Hilbert spaceIn mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space.
Spatial databaseA spatial database is a general-purpose database (usually a relational database) that has been enhanced to include spatial data that represents objects defined in a geometric space, along with tools for querying and analyzing such data. Most spatial databases allow the representation of simple geometric objects such as points, lines and polygons. Some spatial databases handle more complex structures such as 3D objects, topological coverages, linear networks, and triangulated irregular networks (TINs).
SeoulSeoul (soʊl, sʌul; Capital), officially known as the Seoul Special City, is the capital and largest metropolis of the Republic of Korea (South Korea). According to the 2020 census, Seoul has a population of 9.9 million people, and forms the heart of the Seoul Capital Area with the surrounding Incheon metropolis and Gyeonggi province. Considered to be a global city and rated as an Alpha – City by Globalization and World Cities Research Network (GaWC), Seoul was the world's fourth largest metropolitan economy in 2014, following Tokyo, New York City and Los Angeles.
Space (mathematics)In mathematics, a space is a set (sometimes called a universe) with some added structure. While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can be elements of a set, functions on another space, or subspaces of another space.
Permanent residencyPermanent residency is a person's legal resident status in a country or territory of which such person is not a citizen but where they have the right to reside on a permanent basis. This is usually for a permanent period; a person with such legal status is known as a permanent resident. In the United States, such a person is referred to as a green card holder but more formally as a Lawful Permanent Resident (LPR). Permanent residency itself is distinct from right of abode, which waives immigration control for such persons.
Sanitary sewerA sanitary sewer is an underground pipe or tunnel system for transporting sewage from houses and commercial buildings (but not stormwater) to a sewage treatment plant or disposal. Sanitary sewers are a type of gravity sewer and are part of an overall system called a "sewage system" or sewerage. Sanitary sewers serving industrial areas may also carry industrial wastewater. In municipalities served by sanitary sewers, separate storm drains may convey surface runoff directly to surface waters.
FreedomFreedom is the power or right to act, speak, and change as one wants without hindrance or restraint. Freedom is often associated with liberty and autonomy in the sense of "giving oneself one's own laws". In one definition, something is "free" if it can change and is not constrained in its present state. Physicists and chemists use the word in this sense. Philosophy and religion sometimes associate freedom with free will, as distinct from predestination.
Economic geographyEconomic geography is the subfield of human geography which studies economic activity and factors affecting them. It can also be considered a subfield or method in economics. There are four branches of economic geography. Economic geography takes a variety of approaches to many different topics, including the location of industries, economies of agglomeration (also known as "linkages"), transportation, international trade, development, real estate, gentrification, ethnic economies, gendered economies, core-periphery theory, the economics of urban form, the relationship between the environment and the economy (tying into a long history of geographers studying culture-environment interaction), and globalization.
Vector spaceIn mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space.
Environmental issuesEnvironmental issues are disruptions in the usual function of ecosystems. Further, these issues can be caused by humans (human impact on the environment) or they can be natural. These issues are considered serious when the ecosystem cannot recover in the present situation, and catastrophic if the ecosystem is projected to certainly collapse. Environmental protection is the practice of protecting the natural environment on the individual, organizational or governmental levels, for the benefit of both the environment and humans.
Human geographyHuman geography or anthropogeography is the branch of geography that studies spatial relationships between human communities, cultures, economies, and their interactions with the environment, examples of which is studied in schools are urban sprawl, and urban redevelopment. It analyzes spatial interdependencies between social interactions and the environment through qualitative and quantitative methods.
Academic freedomAcademic freedom is a moral and legal concept expressing the conviction that the freedom of inquiry by faculty members is essential to the mission of the academy as well as the principles of academia, and that scholars should have freedom to teach or communicate ideas or facts (including those that are inconvenient to external political groups or to authorities) without fear of repression, job loss, or imprisonment.
