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A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.
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number and is
It is one of the ironic quirks of history that the viability and usefulness of nationalism and the territorial state are rapidly dissipating at precisely the time that the nation-state attained its highest number ( approximately 100 ).
It is worth dwelling in some detail on the crisis of this story, because it brings together a number of characteristic elements and makes of them a curious, riddling compound obscurely but centrally significant for Mann's work.
The cyclist, a sufficiently commonplace young fellow, is not named but identified simply as `` Life '' -- that and a license number, which Piepsam uses in addressing him.
Presumably a cocktail party is expected to fulfill the host's desire to get together a number of people who are inadequately acquainted and thereby arrange for bringing the level of acquaintance up to adequacy for future cooperative endeavors.
The number of primitive ideas in systematically-simple theories is reduced to a minimum.
I assume that the number of readers of this anthology who regard themselves as morally perfect is small, and that most readers are willing to consider procedures by which they may gain more insight into themselves and better understanding of others.
That is how the real routine of resistance goes on, and its strength is directly proportionate to the number of insignificant people who can let themselves be taken to pieces, piece by piece, without quitting.
Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.
There are a number of other considerations besides this one but it is for the Congress, not the Department of Justice, to balance these various considerations and make a judgment about legislation.
Nonetheless, although few in number they are a stubborn crew, as tenacious of life as the Hardshell Baptists, which suggests that there is some kind of vital principle embodied in their faith.
For that is the one an increasingly large number of prominent Americans are now proposing.
and it is still very far from certain how valid the party's claim is that in `` a growing number of kolkhozes '' the peasants are finding it more profitable, to surrender their private plots to the kolkhoz and to let the latter be turned into something increasingly like a state farm.
Too bad your number is in the directory ''.
The number of countries thus favorably situated is small, but their peoples constitute over half of the population of the underdeveloped world.
The resulting setup, it was declared, `` would be similar to that which is in successful operation in a number of metropolitan counties as large or larger than Rhode Island ''.
The Navy, on April 25, announced it is bringing back the carrier Shangri-La from the Mediterranean, increasing to four the number of attack carriers in the vicinity of Cuba.
There is little doubt that the number of those who wish to serve will be far greater than our capacity to absorb them.
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.
During nighttime hours, because of the intense skywave propagation then prevailing, no large number of stations can be permitted to operate on one of these channels, if the wide area service for which these frequencies are assigned is to be rendered satisfactorily by the dominant stations which must be relied upon to render it.
In the daytime, on the other hand, since skywave transmission is relatively inefficient, it is possible to assign a substantially larger number of stations on these channels.
Such additional daytime class 2, assignments are appropriate if optimum use is to be made of these frequencies, and the Commission has over the years made a large number of them.
number and root
In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients ( or equivalently — by clearing denominators — with integer coefficients ).
* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.
An example of such a number is the unique real root of the polynomial ( which is approximately 1. 167304 ).
An algebraic integer is an algebraic number which is a root of a polynomial with integer coefficients with leading coefficient 1 ( a monic polynomial ).
Some subfields of R have nontrivial field automorphisms, which however do not extend to all of R ( because they cannot preserve the property of a number having a square root in R ).
From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played.
Subfolders can contain still more files and folders and so on, thus building a tree-like structure in which one " master folder " ( or " root folder " — the name varies from one operating system to another ) can contain any number of levels of other folders and files.
He then realised that a judicious use of affixes could greatly decrease the number of root words needed for communication.
Jinn is a noun of the collective number in Arabic literally meaning " hidden from sight ", and it derives from the Arabic root meaning " to hide " or " be hidden ".
These include the Governmental Advisory Committee ( GAC ), which is composed of representatives of a large number of national governments from all over the world ; the At-Large Advisory Committee ( ALAC ), which is composed of representatives of organizations of individual Internet users from around the world ; the Root Server System Advisory Committee, which provides advice on the operation of the DNS root server system ; the Security and Stability Advisory Committee ( SSAC ), which is composed of Internet experts who study security issues pertaining to ICANN's mandate ; and the Technical Liaison Group ( TLG ), which is composed of representatives of other international technical organizations that focus, at least in part, on the Internet.
A number of foods have been avoided while eating pork, including Chinese bellflower ( doraji, 도라지 ) and lotus root ( yeonn ppuri, 연뿌리 ), as the combinations have been thought to cause diarrhea.
Note: A number of other plants have been suggested by biblical scholars, e. g., Most notably Ginseng which looks similar to the mandrake root and has fertility enhancing properties, for which it was picked by Reuben in the Bible.
Naming is also a problem for monophyletic groups: because the number of ancestors from which to root monophyletic groups is almost infinite, giving each clade a unique name is impossible-as illustrated by the failed attempts to instigate a system called the Phylocode.
Contains the size and number of segments, the root location of the page table and the address space number.
For a number written in scientific notation, this logarithmic rounding scale requires rounding up to the next power of ten when the multiplier is greater than the square root of ten ( about 3. 162 ).
number and P
In number theory, if P ( n ) is a property of positive integers, and if p ( N ) denotes the number of positive integers n less than N for which P ( n ) holds, and if
The length of the description is just the length of P as a character string, multiplied by the number of bits in a character ( e. g. 7 for ASCII ).
P can be estimated by using the measured speedup ( SU ) on a specific number of processors ( NP ) using
P estimated in this way can then be used in Amdahl's law to predict speedup for a different number of processors.
The standards produced are titled British Standard XXXX: YYYY where XXXX is the number of the standard, P is the number of the part of the standard ( where the standard is split into multiple parts ) and YYYY is the year in which the standard came into effect.
In large churches where they were celebrated the services were usually grouped ; e. g. Matins and Lauds ( about 7. 30 A. M .); Prime, Terce ( High Mass ), Sext, and None ( about 10 A. M .); Vespers and Compline ( 4 P. M .); and from four to eight hours ( depending on the amount of music and the number of high masses ) are thus spent in choir.
The coordinates of P are then X and Y interpreted as numbers x and y on the corresponding number lines.
The number of normalized floating point numbers in a system F ( B, P, L, U ) ( where B is the base of the system, P is the precision of the system to P numbers, L is the smallest exponent representable in the system, and U is the largest exponent used in the system ) is:
The inverse transform, known as Fourier series, is a representation of s < sub > P </ sub >( t ) in terms of a summation of a potentially infinite number of harmonically related sinusoids or complex exponential functions, each with an amplitude and phase specified by one of the coefficients:
The program faced a number of problems including the collapse of the fisheries and the shoddy construction of many of the buildings, particularly the infamous Blok P, and produced a number of problems of its own, including continuing unemployment and alcoholism.
If the cause of the crash is uncertain, this number is rendered as 48454C50, which stands for " HELP " in hexadecimal ASCII characters ( 48 = H, 45 = E, 4C = L, 50 = P ).
Consider a pseudo random number generator ( PRNG ) function P ( key ) that is uniform on the interval 2 < sup > b </ sup > − 1.
Like all subatomic particles, hadrons are assigned quantum numbers corresponding to the representations of the Poincaré group: J < sup > PC </ sup >( m ), where J is the spin quantum number, P the intrinsic parity ( or P-parity ), and C, the charge conjugation ( or C-parity ), and the particle's mass, m. Note that the mass of a hadron has very little to do with the mass of its valence quarks ; rather, due to mass – energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction.
* The P (" plants ") count is the number of boxes the letterboxer has made and placed.
A membrane, or brane, is a multidimensional object, usually called a P-brane, with P referring to the number of dimensions in which it exists.
* NPT ensemble, a name for the isothermal – isobaric ensemble where the number of particles ( N ), pressure ( P ), and temperature ( T ) of the system are in equilibrium
Looney's theory attracted a number of activist followers who published books supplementing his own and added new arguments, most notably Percy Allen, Bernard M. Ward, Louis P. Bénézet and Charles Wisner Barrell.
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