# linear

## Definitions

• Repeated pattern, alternately reversed, forming a linear design
• WordNet 3.6
• adj linear of a circuit or device having an output that is proportional to the input "analogue device","linear amplifier"
• adj linear of or in or along or relating to a line; involving a single dimension "a linear measurement"
• adj linear designating or involving an equation whose terms are of the first degree
• adj linear measured lengthwise "cost of lumber per running foot"
• adj linear (of a leaf shape) long and narrow
• ***

Repeated linear design

Webster's Revised Unabridged Dictionary
• Linear (Bot) Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
• Linear Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
• Linear Thinking in a step-by-step analytical and logical fashion; contrasted with holistic, i.e. thinking in terms of complex interrelated patterns; as, linear thinkers. "Linear thinkers concluded that by taking the world apart, the actions of people were more predictable and controllable."
• ***
Century Dictionary and Cyclopedia
• linear Of or pertaining to a line or lines; composed or consisting of lines: as, linear drawing; linear perspective.
• linear Relating to length only; specifically, in mathematics and physics, involving measurement in one dimension only, or a sum of such measurements; involving only straight lines; unidimensional; of the first degree: as, linear numbers; linear measure. A plane is said to be a linear locus, because of the first order; expansion, if considered in one dimension only, the others being neglected, is termed linear expansion.
• linear In bot., zoöl, and anatomy, like a line or thread; slender; very narrow and elongate: as, a linear leaf.
• linear In prosody, consisting in or pertaining to a succession of single verses all of the same rhythm and length; stichic: as, linear composition; “Paradise Lost” is linear in composition.
• ***
Chambers's Twentieth Century Dictionary
• adj Linear of or belonging to a line: consisting of, or having the form of, lines: straight
• ***

## Quotations

• Thomas Carlyle
“Narrative is linear, but action has breadth and depth as well as height and is solid.”

## Etymology

Webster's Revised Unabridged Dictionary
L. linearis, linearius, fr. linea, line: cf. F. linéaire,. See 3d Line
Chambers's Twentieth Century Dictionary
A.S. líne—L. linealinum, flax.

## Usage

### In literature:

Take the simplest linear border, such as the type common in Greek work.
"Line and Form (1900)" by Walter Crane
LINEAR PERSPECTIVE, for the Use of Schools of Art.
"The Letters of Charles Dickens" by Charles Dickens
All these are merely so much acceptance of shade as may relieve the forms, and give value to the linear portions.
Lhwyd, in his sketch of the inscription, further shows that, following the last I, there is a stop or point of a linear form.
"Archaeological Essays, Vol. 1" by James Y. Simpson
It connects the volcanoes of Kamtschatka with those of Japan, and the linear arrangement is apparent.
"Volcanoes: Past and Present" by Edward Hull
Hence it is impossible to form a satisfactory linear series.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 6" by Various
The straight line of the balcony railing stretches across the foreground without any modification of its rigid linear effect.
"Artists Past and Present" by Elisabeth Luther Cary
The vapour tension may approximate to a linear function of the composition, and the curve will then be practically a straight line.
"Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 5" by Various
Gills linear, free, and close together, at first white, then pink or purplish, turning to black.
"Student's Hand-book of Mushrooms of America, Edible and Poisonous" by Thomas Taylor
Pupil contracting to a linear aperture.
"Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 4" by Various
***

### In poetry:

Thou animatest ancient tales,
To prove our world of linear seed:
Thy very virtue now assails,
"The Last Contention" by George Meredith

### In news:

MLP linear potentiometer is available to measure linear position to 6 in.
Linear potentiometer features ballrod ends and a diameter of 0.5 in.
Hanson Pipe & Precast provides 2,566 linear feet of precast concrete box culverts to allow natural groundwater flow and support for machinery at working mine.
Planning for temporally extended goals (TEGs) expressed as formulae of Linear-time Temporal Logic (LTL) is a proper generalization of classical planning, not only allowing to specify properties of a goal state but of the whole plan execution.
This offshore handling system is built to weigh less than 50 kg, but it still must produce 50 tonnes of pulling force with a linear stroke of 650 mm — highly unlikely without a carefully designed sealing system.
Such systems rely on outstanding linearity in both amplifiers and passive components to process the complex modulation schemes needed data rates.
Irène Guessarian, Jean-Eric Pin, "Linearizing Some Recursive Logic Programs," IEEE Transactions on Knowledge and Data Engineering, vol 7, no.
The VM3224 linear-way VMC from Milltronics features a 38" × 24" table and X-Y-Z travels of 32" × 24" × 26.
Linear-Way VMC with Removable Side Doors.
4 mm Linear Servomotor Operates Under Water.
Many parts manufactured today have functional requirements to mate with parts that have either a rotational or linear motion.
Hearst Television is deploying the Linear Acoustic AERO.air transmission audio loudness manager and LQ-1000 loudness quality at all 29 of its stations, including WESH and WKCF (shown).
Bruce Haug, Linear Technology Corp. Harsh military environments demand high performance power conversion.
Micrel Introduces Two Automotive-Qualified, High-Performance Linear Regulators.
A new version of Max's Model 294 high-resolution , linearizing transmitter is included.
***

### In science:

Although linear, it is not a linear response result.
Generalized Entropy approach to far-from-equilibrium statistical mechanics
The Monte Carlo simulations in agreement with the generalized mean-ﬁeld analysis indicate that the concentration decreases linearly with the branching rate for z ≥ 4 while the coeﬃcient of the linear term becomes zero if z = 3.
Branching annihilating random walk on random regular graphs
The natural K ′ -semi-linear action of G on XK ′ extends to an OK ′ -semi-linear action on XOK ′ .
Ramification of local fields with imperfect residue fields
However, for a quasiperiodic one (Eq.(7)) the patterns are almost linearly dependent, yielding an ill–conditioned set of linear equations.
Predicting and generating time series by neural networks: An investigation using statistical physics
For any linear map F : U → V its Moore-Penrose inverse is a linear map F + : V → U deﬁned as follows.
Moore-Penrose inverse, parabolic subgroups, and Jordan pairs
***