The Mehler kernel is a function that arises in the context of orthogonal polynomials, particularly in relation to the theory of Hermite polynomials and the heat equation. It plays a significant role in probability theory, mathematical physics, and the study of stochastic processes.

Continuous \( q \)-Laguerre polynomials are a family of orthogonal polynomials that generalize the classical Laguerre polynomials by incorporating the concept of \( q \)-calculus, which deals with discrete analogs of calculus concepts. These polynomials arise in various areas of mathematics and physics, including approximation theory, special functions, and quantum mechanics.

"Space by century" could refer to various interpretations, such as the history of space exploration, the development of astronomical knowledge, or the evolution of concepts regarding space in human thought and culture.

Gegenbauer polynomials, denoted as \( C_n^{(\lambda)}(x) \), are a family of orthogonal polynomials that generalize Legendre polynomials and Chebyshev polynomials. They arise in various areas of mathematics and are particularly useful in solving problems involving spherical harmonics and certain types of differential equations.

Hahn polynomials are a class of orthogonal polynomials that arise in the context of the theory of orthogonal polynomials on discrete sets. They are named after the mathematician Wolfgang Hahn, who introduced them in the early 20th century. Hahn polynomials are defined for a discrete variable and are often associated with certain types of hypergeometric functions.

Pseudo-Jacobi polynomials are a class of orthogonal polynomials that are related to the Jacobi polynomials but have some distinct characteristics or domains of applicability. The term "pseudo" typically refers to modifications or generalizations of well-known polynomial families that maintain certain properties or introduce new variables.

The Q-Hahn polynomials are a family of orthogonal polynomials that arise in the context of basic hypergeometric functions and q-series. They are a specific case of the more general class of q-polynomials, which are related to the theory of partition and combinatorics, as well as to special functions in mathematical physics.

Q-Racah polynomials are a class of orthogonal polynomials that arise in the context of the theory of special functions and are associated with the asymptotic theory of orthogonal polynomials. They are a generalization of the Racah polynomials and belong to the family of basic hypergeometric orthogonal polynomials.

OS/2 is an operating system that was originally developed by IBM and Microsoft in the late 1980s. It was designed to be a robust, multitasking operating system for personal computers, especially for business and enterprise use. Although Microsoft eventually exited the OS/2 project to focus on Windows, IBM continued to develop OS/2 into the 1990s.

OS/2, which stands for Operating System/2, is a computer operating system developed by IBM in the late 1980s. Originally created as a successor to DOS, OS/2 was intended to provide a stable and capable environment for running applications in a multitasking and multiuser setting. It was co-developed with Microsoft initially, but after version 1.3, IBM took over development completely.

OS/2 drivers are software components that allow the OS/2 operating system to communicate with hardware devices and facilitate their functioning. OS/2, developed by IBM, is a multi-tasking operating system that was originally designed for personal computers, and it supports a variety of hardware components, including printers, network cards, storage devices, and graphics adapters.

ArcaOS is an operating system that is a modernized version of IBM's OS/2, which was originally developed in the 1980s as a joint project between IBM and Microsoft. ArcaOS is produced by Arca Noae, a company that aims to revive and support the legacy of OS/2 and its applications.

The Graphical Data Display Manager (GDDM) is a software tool developed by IBM, primarily used in mainframe environments. It enables users to create and manage graphical displays and presentations of data, often in conjunction with IBM's mainframe systems. GDDM allows users to visualize data in various forms such as charts, graphs, and maps. It provides a graphical interface for programming and data manipulation, making it easier for users to interpret and analyze data from large databases or mainframe applications.

An Installable File System (IFS) is a type of file system architecture that allows users to add new file system types or formats to an operating system without requiring changes to the core system itself. This is typically accomplished through a plugin or module system, where new file systems can be installed as additional components. ### Key Features of Installable File Systems: 1. **Modularity**: IFS provides a modular approach to file systems.

The fission barrier refers to the energy barrier that must be overcome for a nucleus to undergo nuclear fission. In the context of nuclear physics, fission occurs when a heavy nucleus splits into two or more lighter nuclei, accompanied by the release of energy, usually in the form of kinetic energy of the fission fragments and neutrons. The fission barrier can be conceptualized in terms of potential energy.

The Mainau Declaration is a statement that emphasizes the importance of biodiversity and its conservation. It was adopted in 1998 during a meeting of scientists, politicians, and representatives from various organizations on Mainau Island in Germany. The declaration calls for urgent action to address the global biodiversity crisis, highlighting the need for sustainable practices and policies that protect ecosystems and species.

The "Otto Hahn" is a German research vessel named after the renowned physicist Otto Hahn, who was instrumental in the discovery of nuclear fission. The ship is part of the German research fleet and is primarily used for marine research and oceanographic studies. Launched in the mid-20th century, the Otto Hahn is equipped with laboratories and cutting-edge technology to carry out a variety of scientific missions. This includes studying the marine environment, conducting biological and chemical analyses, and exploring underwater geology.

The Otto Hahn Peace Medal is an award established by the German section of the International Physicians for the Prevention of Nuclear War (IPPNW) in honor of Otto Hahn, a German chemist who was awarded the Nobel Prize in Chemistry in 1944. The medal recognizes individuals or organizations that have made significant contributions to peace, disarmament, and the prevention of nuclear war.

Cosmic dust, also known as interstellar dust or space dust, refers to tiny particles of solid material found in space. These particles are typically made up of various elements and compounds, such as silicates, carbon-based materials, metals, and ice.

Photographs of Earth from outer space refer to images captured from spacecraft, satellites, or space missions that show our planet from various distances and perspectives. These photographs can reveal the Earth's surface, atmosphere, and weather patterns, as well as human impact on the planet. They serve multiple purposes, including scientific research, environmental monitoring, communication, and aesthetic appreciation.