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.
PiThe number pi (paɪ; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number pi appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern.
Dirichlet problemIn mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. The Dirichlet problem can be solved for many PDEs, although originally it was posed for Laplace's equation.
Trigonometric functionsIn mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
Hydrogen storageSeveral methods exist for storing hydrogen. These include mechanical approaches such as using high pressures and low temperatures, or employing chemical compounds that release H2 upon demand. While large amounts of hydrogen are produced by various industries, it is mostly consumed at the site of production, notably for the synthesis of ammonia. For many years hydrogen has been stored as compressed gas or cryogenic liquid, and transported as such in cylinders, tubes, and cryogenic tanks for use in industry or as propellant in space programs.
Continued fractionIn mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
Paper chemicalsPaper chemicals designate a group of chemicals that are used for paper manufacturing, or modify the properties of paper. These chemicals can be used to alter the paper in many ways, including changing its color and brightness, or by increasing its strength and resistance to water. The chemicals can be defined on basis of their usage in the process. Chemical usage is not only for imparting properties to paper but to handle the water cycles in the process, conditioning of fabrics, cleaning of equipment and several other applications.
States' rightsIn American political discourse, states' rights are political powers held for the state governments rather than the federal government according to the United States Constitution, reflecting especially the enumerated powers of Congress and the Tenth Amendment. The enumerated powers that are listed in the Constitution include exclusive federal powers, as well as concurrent powers that are shared with the states, and all of those powers are contrasted with the reserved powers—also called states' rights—that only the states possess.
Coated paperCoated paper (also known as enamel paper, gloss paper, and thin paper) is paper that has been coated by a mixture of materials or a polymer to impart certain qualities to the paper, including weight, surface gloss, smoothness, or reduced ink absorbency. Various materials, including kaolinite, calcium carbonate, bentonite, and talc, can be used to coat paper for high-quality printing used in the packaging industry and in magazines. The chalk or china clay is bound to the paper with synthetic s, such as styrene-butadiene latexes and natural organic binders such as starch.
