ArchitectureArchitecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing buildings or other structures. The term comes ; ; . Architectural works, in the material form of buildings, are often perceived as cultural symbols and as works of art. Historical civilizations are often identified with their surviving architectural achievements.
Public housingPublic housing is a form of housing tenure in which the property is usually owned by a government authority, either central or local. Although the common goal of public housing is to provide affordable housing, the details, terminology, definitions of poverty, and other criteria for allocation vary within different contexts. In the United States, public housing developments are classified either as housing projects that are owned by a city's Housing authority or federally subsidized public housing operated through HUD.
Housing estateA housing estate (or sometimes housing complex, housing development, subdivision or community) is a group of homes and other buildings built together as a single development. The exact form may vary from country to country. Popular throughout the United States and the United Kingdom, they often consist of single family detached, semi-detached ("duplex") or terraced homes, with separate ownership of each dwelling unit. Building density depends on local planning norms.
Architecture of IndiaIndian architecture is rooted in the history, culture, and religion of India. Among several architectural styles and traditions, the best-known include the many varieties of Hindu temple architecture and Indo-Islamic architecture, especially Rajput architecture, Mughal architecture, South Indian architecture, and Indo-Saracenic architecture. Early Indian architecture was made from wood, which did not survive due to rotting and instability in the structures.
Housing associationIn Ireland and the United Kingdom, housing associations are private, non-profit making organisations that provide low-cost "social housing" for people in need of a home. Any budget surplus is used to maintain existing housing and to help finance new homes and it cannot be used for personal benefit of directors or shareholders. Although independent, they are regulated by the state and commonly receive public funding. They are now the United Kingdom's major providers of new housing for rent, while many also run shared ownership schemes to help those who cannot afford to buy a home outright.
Chinese architectureChinese architecture is the embodiment of an architectural style that has developed over millennia in China and has influenced architecture throughout East Asia. Since its emergence during the early ancient era, the structural principles of its architecture have remained largely unchanged. The main changes involved diverse decorative details.
Banach spaceIn mathematics, more specifically in functional analysis, a Banach space (pronounced ˈbanax) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly.
Christophe SouléChristophe Soulé (born 1951) is a French mathematician working in arithmetic geometry. Soulé started his studies in 1970 at École Normale Supérieure in Paris. He completed his Ph.D. at the University of Paris in 1979 under the supervision of Max Karoubi and Roger Godement, with a dissertation titled K-Théorie des anneaux d'entiers de corps de nombres et cohomologie étale. In 1979, he was awarded a CNRS Bronze Medal. He received the Prix J. Ponti in 1985 and the Prize Ampère in 1993.
Fréchet spaceIn functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm). All Banach and Hilbert spaces are Fréchet spaces. Spaces of infinitely differentiable functions are typical examples of Fréchet spaces, many of which are typically Banach spaces.
Software architectureSoftware architecture is the set of structures needed to reason about a software system and the discipline of creating such structures and systems. Each structure comprises software elements, relations among them, and properties of both elements and relations. The architecture of a software system is a metaphor, analogous to the architecture of a building. It functions as the blueprints for the system and the development project, which project management can later use to extrapolate the tasks necessary to be executed by the teams and people involved.
Affordable housingAffordable housing is housing which is deemed affordable to those with a household income at or below the median as rated by the national government or a local government by a recognized housing affordability index. Most of the literature on affordable housing refers to mortgages and a number of forms that exist along a continuum – from emergency homeless shelters, to transitional housing, to non-market rental (also known as social or subsidized housing), to formal and informal rental, indigenous housing, and ending with affordable home ownership.
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.
Sequence spaceIn functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication.
Lp spaceDISPLAYTITLE:Lp space In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue , although according to the Bourbaki group they were first introduced by Frigyes Riesz . Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces.
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.
Normed vector spaceIn mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If is a vector space over , where is a field equal to or to , then a norm on is a map , typically denoted by , satisfying the following four axioms: Non-negativity: for every ,. Positive definiteness: for every , if and only if is the zero vector.
Geometric transformationIn mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).
Euclidean spaceEuclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension. For n equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes.
CapitalismCapitalism is an economic system based on the private ownership of the means of production and their operation for profit. Central characteristics of capitalism include capital accumulation, competitive markets, price systems, private property, property rights recognition, voluntary exchange, and wage labor. In a market economy, decision-making and investments are determined by owners of wealth, property, or ability to maneuver capital or production ability in capital and financial markets—whereas prices and the distribution of goods and services are mainly determined by competition in goods and services markets.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
