In general, a letter of an abugida transcribes a consonant.Letters are written as a linear sequence, in most cases left to right.Vowels are written through modification of these consonantal letters, either by means of diacritics (which may not follow the direction of writing the letters), or by changes in the form of the letter itself.…

The large reels would occasionally move to take up written tape and play out more blank tape into the vacuum columns.Some modern designs are still developed to operate in a non-linear fashion.IBM's 3xxx formats are designed to keep the tape moving irrespective of the data buffer - segments are written when data is available, but gaps are written when buffers run empty.…

During the second half of the twentieth century, mathematicians such as Chevalley and Steinberg also increased our understanding of finite analogs of classical groups, and other related groups.One such family of groups is the family of general linear groups over finite fields.Finite groups often occur when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations.…

Sign languages exploit the unique features of the visual medium (sight), but may also exploit tactile features (tactile sign languages).Spoken language is by and large linear; only one sound can be made or received at a time.Sign language, on the other hand, is visual and, hence, can use simultaneous expression, although this is limited articulatorily and linguistically.…

This fact plays a key role in the impossibility of solving a general algebraic equation of degree in radicals.The next important class of groups is given by matrix groups, or linear groups.Here G is a set consisting of invertible matrices of given order n over a field K that is closed under the products and inverses.…

They can be joined together in one long linear chain, or they may be branched.Two of the most common polysaccharides are cellulose and glycogen, both consisting of repeating glucose monomers.…

The function is called the potential energy of a linear spring.Elastic potential energy is the potential energy of an elastic object (for example a bow or a catapult) that is deformed under tension or compression (or stressed in formal terminology).…

Common to all games in the Exile series are 2D graphics and basic sound.The games are designed to be non-linear and long in gameplay length.…

An example of a linear time series model is an autoregressive moving average model.

To do this, one must add all powers of and their linear combinations as well.Formation of the polynomial ring, together with forming factor rings by factoring out ideals, are important tools for constructing new rings out of known ones.…

The condition number is frequently applied to questions in linear algebra, in which case the derivative is straightforward but the error could be in many different directions, and is thus computed from the geometry of the matrix.More generally, condition numbers can be defined for non-linear functions in several variables.A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned.…

Valley erosion is occurring due to the flow of the stream, and the boulders and stones (and much of the soil) that are lying on the edges are glacial till that was left behind as ice age glaciers flowed over the terrain.Valley or stream erosion occurs with continued water flow along a linear feature.The erosion is both downward, deepening the valley, and headward, extending the valley into the hillside, creating head cuts and steep banks.…

The presence of continuous symmetries expressed via a Lie group action on a manifold places strong constraints on its geometry and facilitates analysis on the manifold.Linear actions of Lie groups are especially important, and are studied in representation theory.In the 1940s-1950s, Ellis Kolchin, Armand Borel, and Claude Chevalley realised that many foundational results concerning Lie groups can be developed completely algebraically, giving rise to the theory of algebraic groups defined over an arbitrary field.…

Determinants could also be used to solve systems of linear equations (see Cramer's rule), but in real applications, Gaussian elimination is a faster method.In general, the action of a linear transformation may be quite complex.Attention to low-dimensional examples gives an indication of the variety of their types.…

Conversely, any linear program can be converted into a two-player, zero-sum game by using a change of variables that puts it in the form of the above equations.So such games are equivalent to linear programs, in general.Many economic situations are not zero-sum, since valuable goods and services can be created, destroyed, or badly allocated in a number of ways, and any of these will create a net gain or loss of utility to numerous stakeholders.…

Their placement on the walls required the devotee to walk through the aisles and 'read' the narratives depicted in various episodes.The narrative episodes are depicted one after another although not in a linear order.Their identification has been a core area of research since the site's rediscovery in 1819.…

Recently, complexity has become a natural domain of interest of real world socio-cognitive systems and emerging systemics research.Complex systems tend to be high-dimensional, non-linear, and difficult to model.In specific circumstances, they may exhibit low-dimensional behaviour.…

A relation that is reflexive, antisymmetric, and transitive is called a partial order.A partial order that is total is called a total order, simple order, linear order, or a chain.A linear order where every nonempty subset has a least element is called a well-order.…

In statistics, the term linear model is used in different ways according to the context.The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model.…

For example, bijective operators preserving the structure of a vector space are precisely the invertible linear operators.They form the general linear group under composition.They do not form a vector space under the addition of operators, e.g. both id and -id are invertible (bijective), but their sum, 0, is not.…