For purposes of this explanation, this percentage is referred to as the State's `` unadjusted Federal share ''.

For purposes of sample selection only ( individual tests were given later ) we obtained group test scores of reading achievement and intelligence from school records of the entire third-grade population in each school system.

For expository purposes, this is best treated as a model which spells out the conditions under which an important industry affected with the public interest would find it profitable to raise wages even in the absence of union pressures for higher wages.

For the purposes of setting the product price, the industry behaves as a single entity.

For the purposes of this discussion, the problem of relative prices is encompassed in these two variables, since GNP includes other prices.

For our present purposes we assume that the sole subject of bargaining is the basic wage rate ( not including productivity improvement factors or cost-of-living adjustments ), and it is this basic wage rate which determines the level of costs.

'' For present purposes it may be assumed that this charge so narrowly limited speech as to violate the federal Constitution.

For all practical purposes, the West stands disunited, undedicated, and unprepared for the tasks of world leadership.

For their purposes, oxygen and other gases were not drawn from the surrounding atmosphere through the medium of lungs but sustained artificially by solution in their shells.

For the purposes of the treaty system, Antarctica is defined as all of the land and ice shelves south of 60 ° S latitude.

For geopolitical purposes, the Sinai Peninsula of Egypt – east of the Suez Canal – is often considered part of Africa.

For socket numbers, a few well-known numbers were reserved for special purposes specific to the AppleTalk protocol itself.

For example, letters 1, 5, and 8 contain a discussion on the question, whether the use of a piece of metal with the figure of a lion, as a talisman, is permitted by Jewish law for medicinal purposes, or is prohibited as idolatrous.

For administrative purposes the archipelago constitutes the comune of Favignana in the Province of Trapani.

For comparison purposes that is approximately the same size as Aylesbury, Carlisle, Guildford or Scunthorpe urban areas.

For commercial purposes, it is derived primarily from Gelidium amansii.

For statistical purposes, Baker is grouped with the United States Minor Outlying Islands.

For purposes of scoring and reference, each player is identified by one of the points of the compass and thus North and South play against East and West.

For calendric purposes, Bede made a new calculation of the age of the world since the creation, which he dated as 3952 BC.

For scoring purposes, a standing eight count is treated as a knockdown.

For all practical purposes that was the Baltic language until 1919.

For most purposes, most jurisdictions, including the U. S. federal system and most states, have merged the two courts.

For purposes of international communication and trade, the official names of the chemical elements both ancient and more recently recognized are decided by the International Union of Pure and Applied Chemistry ( IUPAC ), which has decided on a sort of international English language, drawing on traditional English names even when an element's chemical symbol is based on a Latin or other traditional word, for example adopting " gold " rather than " aurum " as the name for the 79th element ( Au ).

For international banks, including the 55 member central banks of the Bank for International Settlements, the threshold is 8 % ( see the Basel Capital Accords ) of risk-adjusted assets, whereby certain assets ( such as government bonds ) are considered to have lower risk and are either partially or fully excluded from total assets for the purposes of calculating capital adequacy.

For enumeration purposes the country is demarcated into 4, 042 enumeration areas.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

For example, in the Schrödinger picture, there is a linear operator U with the property that if an electron is in state right now, then in one minute it will be in the state, the same U for every possible.

For example, observable physical quantities are represented by self-adjoint operators, such as energy or momentum, whereas transformative processes are represented by unitary linear operators such as rotation or the progression of time.

For example, the condition number associated with the linear equation

For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems.

For any n, the divergence is a linear operator, and it satisfies the " product rule "

For the statistics usage, see hierarchical linear modeling.

For a flow, the vector field Φ ( x ) is a linear function of the position in the phase space, that is,

For example, an endomorphism of a vector space V is a linear map ƒ: V → V, and an endomorphism of a group G is a group homomorphism ƒ: G → G. In general, we can talk about endomorphisms in any category.

For other ways to solve this kind of equations, see below, System of linear equations.

For example, according to ancient Hebrew belief, life takes a linear ( and not cyclical ) path ; the world began with God and is constantly headed toward God ’ s final goal for creation.

For an overview of a linear implementation of this framework, see linear regression.

For other examples of quotient objects, see quotient ring, quotient space ( linear algebra ), quotient space ( topology ), and quotient set.

For example, a bijective linear map is an isomorphism between vector spaces, and a bijective continuous function whose inverse is also continuous is an isomorphism between topological spaces, called a homeomorphism.

For molecules with N atoms in them, linear molecules have 3N – 5 degrees of vibrational modes, whereas nonlinear molecules have 3N – 6 degrees of vibrational modes ( also called vibrational degrees of freedom ).

For every finite dimensional matrix Lie algebra, there is a linear group ( matrix Lie group ) with this algebra as its Lie algebra.

For a population of size n, with a sequence of values y < sub > i </ sub >, i = 1 to n, that are indexed in non-decreasing order ( y < sub > i </ sub > ≤ y < sub > i + 1 </ sub >), the Lorenz curve is the continuous piecewise linear function connecting the points ( F < sub > i </ sub >, L < sub > i </ sub > ), i

For linear relations, regression analyses here are based on forms of the general linear model.

For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

For example, consider the case where the function is a linear function of the form

For example, bacterial chromosomes, plasmids, mitochondrial DNA and chloroplast DNA are usually circular double-stranded DNA molecules, while chromosomes of the eukaryotic nucleus are usually linear double-stranded DNA molecules.

For example, in classical mechanics, the derivative is used ubiquitously, and in quantum mechanics, observables are represented by linear operators.