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In 3 dimensions, a differential 0-form is simply a function f ( x, y, z ); a differential 1-form is the following expression: a differential 2-form is the formal sum: and a differential 3-form is defined by a single term: ( Here the a-coefficients are real functions ; the " wedge products ", e. g. can be interpreted as some kind of oriented area elements,, etc.

from
Wikipedia

## Some Related Sentences

3 and dimensions

Geometrically

**,**one studies**the**Euclidean plane**(**2__dimensions__)**and**Euclidean space**(**__3____dimensions__).
Right angle weave lends itself better

**as****a**technique to 3D beading**,**but peyote stitch offers**the**advantage**of**more tightly knit beads**,**which**is**sometimes necessary to properly portray an object in__3____dimensions__**.**
The geometric interpretation

**of**curl**as**rotation corresponds to identifying bivectors**(**2-vectors ) in__3____dimensions__with**the**special orthogonal Lie algebra so**(**__3__)**of**infinitesimal rotations**(**in coordinates**,**skew-symmetric__3__×__3__matrices ), while representing rotations**by**vectors corresponds to identifying 1-vectors**(**equivalently**,**2-vectors )**and**so**(**__3__), these all being 3-dimensional spaces**.****"**From these principles

**and**

**some**additional constraints —( 1a )

**a**lower bound on

**the**linear

__dimensions__

**of**any

**of**

**the**parts

**,**

**(**1b ) an upper bound on speed

**of**propagation

**(**

**the**velocity

**of**light ),

**(**2 ) discrete progress

**of**

**the**machine

**,**

**and**

**(**

__3__) deterministic behavior — he produces

**a**theorem that

**"**What

**can**

**be**calculated

**by**

**a**device satisfying principles I – IV

**is**computable

**.**

**In**Chaosmosis

**,**Guattari proposes an analysis

**of**subjectivity in terms

**of**four

__dimensions__

**:**

**(**1 ) material

**,**energetic

**,**

**and**semiotic fluxes

**;**

**(**2 ) concrete

**and**abstract machinic phylums

**;**

**(**

__3__) virtual universes

**of**value

**;**

**and**

**(**4 ) finite existential territories

**.**

*

**(**for ideal mixtures )**is****the**concentration in__dimensions__**of****of**substance ) length < sup >−__3__</ sup >, example
The

__dimensions__**of****the**factors correspond to**the**1 photon +__3__vector bosons + 8 gluons**of****the**standard model**.**
Assume further that

**the**coordinate systems**are****oriented**so that**,**in__3____dimensions__**,****the**x-axis**and****the****x**' - axis**are**collinear**,****the**y-axis**is**parallel to**the****y**' - axis**,****and****the**z-axis parallel to**the****z**' - axis**.**
The

__dimensions__**of**density**are**mass divided**by**volume with units**:**kg / m < sup >__3__</ sup > or**g**/ cm < sup >__3__</ sup >.
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**.**
This

**is**further complicated**by****the**fact that gravitons**can**propagate in**(**__3__+ 1 )__dimensions__**and**consequently that would imply gravitons**and**dilatons exist in**the****real**world**.**
This

**is**inadequate to describe gravity in__3__+ 1__dimensions__which has local degrees**of**freedom according to general relativity**.**
At close range

**,**fine control**of****the**tip in all three__dimensions__when near**the**sample**is**typically piezoelectric**,**maintaining tip-sample separation W typically in**the**4-7 Å**(**0**.**4-0**.**7 nm ) range**,**which**is****the**equilibrium position between attractive**(**__3__< W < 10Å )**and**repulsive**(**W < 3Å ) interactions**.**

3 and differential

The notation ∇ × F has its origins in

**the**similarities to**the**__3__dimensional cross product**,****and**it**is**useful**as****a**mnemonic in Cartesian coordinates if we take ∇**as****a**vector__differential__operator del**.**
The potential field

**is**given**by****a****function**V**:**R < sup >__3__</ sup > → R**and****the**trajectory**is****a**solution**of****the**__differential__equation
Oliver Heaviside FRS

**(****(**18 May 1850 –__3__February 1925 ) was**a**self-taught English electrical engineer**,**mathematician**,****and**physicist who adapted complex numbers to**the**study**of**electrical circuits**,**invented mathematical techniques to**the**solution**of**__differential__equations**(**later found to**be**equivalent to Laplace transforms ), reformulated Maxwell's field equations in terms**of**electric**and**magnetic forces**and**energy flux**,****and**independently co-formulated vector analysis**.**
The

__3__**.**15**:**1 ratio__differential__was introduced in 2005 to**be**used at Bathurst-cars with this ratio**can**now exceed 300 km / h**(**186 mph ) on Conrod Straight**(**this has yet to**be**demonstrated**,**although Perkins Engineering claims to have exceeded this speed multiple times in**the**2005 event ).
where d < sup >

__3__</ sup > k = dk < sub >**x**</ sub > dk < sub >**y**</ sub > dk < sub >**z**</ sub >**is****the**__differential__volume element in k-space**,****and****the**integrals**are**taken over all k-space**.**
* Cancer

**is**included in**the**__differential__diagnosis**(**elucidated**by**biopsy ), Helicobacter pylori**as****the**etiological factor making it__3__to 6 times more likely to develop stomach cancer from**the**ulcer**.**
The Bulls also posted

**the**second-best home record in history**(**39 – 2 ), behind only**the**1985 – 86 Celtics 40 – 1 home mark**,****and****the**second-best point__differential__in history**,**trailing**the**1972 Lakers**by**__3__points over**the**course**of**an entire season**.**
The drift rate

**of****the**SAA**is**very close to**the**rotation__differential__between**the**Earth's core**and**its surface**,**estimated to**be**between 0**.**__3__**and**0**.**5 degrees per year**.**
For example

**,****the**three-dimensional object physics calls angular velocity**is****a**__differential__rotation**,**thus**a**vector in**the**Lie algebra tangent to SO**(**__3__).
Even though

**the**elevation__differential__**is**only 334 metres**(**1096 feet )**and****the**walk**is**not particularly long**(**__3__**.**8 km each way ),**the**total elevation gain**and**loss over**the**course**of****the**hike**is**more than one might initially expect**,****as****the**path climbs**and**descends various ridges**.**
These included

__3__additional oil coolers**,**revised ECU map**,**full Connelly leather interior**,**underbody diffusers**,**stiffer suspension**,**active rear limited slip__differential__**,**extra display feature on**the**in car display**.**
It

**is****a**very broad**and**abstract generalization**of****the**__differential__geometry**of**surfaces in R < sup >__3__</ sup >.
Car Life tested

**a**1965 GTO with Tri-Power**and**what they considered**the**most desirable options**(**close-ratio four-speed manual transmission**,**power steering**,**metallic brakes**,**rally wheels**,**4**.**11 limited-slip__differential__**,****and**Rally Gauge Cluster ), with**a**total sticker price**of**US $__3__**,**643**.**79**.**
Motor Trend clocked

**a**four-speed Ram Air with 4**.**33 rear__differential__at 14**.**45 seconds at**and****a**standard GTO with Turbo-Hydramatic**and****a**__3__**.**23 rear axle ratio at 15**.**93 seconds at**.**
Car Lifes Turbo-Hydramatic 455

**,**with**a**__3__**.**35 rear__differential__**,**clocked 14**.**76 seconds at**,**with identical 6**.**6 second 0-60 mph acceleration**.**
The car was able to match

**the**Shelby Daytona's speed despite running**a**higher__differential__ratio**(**2**.**88 instead**of**__3__**.**07 )**and****a**lower state**of**engine tune for reliability**(**355 hp instead**of****the**Daytona's 385 hp ).
Other changes included

**a**race developed carbon fibre nose cone**and**rear spoiler**,****a**carbon fibre 120 L fuel tank**(****as**opposed to**the**76 L tank in**the**standard car ),**a**4**.**__3__**:**1-ratio rear__differential__**,**17 in diameter wheels**,**larger brake rotors**and**calipers**.**
The expectation values

**can****be****interpreted****as****:**The mean salary**of**public school teachers in**the**West**is**equal to**the**intercept**term**α < sub > 1 </ sub > in**the**multiple regression equation**and****the**__differential__intercept coefficients**,**α < sub > 2 </ sub >**and**α < sub >__3__</ sub >, explain**by**how much**the**mean salaries**of**teachers in**the**North**and**South Regions vary from that**of****the**teachers in**the**West**.**
Suppose all

**the**__3____differential__dummy coefficients**are**negative**,**it means that**,**female non-white**and**non-Hispanic workers earn much lower mean wages than female OR non-white**and**non-Hispanic workers**as**compared to**the**base group**,**which in this case**is**male**,**white or Hispanic**(**omitted category ).
Chapter

__3__**(**Prerequisites for Space Drive Science ) provides refinements**and**deeper explanation**of****the****following**hypothetical**"**space drive**"**propulsion methods**:**diametric drive**,**pitch drive**,**bias drive**,**disjunction drive**,****and**three variations**of**__differential__sails**.**

3 and 0-form

**In**

__3__

**dimensions**

**,**an exact vector field

**(**thought

**of**

**as**

**a**

**1-form**)

**is**called

**a**conservative vector field

**,**meaning that it

**is**

**the**derivative

**(**gradient )

**of**

**a**

__0-form__

**(**

**function**), called

**the**scalar potential

**.**

3 and is

**In**

**the**extreme

**and**oversimplified example suggested in Figure

__3__

**,**

**the**organization

__is__more easily understood

**and**more predictable in behavior

**.**

The assumptions upon which

**the**example shown in Figure__3____is__based**are****:****(**A ) One man**can**direct about six subordinates if**the**subordinates**are**chosen carefully so that they do not need too much personal coaching**,**indoctrinating**,**etc.**.**
Furthermore

**,****the**network in Figure__3____is__only**the**basic net through which other networks pertaining to logistics**and****the**like**are**interlaced**.**
Be it enacted

**by****the**Senate**and**House**of**Representatives**of****the**United States**of**America in Congress assembled**,**That**the**Act**of**July__3__**,**1952**(**66 Stat. 328 )**as**amended**(**42 U.S.C. 1952-1958 )**,**__is__further amended to read**as**follows**:**Section 1**.**
in

**the**case**of****a**partnership or corporation**,****the**existence**of**which has been terminated**and**on behalf**of**which an award__is__made**,**payment shall**be**made**,**except**as**provided in paragraphs**(**__3__)**and****(**4 )**,**to**the**person or persons found**by****the**Comptroller General**of****the**United States to**be**entitled thereto**;****;**
Research

**,**development test**and**evaluation funds**,**devoted to missiles in 1960 were__3__to 4 times**as**large**as**those devoted to aircraft**,****and**actual missile procurement__is__expected to exceed aircraft procurement**by**1963**.**
This covered

**,**wooden bridge__is__so closely identified with**the**first action in**the**early morning**of**June__3__**,**1861**,****and**with subsequent troop movements**of**both armies in**the**Philippi**area**that it has become**a**part**and**parcel**of****the**war story**.**
The observed intensity

**of****the**radio emission**of**Venus__is__much higher than**the**expected thermal intensity**,**although**the**spectrum indicated**by**measurements at wave lengths near__3__cm**and**10 cm__is__like that**of****a**black body at about 600-degrees**.**
A randomization

**of**`` ups ''**and**`` downs ''__is__more likely than ordered `` ups ''**and**`` downs '' in position**(**__3__) since**the**hydrogen atoms**are**well separated**and**so**the**position**of**one could hardly affect**the**position**of**another**,****and**also since ordered `` up ''**and**`` down '' implies**a**larger unit cell**,**for which no evidence exists**.**
Arterial supply to

**the**pleura in types 1**and**__3____is__provided**by****the**bronchial artery**,****and**in type 2**,****by****the**pulmonary artery**.****In**type

__3__

**,**this general relationship

__is__maintained peripherally but not centrally where

**the**pulmonary vein follows

**a**more independent path to

**the**hilum

**as**

__is__

**the**case throughout

**the**lung in type 2

**.**

For example

**,**arrow 17 in Figure__3__portrays**the**proximal radial epiphysis for boy 34**,**whereas**the**same epiphysis for girl 2__is__portrayed**by**arrow 18 in Figure 4**.**
The nuclei

**of**these fibers**,****as**__is__shown in Figures__3__**and**4**,**showed remarkable proliferation**and**were closely approximated**,**forming**a**chainlike structure at either**the**center or**the**periphery**of****the**fiber**.**
When three dice

**are**tossed repeatedly**,**what__is__**the**probability that**the**number**of**aces__is__0**(**or 1**,**or 2**,**or__3__)??
For example

**,****the**marksman gets 5 shots**,**but we take his score to**be****the**number**of**shots before his first bull's-eye**,**that__is__**,**0**,**1**,**2**,**__3__**,**4**(**or 5**,**if he gets no bull's-eye )**.**
During

**the**first pass**of**Phase__3__**,****,**references to**the**actual addresses**of**index words**and**electronic switches**are**collected**and****the**availability table__is__updated**.**
The one- or two-digit number

**of****the**index word or electronic switch was used in**the**operand**of****a**symbolic machine instruction to specify indexing or**as****a**parameter which__is__always an index word or electronic switch**,**e.g.**,**__3__**.**0.195 seconds.