In mathematics, the term linear is used in two distinct senses for two different properties:
An example of a linear function is the function defined by that maps the real line to a line in the Euclidean plane R that passes through the origin. An example of a linear polynomial in the variables and is
In fluid dynamics and nautical terminology, a breaking wave or breaker is a wave with enough energy to "break" at its peak, reaching a critical level at which linear energy transforms into wave turbulence energy with a distinct forward curve. At this point, simple physical models that describe wave dynamics often become invalid, particularly those that assume linear behaviour.
The most generally familiar sort of breaking wave is the breaking of water surface waves on a coastline. Wave breaking generally occurs where the amplitude reaches the point that the crest of the wave actually overturns. Certain other effects in fluid dynamics have also been termed "breaking waves", partly by analogy with water surface waves. In meteorology, atmospheric gravity waves are said to break when the wave produces regions where the potential temperature decreases with height, leading to energy dissipation through convective instability; likewise, Rossby waves are said to break when the potential vorticity gradient is overturned. Wave breaking also occurs in plasmas, when the particle velocities exceed the wave's phase speed. Another application in plasma physics is plasma expansion into a vacuum, in which the process of wave breaking and the subsequent development of a fast ion peak is described by the Sack-Schamel equation.
Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.
In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat, as in the Euclidean space. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.
A timeline is a list of events displayed in chronological order. It is typically a graphic design showing a long bar labelled with dates paralleling it, and usually contemporaneous events.
Timelines can use any suitable scale representing time, suiting the subject and data; many use a linear scale, in which a unit of distance is equal to a set amount of time. This timescale is dependent on the events in the timeline. A timeline of evolution can be over millions of years, whereas a timeline for the day of the September 11 attacks can take place over minutes, and that of an explosion over milliseconds. While many timelines use a linear timescale—especially where very large or small timespans are relevant -- logarithmic timelines entail a logarithmic scale of time; some "hurry up and wait" chronologies are depicted with zoom lens metaphors.
Responsivity is a measure of the input–output gain of a detector system. In the specific case of a photodetector, it measures the electrical output per optical input.
A photodetector's responsivity is usually expressed in units of amperes or volts per watt of incident radiant power. For a system that responds linearly to its input, there is a unique responsivity. For nonlinear systems, the responsivity is the local slope. Many common photodetectors respond linearly as a function of the incident power.
An audiogram is a graph that shows the audible threshold for standardized frequencies as measured by an audiometer. The Y axis represents intensity measured in decibels (dB) and the X axis represents frequency measured in hertz (Hz). The threshold of hearing is plotted relative to a standardised curve that represents 'typical' hearing, in dB(HL) (hearing level). They are not the same as equal-loudness contours, which are a set of curves representing equal loudness at different levels, as well as at the threshold of hearing, in absolute terms measured in dB(SPL) (sound pressure level).
The frequencies displayed on the audiogram are octaves, which represent a doubling in frequency (e.g., 250 Hz, 500 Hz, 1000 Hz, wtc). Commonly tested "inter-octave" frequencies (e.g., 3000 Hz) may also be displayed. The intensities displayed on the audiogram appear as linear 10 dBHL steps. However, decibels are a logarithmic scale, so that successive 10 dB increments represent greater increases in loudness.
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).
More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polytope. A linear programming algorithm finds a point in the polytope where this function has the largest (or smallest) value if such a point exists.
In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. A key difference is that unlike covariance, this correlation coefficient does not have units, allowing comparison of the strength of the joint association between different pairs of random variables that do not necessarily have the same units. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation).
An aseismic ridge is “a long, linear and mountainous structure that crosses the basin floor of some oceans.” They do not cause earthquakes.
It is called an “aseismic ridge” because they do not receive seismic activity. As a result, they tend to be stable. They are 700-5000 kilometers in length.
