For example, the Cobb-Douglas equation — often used in economics — is nonlinear:

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 instance, laser microscopy focused on biological applications uses ultrashort pulse lasers, or femtosecond lasers, in a number of techniques labeled as nonlinear microscopy, saturation microscopy, and multiphoton fluorescence microscopy.

For nonlinear medium Gauss's law does not imply that the identity

For nonlinear systems, the responsivity is the local slope ( derivative ).

For instance, when notes are played forcefully, the sound becomes less sweet, as nonlinear distortion creates a characteristic " growling " or " snarling ", called " bark " by pianists.

For a description of linear and nonlinear equations, see linear equation.

For example, hypertext fiction can be an example of nonlinear narrative, but there are also websites designed to go in a specified, organized manner, following a linear path.

For example, the nonlinear equation

For example, the ( very ) nonlinear Navier-Stokes equations can be simplified into one linear partial differential equation in the case of transient, laminar, one dimensional flow in a circular pipe ; the scale analysis provides conditions under which the flow is laminar and one dimensional and also yields the simplified equation.

For example, when two unpatterned lights are modulated at slightly different frequencies ( F1 and F2 ) and superimposed, multiple nonlinear cross-modulation components of frequency ( mF1 ± nF2 ) are created in the SSEP, where m and n are integers.

For example, in electrical engineering, negative feedback is used in amplifiers to trade gain for other desirable properties, such as improved bandwidth, stability of the gain and / or bias point, noise immunity, and reduction of nonlinear distortion.

For many applications, the infrared light is frequency-doubled or-tripled using nonlinear optical materials such as lithium triborate to obtain visible ( 532 nm, green ) or ultraviolet light.

: For p a non-negative number, the p-Laplacian is a nonlinear elliptic operator defined by

For example, parametric nonlinear processes can generate so-called twin beams, where ideally each photon of one beam is associated with a photon in the other beam.

For a nonlinear material, the electric polarization field P will depend on the electric field E:

For details concerning nonlinear data modeling see least squares and non-linear least squares.

For example, consider the nonlinear regression problem

For instance, at the upper treeline, where the tree is " cold limited ", it's unlikely that nonlinear effects of high temperature (" inverted quadratic ") will have numerically significant impact on ring width over the course of a growing season.

For example, the harmonic oscillator equation is an approximation to the nonlinear pendulum equation that is valid for small amplitude oscillations ( see below ).

For simplicity consider the all-inequality version of a nonlinear optimization problem:

For example, the Ernst equation is a nonlinear partial differential equation somewhat resembling the nonlinear Schrödinger equation ( NLS ).

For R = 0, no reflection from the first surface and the resultant nonlinear phase shift is equal to the round-trip phase change () – linear response.

For example, the term is used to describe systems such as verlan and louchébem, which retain French syntax and apply transformations only to individual words ( and often only to a certain subset of words, such as nouns, or semantic content words ).

For example, autopilot systems that are prolific today were started to help bomber planes fly steadily enough to hit precision targets from high altitudes.

* For tramway systems: see List of town tramway systems in Belarus

For a time, the combined company retained the Burroughs processors as the A and V systems lines.

For example, an information systems specialist will view computing somewhat differently from a software engineer.

For example, programming language theory studies approaches to description of computations, while the study of computer programming itself investigates various aspects of the use of programming languages and complex systems, and human-computer interaction focuses on the challenges in making computers and computations useful, usable, and universally accessible to humans.

For instance, NASA has extremely rigorous software testing procedures for many operating systems and communication functions.

For example, programming language theory considers various approaches to the description of computation, whilst the study of computer programming itself investigates various aspects of the use of programming language and complex systems.

For example, kinship and leadership function both as symbolic systems and as social institutions.

For very large systems, the relative total energies can be compared using molecular mechanics.

For π-electron systems, this was the Hückel method proposed by Erich Hückel, and for all valence electron systems, the extended Hückel method proposed by Roald Hoffmann.

For example, the conservation of energy follows from the time-invariance of physical systems, and the fact that physical systems behave the same regardless of how they are oriented in space gives rise to the conservation of angular momentum.

For some distributed parameter systems the vectors may be infinite-dimensional ( typically functions ).

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

For example, there is a hard disk, from which most operating systems run and on which most store their files.

For instance, on newer MS Windows computers, the older FAT-type file systems of MS-DOS and old versions of Windows are supported, in addition to the NTFS file system that is the normal file system for recent versions of Windows.

For continuous, frequent or prolonged intravenous chemotherapy administration, various systems may be surgically inserted into the vasculature to maintain access.

For example, Burris has reviewed sociological publications and used the theories of Weber and Bourdieu to describe academic caste systems.

For this reason it is not hard to port games between these systems.

For embedded systems, the highest performance levels are often not needed or desired due to the power consumption requirements.

For a while hybrid cable / electric systems operated, for example in Chicago where electric cars had to be pulled by grip cars through the loop area, due to the lack of trolley wires there.

For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by