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Since all maximal paths have the same number of black nodes, by property 5, this shows that no path is more than twice as long as any other path.

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## Some Related Sentences

Since and all

__Since__it was issued in

**the**spring

**of**1611

**,**

**the**King James Version has been most generally considered

**the**most poetic and beautiful

**of**

__all__translations

**of**

**the**Bible

**.**

__Since__

**the**validity

**of**

__all__subsequent planning depends on

**the**accuracy

**of**

**the**basic inventory information

**,**great care

**is**being taken

**that**

**the**inventory

**is**

**as**complete

**as**possible

**.**

__Since__broadcast frequencies are very limited in

**number**

**,**these objectives are to some extent inconsistent in

**that**not

__all__

**of**them can be fully realized

**,**and to

**the**extent

**that**each

**is**realized

**,**there

**is**a corresponding reduction

**of**

**the**possibilities for fullest achievement

**of**

**the**others

**.**

__Since__he can neither accept nor reject them

__all__

**,**he must be governed

**by**

**the**time and energy available for his prime professional obligations

**.**

__Since__they are

__all__either rented or borrowed

**,**

**the**requested dates for their use

**have**to be far in advance

**.**

__Since__American life

**is**committed above

__all__to productivity and a higher standard

**of**economic life

**,**

**the**countervailing forces

**of**residential and religious exclusiveness

**have**fought a desperate

**,**rearguard action against

**the**expanding interdependence

**of**

**the**metropolis

**.**

__Since__rococo music tends to be pretty and elegant above

__all__

**,**it can seem rather vacuous to twentieth-century ears

**that**

**have**grown accustomed to

**the**stress and dissonances

**of**composers from Beethoven to Boulez

**.**

__Since__"

__all__beings " includes

**the**individual

**,**love and compassion in Buddhism are outside

**the**opposition between self and

**other**

**.**

__Since__a player cannot control another player's bids

**,**and since

__all__bids are non-refundable

**,**

**the**auction involves a considerable amount

**of**strategizing and prioritization

**by**players

**.**

__Since__

__all__anchors

**that**embed themselves in

**the**bottom require

**the**strain to be along

**the**seabed

**,**anchors can be broken out

**of**

**the**bottom

**by**shortening

**the**rode until

**the**vessel

**is**directly above

**the**anchor ( at

**this**point

**the**anchor chain

**is**" up and down " in naval parlance ).

__Since__

**the**1970s

**,**self-help books

**,**psychology

**,**and some modern expressions

**of**Christianity

**have**viewed

**this**disparity in terms

**of**grace being an innate quality within

__all__people who must be inspired or strong enough to find it: something to achieve

**.**

__Since__

**the**implementation

**of**

**the**Statute

**of**Westminster 1931 in each

**of**

**the**Commonwealth realms ( on successive dates from 1931 onwards ),

**the**Act

**of**Settlement cannot be altered in

**any**realm except

**by**

**that**realm's own parliament and

**,**

**by**convention

**,**only with

**the**consent

**of**

__all__

**the**

**other**realms

**,**

**as**it touches on

**the**succession to

**the**shared throne

**.**

__Since__John Wesley ordained and sent forth every Methodist preacher in his day

**,**who preached and baptized and ordained

**,**and since every Methodist preacher who has ever been ordained

**as**a Methodist was ordained in

**this**direct " succession " from Wesley

**,**then

**the**Methodist Church teaches

**that**it has

__all__

**the**direct merits coming from apostolic succession

**,**if

**any**such there be

**.**

__Since__

**the**Plebeian Aediles were elected

**by**

**the**Plebeians ( commoners ), rather

**than**

**by**

__all__

**of**

**the**People

**of**Rome ( Plebeians

**as**well

**as**members

**of**

**the**Patrician aristocracy ), they were not technically magistrates

**.**

__Since__

**the**implementation

**of**concordats between

**the**ELCA and

**the**Episcopal Church

**of**

**the**United States and

**the**ELCIC and

**the**Anglican Church

**of**Canada

**,**

__all__bishops

**,**including

**the**Presiding Bishop ( ELCA ) or

**the**National Bishop ( ELCIC ),

**have**been consecrated using

**the**historic succession

**,**with at least one Anglican bishop serving

**as**co-consecrator

**.**

__Since__going into ecumenical communion with their respective Anglican body

**,**bishops in

**the**ELCA or

**the**ELCIC not only approve

**the**" rostering "

**of**

__all__ordained pastors

**,**diaconal ministers

**,**and associates in ministry

**,**but they serve

**as**

**the**principal celebrant

**of**

__all__pastoral ordination and installation ceremonies

**,**diaconal consecration ceremonies

**,**

**as**well

**as**serving

**as**

**the**" chief pastor "

**of**

**the**local synod

**,**upholding

**the**teachings

**of**Martin Luther

**as**well

**as**

**the**documentations

**of**

**the**Ninety-Five Theses and

**the**Augsburg Confession

**.**

*

__Since__Big Brother 2**,****the**UK series always opens with a twist which**have**included**the**public being able to choose**the**final housemate out**of**three possibilities ( Big Brother 2 ),**the**public voting for a housemate to leave during**the**first week and then**the**housemates choosing between**the**two housemates with**the**least**number****of**votes ( Big Brother 3 ), First Night Nominations ( Big Brother 4 ), Suitcase Nominations ( Big Brother**5**), Unlucky Housemate 13 ( Big Brother 6 ), Big Brother Hood ( Big Brother 7 ), an all-female House and**the**first inclusion**of**twins**as**contestants ( Big Brother 8 ),**the**first couple to enter**as**housemates and set a secret task to hide their real relationship ( Big Brother 9 ),__all__" housemates " really being " non-housemates " who had to earn their housemate status ( Big Brother 10 ), a mole entering**the**House with an " Impossible Task " ( Big Brother 11 ), Jackie Stallone entering a house containing her son's ex-wife ( Celebrity Big Brother 3 ),**the**entrance**of**a non-celebrity in a celebrity edition ( Celebrity Big Brother 4 ) and Jade Goody's family announced to be visiting**.**__Since__

**the**gene

**is**recessive

**,**

__all__offspring will be heterozygous

**,**and

**the**offspring from

**that**mating will not be resistant to Bt and therefore

**no**longer a threat

**.**

__Since__a

**maximal**ideal in A

**is**closed

**,**

**is**a Banach algebra

**that**

**is**a field

**,**and it follows from

**the**Gelfand-Mazur theorem

**that**there

**is**a bijection between

**the**set

**of**

__all__

**maximal**ideals

**of**A and

**the**set Δ ( A )

**of**

__all__nonzero homomorphisms from A to C

**.**The set Δ ( A )

**is**called

**the**" structure space " or " character space "

**of**A

**,**and its members " characters

**.**

__Since__

**the**donation

**of**

**the**Abbey Moutier-Grandvalto and

__all__its possessions to Bishop Adalbero II in 999 till

**the**Reformation

**,**Basel was ruled

**by**prince-bishops ( see Bishop

**of**Basel

**,**whose memory

**is**preserved in

**the**crosier shown on

**the**Basel coat-of-arms – see above ).

Since and maximal

Let A be a unital commutative Banach algebra over C

**.**__Since__A**is**then a commutative ring with unit**,**every non-invertible element**of**A belongs to some__maximal__ideal**of**A**.**__Since__a one sided

__maximal__ideal A

**is**not necessarily two-sided

**,**

**the**quotient R / A

**is**not necessarily a ring

**,**but it

**is**a simple module over R

**.**If R has a unique

__maximal__right ideal

**,**then R

**is**known

**as**a local ring

**,**and

**the**

__maximal__right ideal

**is**also

**the**unique

__maximal__left and unique

__maximal__two-sided ideal

**of**

**the**ring

**,**and

**is**in fact

**the**Jacobson radical J ( R ).

Every prime ideal P in a Boolean ring R

**is**__maximal__:**the**quotient ring R / P**is**an integral domain and also a Boolean ring**,**so it**is**isomorphic to**the**field F < sub > 2 </ sub >, which**shows****the**maximality**of**P**.**__Since____maximal__ideals are always prime**,**prime ideals and__maximal__ideals coincide in Boolean rings**.**__Since__

**as**shown above

**,**

**the**classical definition

**is**essentially

**the**modern definition with only

__maximal__ideals considered

**,**

**this**

**shows**

**that**

**the**interpretation

**of**

**the**modern definition

**as**" zero sets

**of**functions " agrees with

**the**classical definition where they both make sense

**.**

__Since__it

**is**a collection

**of**trees

**,**and trees are contractible

**,**consider

**the**space where

**the**equivalence relation

**is**generated

**by**if they are contained in a common tree in

**the**

__maximal__forest F

**.**The quotient map

**is**a homotopy equivalence

**.**

*

__Since__**the**conjugate**of**a__maximal__torus**is**a__maximal__torus**,**every element**of**G lies in some__maximal__torus**.**
) This follows from

**the**fact**that**R has a__maximal__left ideal M**,**and**the**fact**that****the**quotient module R / M**is**a simple left R-module**,**and**that**its annihilator**is**a proper two-sided ideal in R**.**__Since__R**is**a simple ring**,****this**annihilator**is**__Since__

**the**compact operators

**is**a ( in fact

**,**

**the**only )

__maximal__norm-closed ideal in B ( H ),

**the**Calkin algebra

**is**simple

**.**

__Since__

**the**

**number**

**of**edges in a

__maximal__spanning forest

**of**a graph

**is**equal to

**the**

**number**

**of**vertices minus

**the**

**number**

**of**components

**,**

**the**formula above for

**the**cyclomatic

**number**follows

**.**

__Since__power

**is**equal to force times velocity

**,**

**the**muscle generates

**no**power at either isometric force ( due to zero velocity ) or

__maximal__velocity ( due to zero force ).

__Since__

**the**technostructure

**is**composed

**of**an hierarchical system

**of**influential employees inside

**the**enterprise

**,**its primary goal

**is**not to maximize their profits but rather survival

**,**continuous growth and

__maximal__size

**.**

__Since__

**the**alcohol in wine

**is**produced

**by**fermentation

**of**

**the**sugar

**,**

**the**Oechsle scale

**is**used to predict

**the**

__maximal__possible alcohol content

**of**

**the**finished wine

**.**

Since and paths

__Since__

**the**overwhelming majority

**of**light rays from a given light source do not make it directly into

**the**viewer's eye

**,**a " forward " simulation could potentially waste a tremendous amount

**of**computation on light

__paths__

**that**are never recorded

**.**

__Since__

**all**

**of**these

__paths__are

**of**different lengths-plus some

**of**these effects will also slow

**the**signal down-this results in

**the**different versions

**of**

**the**signal arriving at

**the**receiver at different times

**.**

__Since__

**the**1960s

**,**many

**of**these schools

**have**become defunct

**as**a result

**of**financial difficulties stemming from parents ' decreased interest in paying for such an education for their daughters

**,**and changing societal norms making it easier for daughters to pursue academic and professional

__paths__not open to previous generations

**.**

__Since__these frequencies propagate

**by**ground wave only

**,**

**the**precision

**of**time signals

**is**not affected

**by**varying propagation

__paths__between

**the**transmitter

**,**

**the**ionosphere

**,**and

**the**receiver

**.**

__Since__for

**all**mother nature knows ( or could know ) it

**is**possible

**that**these insects will cross

__paths__( sometime

**,**somewhere ) with insectivorous birds

**,**they had better be designed with some avoidance machinery

**.**

__Since__

**the**unit interval

**is**simply connected

**,**

**the**lifting

**property**for

__paths__

**is**a special case

**of**

**the**lifting

**property**for maps stated above

**.**

__Since__service roads serve a dual purpose

**,**they are an inexpensive way to create routes in cycling network

**,**compared to cycletracks or stand-alone bike

__paths__

**.**

__Since__

**the**lenses

**of**their eyes modify reciprocally

**the**

__paths__

**of**

**the**incoming and outgoing light

**the**effect

**is**

**that**

**the**eyes act

**as**a strong retroreflector

**,**sometimes seen at night when walking in wildlands with a flashlight

**.**

__Since__

**the**conception

**of**

**the**welfare state was intensifying

**the**demand for social equality and democratisation

**,**middle schools were reorganised in 1958 to include two academic

__paths__: a 3-year academically oriented real department and

**the**8th-10th forms

**.**

__Since__then

**,**we

**have**traveled

**the**globe

**,**released many records

**,**and played thousands

**of**

**shows**; pedaling

**the**righteous name

**of**piebald to

**all**whose

__paths__we crossed

**.**

__Since__light

**is**deflected in a gravitational field

**,**it

**is**possible for

**the**light

**of**a distant object to reach an observer along two or

**more**

__paths__

**.**

__Since__graze

__paths__rarely pass over established observatories

**,**amateur astronomers

**have**become

**the**primary recorders

**of**graze data

**.**

__Since__

**the**two

__paths__through a neutron interferometer can be

**as**far

**as**to apart

**,**

**the**effect

**is**hardly microscopic

**.**

__Since__

**the**underlying random process

**is**

**the**

**same**

**,**for enough price

__paths__

**,**

**the**value

**of**a european option here should be

**the**

**same**

**as**under Black Scholes

**.**

As James stated

**,**"__Since__then we**have**moved on and actually made a second album but decided**that**we both wanted to go down different__paths__in our lives and going on**the**road**as**BodyRockers again for another three years promoting another album wasn't what we wanted ".__Since__STA

**is**capable

**of**verifying every

**path**

**,**it can detect

**other**problems like glitches

**,**slow

__paths__and clock skew

**.**

0.687 seconds.