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However, linear equations that have non-zero y-intercepts, when written in this manner, produce functions which will have neither property above and hence are not linear functions in this sense.

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## Some Related Sentences

However and linear

__However__

**,**one must expect

**that**vaporization

**and**ejection of material by hypervelocity impacts would cause a deviation from a

__linear__relationship

**.**

__However__

**,**the bilinear transformation can also be interpreted as a single

__linear__transformation from the tensor product to Z

**.**

__However__

**,**Judeo-Christian thought also makes an " innovation of the first importance ", Eliade says

**,**because it embraces the notion of

__linear__

**,**historical time ;

**in**Christianity

**,**" time is no longer the circular Time of the Eternal Return ; it has become

__linear__

**and**irreversible Time ".

__However__

**,**it seems

**that**many of the methods for solving

__linear__

**and**quadratic

**equations**used by Diophantus go back to Babylonian mathematics

**.**

__However__

**,**it is more usual to use a

__linear__transformation to transform these absolute values into values

**which**resemble the more familiar Pauling values

**.**

__However__the general concept of

__linear__filtering is broader

**,**also used

**in**statistics

**,**data analysis

**,**

**and**mechanical engineering among other fields

**and**technologies

**.**

__However__

**,**for

__linear__acceleration

**,**Newton expressed the idea of undetectability of straight-line accelerations held

**in**common:

__However__

**,**iterative methods

**are**often useful even for

__linear__problems involving a large number of variables ( sometimes of the order of millions ), where direct methods would be prohibitively expensive (

**and**

**in**some cases impossible ) even with the best available computing power

**.**

__However__

**,**the process of binary fission is very much different from the process of mitosis

**,**because of the non-involvement of nuclear dynamics

**and**lack of

__linear__chromosomes

**.**

__However__

**,**the delivering of the consolamentum

**,**on

**which**historical Catharism was based

**,**required a

__linear__succession by a bon homme

**in**good standing

**.**

__However__

**,**using interaction techniques

**that**

**are**

**not**pointer based

**have**proven problematic with both pie

**and**

__linear__menus

**.**

__However__

**,**Buckhardt has been accused of setting forth a

__linear__Whiggish view of history

**in**seeing the Renaissance as the origin of the modern world

**.**

__However__the first result is for positive

__linear__functionals

**,**

**not**bounded

__linear__functionals

**,**so the two facts

**are**

**not**equivalent

**.**

__However__a section near Madrid has been squatted

**,**becoming a

__linear__city of about 40

**,**000 people

**and**15 km

**in**length

**.**

__However__

**,**angular speed must be

**in**radians

**,**by the assumed direct relationship between

__linear__speed

**and**angular speed at the beginning of the derivation

**.**

__However__

**,**modern tape drives

**that**used advanced techniques like multilevel forward error correction

**,**shingling

**,**

**and**

__linear__serpentine layout for writing data to tape

**,**along with lower disk drive prices

**,**

**have**made such alternatives obsolete

**.**

__However__

**,**it may be convenient for notation to consider n-ary

**functions**

**,**as for example multilinear maps (

**which**

**are**

**not**

__linear__maps on the product space

**,**if n ≠ 1 ).

__However__

**,**the direct current homopolar

__linear__motor railgun is another high acceleration

__linear__motor design

**.**

However and equations

__However__

**,**it is essential

**that**the various mathematical symbols used

**in**the

__equations__be understood so

**that**the mathematical processes can be done properly

**and**

**in**their correct order

**.**

__However__

**,**the law of mass action is valid only for concerted one-step reactions

**that**proceed through a single transition state

**and**is

**not**valid

**in**general because rate

__equations__do

**not**

**,**

**in**general

**,**follow the stoichiometry of the reaction as Guldberg

**and**Waage had proposed ( see

**,**for example

**,**nucleophilic aliphatic substitution by S < sub > N </ sub > 1 or reaction of hydrogen

**and**bromine to form hydrogen bromide ).

__However__

**,**he realized

**that**his

__equations__permitted the introduction of a constant term

**which**could counteract the attractive force of gravity on the cosmic scale

**.**

__However__

**,**

**in**the far-field EM radiation

**which**is described by the two source-free Maxwell curl operator

__equations__

**,**a more correct description is

**that**a time-change

**in**one type of field is proportional to a space-change

**in**the other

**.**

__However__

**,**if either the electric or magnetic field has a time-dependence

**,**then both fields must be considered together as a coupled electromagnetic field using Maxwell's

__equations__

**.**

__However__

**,**

**when**multiple nucleons

**are**assembled into an atomic nucleus ( nuclide ), these fundamental

__equations__become too difficult to solve directly ( see lattice QCD ).

__However__

**in**general the Ricci flow

__equations__lead to singularities of the metric after a finite time

**.**

__However__

**,**

**this**theory needs to be generalized

**in**( 2 + 1 ) or ( 3 + 1 ) dimensions although

**,**

**in**principle

**,**the field

__equations__

**are**amenable to such generalization as shown with the inclusion of a one-graviton process

**and**yielding the correct Newtonian limit

**in**d dimensions if a dilaton is included

**.**

__However__

**,**the interpretations leading to the development of the

__equations__were very different

**,**since at the time of development

**,**statistical dynamics had

**not**yet unified the separate studies of thermodynamics

**and**classical dynamics

**.**

__However__

**,**soon after Einstein developed his static theory

**,**observations by Edwin Hubble indicated

**that**the universe appears to be expanding ;

**this**was consistent with a cosmological solution to the original general-relativity

__equations__

**that**had been found by the mathematician Friedmann

**.**

__However__

**,**the

__equations__of quantum mechanics can also be considered

__equations__of motion

**,**since they

**are**differential

__equations__of the wavefunction

**,**

**which**describes how a quantum state behaves analogously using the space

**and**time coordinates of the particles

**.**

__However__

**,**Newton's original precession

__equations__did

**not**work

**and**were revised considerably by Jean le Rond d ' Alembert

**and**subsequent scientists

**.**

__However__

**,**the

__equations__can be further generalized to then be extended to apply to quantum mechanics as well as to classical mechanics

**,**through the deformation of the Poisson algebra over p

**and**q to the algebra of Moyal brackets

**.**

__However__

**,**classical mechanics still remains useful today ( e

**.**g

**.**for calculating spacecraft trajectories ), because its

__equations__

**are**much simpler

**and**its predictive power is sufficiently accurate

**in**most circumstances ; the difference is

**that**the accuracy of relativity is even greater

**.**

__However__

**,**even before Limits to Growth was published

**,**Eduard Pestel

**and**Mihajlo Mesarovic of Case Western Reserve University had begun work on a far more elaborate model ( it distinguished ten world regions

**and**involved 200

**,**000

__equations__compared with 1000

**in**the Meadows model ).

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