 1. **William Lawrence Bragg (1890-1971)**: Bragg was a physicist who, along with his father, William Henry Bragg, won the Nobel Prize in Physics in 1915 for their work in X-ray crystallography.

The 20th century was a remarkable period for British physics, marked by significant contributions from numerous physicists who made groundbreaking advancements in various fields. Here are some notable British physicists from that era: 1. **J.J. Thomson (1856-1940)**: Known for discovering the electron in 1897, he was awarded the Nobel Prize in Physics in 1906 for his work on electrical conductivity in gases.

A Dedekind group is a specific type of group in the field of abstract algebra, characterized by certain structural properties. The most common definition is that a Dedekind group is a group in which every subgroup is normal. This means that for any subgroup \( H \) of a Dedekind group \( G \), the condition \( gHg^{-1} = H \) holds for every element \( g \) in \( G \).