First, for any value of T for which all values of f{t} are ordinary points the number of values of f{t} must be odd.

For it is clear that the total number of ordinary intersections of C and Af must be even ( otherwise, starting in the interior of C, Af could not finally return to the interior ), and the center of rotation at T is the argument of the function, not a value.

The remaining ( incomplete ) components all have an even number of ordinary points at any argument, and are defined only on a proper sub-interval of Aj.

Following the defeat of the Independent State of Croatia at the end of the war, a large number of Ustaše, and civilians supporting them ( ranging from sympathisers, young conscripts, anti-communists, and ordinary serfs who were allegedly motivated by Partisan crimes ) attempted to flee in the direction of Austria hoping to surrender to British forces and to be given refuge.

Whereas his father and brother had concentrated consular power largely in the hands of the Flavian family, Domitian admitted a surprisingly large number of provincials and potential opponents to the consulship, allowing them to head the official calendar by opening the year as an ordinary consul.

The result can be considered as a type of generalized geometry, projective geometry, but it can also be used to produce proofs in ordinary Euclidean geometry in which the number of special cases is reduced.

They are issued in response to questions by ordinary Muslims, and go unnoticed by those not concerned, while the much smaller number of fatwā issued on controversial subjects, such as war, jihad, and dhimmis ( particularly by extremist preachers ), sometimes get wide coverage in the media because of their political content ( see examples below ).

Various reasons have been suggested for the resistance to the Celsius system in the U. S., including the larger size of each degree Celsius ( resulting in the need for decimals where integer Fahrenheit degrees were adequate for much non-technical work ), the lower zero point in the Fahrenheit system ( which reduces the number of negative signs when measurements such as weather data were averaged ), and the more intuitive alignment of its 0-100 scale to the ordinary range of outdoor temperatures seen in most of the U. S. ( e. g., 0 ° F

When the domain of the input function is time ( t ), and the domain of the output function is ordinary frequency, the transform of function s ( t ) at frequency ƒ is given by the complex number:

Indeed, the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies at least one Planck volume.

Almost all of the captured officers and a large number of ordinary soldiers were then murdered ( see Katyn massacre ) or sent to Gulag.

The invasion was stopped decisively at the Battle of Flodden Field during which the King, many of his nobles, and a large number of ordinary troops were killed, commemorated by the song Flowers of the Forest.

They capture small-scale behavior, just like infinitesimals, but use the ordinary real number system.

The basic dress of a player is a protective equestrian helmet ( usually of a distinctive color, to be distinguished at the considerable distance from which onlookers are watching the game ), riding boots to just below the knees, white trousers ( often ordinary denim jeans ), and a coloured shirt bearing the number of the player's position.

All ordinary matter is made up of combinations of chemical elements, each with its own atomic number, indicating the number of protons in the atomic nucleus.

There are a number of symbolic and real barriers that exist between the normal world and the shrine grounds including: statues of protection, gates, fences, ropes, and other delineations of ordinary to sacred space.

In this situation, a spinor is an ordinary complex number.

The leader of a gang was called the ' jemadar ': this is an ordinary Indian word and is now used as the rank of an Army officer ( Lieutenant ), who would command a similar number of men to a Thuggee gang-leader.

Thus, while in an ordinary ( finite ) hotel with more than one room, the number of odd-numbered rooms is obviously smaller than the total number of rooms.

The plane of all dual numbers is an " alternative complex plane " that complements the ordinary complex number plane C and the plane of split-complex numbers.

Thus, the reading for metric micrometers of this type is the number of whole millimetres ( if any ) and the number of hundredths of a millimetre, as with an ordinary micrometer, and the number of thousandths of a millimetre given by the coinciding vernier line on the sleeve vernier scale.

Their expressed standards concerning sex roles, desirable age for marriage, characteristics of an ideal mate, number of children desired are congruent with the values and stereotypes of the preceding generation -- minus compulsive rebellion.

These data are not of the precision obtainable by the methods previously mentioned, but the vast number of approximate values available will be useful in many areas.

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.

Therefore, for any value of T the number of values of f{t} is equal to the ( finite ) number of tangent points corresponding to the argument T plus an odd number.

; Random effect: An effect associated with input variables chosen at random from a population having a large or infinite number of possible values.

It differs from a digital signal, in which a continuous quantity is represented by a discrete function which can only take on one of a finite number of values.

The addition of the Plus 1 added a number of new * FX and OSBYTE calls that allowed the OS to read the values from the Analogue and parallel interfaces.

In physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion ( variation of refractive index with wavelength ) in relation to the refractive index, with high values of V indicating low dispersion ( low chromatic aberration ).

Blowfish's key schedule starts by initializing the P-array and S-boxes with values derived from the hexadecimal digits of pi, which contain no obvious pattern ( see nothing up my sleeve number ).

For example, one type of " compare " instruction considers two values and sets a number in the flags register according to which one is greater.

In 2005, a reassessment of residential property values resulted in a disproportionate number of houses owned by non-affluent people jumping in value relative to other houses, with hundreds having their property tax increased by over 100 %; this forced many homeowners in Cambridge to move elsewhere.

* Truncated mean – the arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded.

These shells can be constructed from pentamers and hexamers by minimizing the number T ( triangulation number ) of nonequivalent locations that subunits occupy, with the T-number adopting the particular integer values 1, 3, 4, 7, 12, 13 ,...( T

and all the signal values within an interval are quantized to the same number.

Positional decimal systems include a zero and use symbols ( called digits ) for the ten values ( 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 ) to represent any number, no matter how large or how small.

Clones of board games must use computer generated dice ; the values are usually determined by a pseudorandom number generator, then displayed as a visual representation of a die.

The sum of the two values, i. e. the total number of pips, may be referred to as the rank or weight of a tile, and a tile with more pips may be called heavier than a lighter tile with fewer pips.

If the initial value of a polynomial ( and of its finite differences ) is calculated by some means for some value of X, the difference engine can calculate any number of nearby values, using the method generally known as the method of finite differences.

When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.

Furthermore, one can find a neighborhood of Q in which the difference function is monotone, for since it is analytic it can have only a finite number of extrema in any interval.

Moreover, whereas in Interstate Commerce Commission parlance `` variable cost '' means a cost deemed to vary in direct proportion to changes in rate of output, in the type of analysis now under review `` variable cost '' has been used more broadly, so as to cover costs which, while a function of some one variable ( such as output of energy, or number of customers ), are not necessarily a linear function.

* Argument ( complex analysis ), a function which returns the polar angle of a complex number

( A formal proof for all finite sets would use the principle of mathematical induction to prove " for every natural number k, every family of k nonempty sets has a choice function.

The standard structure is where is the set of natural numbers, is the successor function and is naturally interpreted as the number 0.

Usually the efficiency or running time of an algorithm is stated as a function relating the input length to the number of steps ( time complexity ) or storage locations ( space complexity ).

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

In number theory, an arithmetic, arithmetical, or number-theoretic function is a real or complex valued function ƒ ( n ) defined on the set of natural numbers ( i. e. positive integers ) that " expresses some arithmetical property of n ."

Bishop Alexander, so the tale runs, had invited a number of fellow prelates to meet him at breakfast after a great religious function.

The concept of binary function generalises to ternary ( or 3-ary ) function, quaternary ( or 4-ary ) function, or more generally to n-ary function for any natural number n.

A BMX bike, an example of a bicycle designed for sport Bicycles can be categorized in different ways: e. g. by function, by number of riders, by general construction, by gearing or by means of propulsion.

The number of qubits in the computer is allowed to be a polynomial function of the instance size.

where is the Boltzmann constant, T is temperature ( assumed to be a well-defined quantity ), is the degeneracy ( meaning, the number of levels having energy ; sometimes, the more general ' states ' are used instead of levels, to avoid using degeneracy in the equation ), N is the total number of particles and Z ( T ) is the partition function.

/* The following function will print a non-negative number, n, to

A number of internal groups flourished within the new party, the most notable of which was the Tawney Society ( mirroring the function of the Fabian Society within the Labour Party ).