If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

When Af for each i, we shall have Af, because the operator Af will then be 0 on the range of Af.

for, using the fact that N and N' commute Af and so when R is sufficiently large every term in this expression for Af will be 0.

hence Af and the minimal polynomial is simply x, which says the operator is 0.

A trained marksman shooting five rounds at a target, all under practically the same conditions, may hit the bull's-eye from 0 to 5 times.

In litters of eight mice from similar parents, the number of mice with straight instead of wavy hair is an integer from 0 to 8.

Each performance of an n-trial binomial experiment results in some whole number from 0 through N as the value of the random variable X, where Af.

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 ).

then the number of successes is always 0 ).

Each binomial trial of a binomial experiment produces either 0 or 1 success.

Therefore each binomial trial can be thought of as producing a value of a random variable associated with that trial and taking the values 0 and 1, with probabilities Q and P respectively.

The numbers of successes on the five individual shots are, then, 0, 0, 1, 0, 1.

The number of successes on each shot is a value of a random variable that has values 0 or 1, and there are 5 such random variables here.

If the distribution of the 71 items were wholly concordant in the two families, the distance would of course be 0.

The actual mean of 1.07 being about halfway between 0 of complete correlation and 2.0 of no correlation, it is evident that there is a pretty fair degree of similarity in the behavior even of particular individual items of meaning as regards long-term stem displacement.

However much football has been over-emphasized, the public likes to measure its collegiate favorites by the scoreboard, so, while Yale need never give its record a thought again since outscoring its opponents 694 to 0 in the season of 1888, Dartmouth had to wait until its championship team of 1925 for national recognition.

The Senate put other business aside as it moved with unaccustomed speed and unanimity to pass -- 85 to 0 -- the largest peacetime defense budget in U.S. history.

Eight-bit machines ( with octets as the native data type ) that did not use parity checking typically set the eighth bit to 0.

The digits 0 – 9 were arranged so they correspond to values in binary prefixed with 011, making conversion with binary-coded decimal straightforward.

The parentheses could not correspond to 9 and 0, however, because the place corresponding to 0 was taken by the space character.

Cohen ( 1992 ) suggests effect sizes for various indexes, including ƒ ( where 0. 1 is a small effect, 0. 25 is a medium effect and 0. 4 is a large effect ).

10, 000 square metres = 0. 01 square kilometres

Since the difference between the U. S. and International acre is only about a quarter of the size of an A4 sheet of paper ( 0. 016 square metres, 160 square centimetres or 24. 8 square inches ), it is usually not important which one is being discussed.

* 0. 40468564224 hectare ( A square with 100 m sides has an area of 1 hectare.

A perch is equal to a square rod ( 1 square rod is 0. 00625 acre )

There were 142 housing units at an average density of 109. 0 per square mile ( 42. 2 / km² ).

The population density was 2, 307. 0 people per square mile ( 890. 7 / km² ).

There were 4, 748 housing units at an average density of 813. 0 per square mile ( 313. 9 / km² ).

There were 49, 454 housing units at an average density of 2, 794. 6 per square mile ( 1, 079. 0 / km² ), of which 18, 846 ( 40. 9 %) were owner-occupied, and 27, 183 ( 59. 1 %) were occupied by renters.

Taking m to be 2 gives the square pyramidal numbers 0, 1, 5, 14, ....

where Fε < sup >- D </ sup > must be the number of units ε required to obtain L. The fractal dimension is the number of the dimensions of the figure being used to approximate the fractal: 0 for a dot, 1 for a line, 2 for a square.

( 1962 ) Atlas Borealis 1950. 0, Czechoslovak Academy of Sciences ( Ceskoslovenske Akademie Ved ), Praha, Czechoslovakia, 1st Edition, elephant folio hardcover, with small transparency overlay coordinate grid square and separate paper magnitude legend ruler.

( 1958 ) Atlas Eclipticalis 1950. 0, Czechoslovak Academy of Sciences ( Ceskoslovenske Akademie Ved ), Praha, Czechoslovakia, 1st Edition, elephant folio hardcover, with small transparency overlay coordinate grid square and separate paper magnitude legend ruler.

Atlas Australis 1950. 0, Czechoslovak Academy of Sciences ( Ceskoslovenske Akademie Ved ), Praha, Czechoslovakia, 1st Edition, elephant folio hardcover, with small transparency overlay coordinate grid square and separate paper magnitude legend ruler.

Most of its ethnically and linguistically diverse population lives in the south, with densities ranging from 54 persons per square kilometers in the Logone River basin to 0. 1 persons in the northern B. E. T.

To illustrate this point, Bairoch offers an example: " Western Europe during the pre-Neolithic, the density must have been less than 0. 1 person per square kilometer ".

The northern boundary of the state with Massachusetts is marked by the Southwick Jog or Granby Notch, an approximately 2. 5 mile ( 4. 0 km ) square detour into Connecticut.

The population density was 1, 466. 0 per square mile ( 566. 1 / km² ).

The silicon cost of an 8051 is now as low as US $ 0. 001, because some implementations use as few as 2, 200 logic gates and take 0. 0127 square millimeters of silicon.

The Robert F. Henry Lock & Dam is located at river mile 236. 2, the Millers Ferry Lock & Dam is located at river mile 133. 0, and the Claiborne Lock & Dam is located at river mile 72. 5.

The population density was 2, 033. 0 people per square mile ( 785. 9 / km² ).

There were 1, 325 housing units at an average density of 900. 3 per square mile ( 348. 0 / km² ).

There were 47, 755 housing units at an average density of 1, 026. 0 per square mile ( 396. 2 / km² ).

This means that one kilometre is roughly equal to ( 1 / 40, 000 ) * 360 * 60 meridional minutes of arc, which equals 0. 54 nautical mile, though this is not exact because the two units are defined on different bases ( the international nautical mile is defined as exactly 1, 852 m, corresponding to a rounding of 1000 / 0. 54 m to four digits ).

The population density was 221. 0 people per square mile ( 85. 3 / km < sup > 2 </ sup >).

There were 54, 181 housing units at an average density of 1, 505. 0 per square mile ( 581. 3 / km < sup > 2 </ sup >).

They have overlapping home ranges of several square kilometres and typically occur at densities of about 0. 6 animals per square kilometre ( about 1. 5 animals per square mile ).

The population density was 6, 019. 0 people per square mile ( 2, 324. 1 / km < sup > 2 </ sup >).

The population density was 3, 890. 2 people per square mile ( 1, 502. 0 / km² ).

The population density was 1, 873. 0 people per square mile ( 723. 2 / km² ).

The population density was 256. 4 people per square mile ( 99. 0 / km² ).