[permalink] [id link]
Page "Curl (mathematics)" ¶ 67
from Wikipedia
Promote Demote Fragment Fix

Some Related Sentences

3 and dimensions
Geometrically, one studies the Euclidean plane ( 2 dimensions ) and Euclidean space ( 3 dimensions ).
* A simple anthropic argument for why there are 3 spatial and 1 temporal 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.
The 4: 3 screen has dimensions of and area, while the widescreen is,.
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
* 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.
In 3 dimensions, the volume inside a sphere ( that is, the volume of a ball ) is derived to be

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.
So the probability of finding a particle in a differential volume element d < sup > 3 </ sup > r is
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.
Tanker T., 3, 2:05.3 is now wearing hopples and has trained in 2:19 ; ;
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.
Another anode holder used in the experiments is shown in figure 3.
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.
Lung type 3 ( ( fig. 3 ) is to some degree a composite of types 1, and 2.
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 )??
Considering only these Fridays, what is the probability that the coach had drivers all 3 times??
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.