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Another polynomial associated with A is the Whitney-number polynomial w < sub > A </ sub >( x, y ), defined by
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Another and polynomial
Another polynomial viewpoint is exploited by the Winograd algorithm, which factorizes into cyclotomic polynomials — these often have coefficients of 1, 0, or − 1, and therefore require few ( if any ) multiplications, so Winograd can be used to obtain minimal-multiplication FFTs and is often used to find efficient algorithms for small factors.
Another method based on the Cayley – Hamilton theorem finds an identity using the matrices ' characteristic polynomial, producing a more effective equation for A < sup > k </ sup > in which a scalar is raised to the required power, rather than an entire matrix.
Another method with this style is the Dandelin – Gräffe method ( actually due to Lobachevsky ) which factors the polynomial.
Another characterization: A matrix or linear map is diagonalizable over the field F if and only if its minimal polynomial is a product of distinct linear factors over F. ( Put in another way, a matrix is diagonalizable if and only if all of its elementary divisors are linear.
Another example is an implicit function given by x − C ( y ) = 0 where C is a cubic polynomial having a " hump " in its graph.
Another example is that the maximum height ( maximum absolute value of coefficients ) of all the factors of x < sup > n </ sup > − 1 appears to be the same as height of nth cyclotomic polynomial.
Another paper by Hartmanis from 1977, with Leonard Berman, introduced the still-unsolved Berman – Hartmanis conjecture that all NP-complete languages are polynomial time isomorphic.
Another example: P being as above, a resolvent R for a group G is a polynomial whose coefficients are polynomials in the coefficients of p, which provides some information on the Galois group of P. More precisely, if R is separable and has a rational root then the Galois group of P is contained in G. For example, if D is the discriminant of P then is a resolvent for the alternating group.
Another possibility to transform a polynomial so as to satisfy the criterion, which may be combined with applying a shift, is reversing the order of its coefficients, provided its constant term is nonzero ( without which it would be divisible by x anyway ).
Another proof is that its Alexander polynomial does not satisfy the Fox-Milnor condition.
Another way is to find two factors of the polynomial and divide the original polynimial by them.
Another important basic class of examples are representations of polynomial algebras, the free commutative algebras – these form a central object of study in commutative algebra and its geometric counterpart, algebraic geometry.
Another special case of an abelian integral is a hyperelliptic integral, where, in the formula above, is a polynomial of degree greater than 4.
Another well known example is the polynomial, whose roots are the golden ratio and its conjugate, showing that it is reducible over the field, although it is irreducible over the non-UFD which has as field of fractions.
Another and associated
Another hit song associated with McLean ( though never recorded by him ) is " Killing Me Softly with His Song ", which was written about McLean after Lori Lieberman, also a singer / songwriter, saw him singing his composition " Empty Chairs " in concert.
Another term which is commonly associated to Swap is Swaption which is basically an option on the forward Swap.
Another example of a fictitious force associated with rotating reference frames is the centrifugal force.
Another interesting and useful property of the collinear Lagrangian points and their associated Lissajous orbits is that they serve as " gateways " to control the chaotic trajectories of the Interplanetary Transport Network.
Another trend in art associated with neo-Dada is the use of a number of different media together.
Another trend in art which has been associated with the term postmodern is the use of a number of different media together.
Another application of the material sciences is the structures of glass and ceramics, typically associated with the most brittle materials.
Another important influence on Schaeffer ’ s practice was cinema and the techniques of recording and montage, which were originally associated with cinematographic practice, came to " serve as the substrate of musique concrète.
Another mascot associated with the Vikings was " Vikadontis Rex ", a purple foam dinosaur.
Another clear indication is from the Readycon Dene site in West Yorkshire, where 35 microliths appear to be associated with a single projectile.
Another example is purchasing economies due to increased order size and associated bulk-buying discounts.
Another barrister said that it was a " matter of embarrassment that a senior British lawyer would want to allow himself to be associated with such a silly idea ".
Another scepter associated with the king is the was-scepter.
Another common thread among thinkers associated with the Post-Structuralist movement is the criticism of the absolutist, quasi-scientific claims of Structuralist theorists as more reflective of the mechanistic bias inspired by bureaucratization and industrialization than of the inner-workings of actual primitive cultures, languages or psyches.
Another 2011 study found that the p53 homozygous ( Pro / Pro ) genotype was associated with a significantly increased risk for renal cell carcinoma.
" Another science fiction project associated with Scott is an adaptation of Aldous Huxley's Brave New World, with Leonardo DiCaprio potentially involved.
Another study of the same group has shown that, after training, measured brain activity related to working memory increased in the prefrontal cortex, an area that many researchers have associated with working memory functions.
Another study from The Harvard School of Public Health appearing in Circulation ( journal ) found " Consumption of processed meats, but not red meats, is associated with higher incidence of coronary heart disease and diabetes mellitus.
Another investigation found the cosmological time, dt, diverges for any finite interval, ds, associated with an observer approaching the cosmological horizon, representing a physical limit to observation for the standard model when the cosmological term is included.
Another important source of pitchblende is at Great Bear Lake in the Northwest Territories of Canada, where it is found in large quantities associated with silver.
Another story, " The Tale of Truth and Falsehood ", adapts the conflict of Horus and Set into an allegory, in which the characters are direct personifications of truth and lies rather than deities associated with those concepts.
Another common type of formation is associated with sea fog ( also known as haar or fret ).
* Mad Scientist: Another monster parody, this time with an evil scientist ( Morgan Freeman ) and his assistant Igor ( Luis Avalos ), who tried to read words associated with their experiments.
Another school of thought emphasizes hair pulling as addictive or positively reinforcing as it is associated with rising tension beforehand and relief afterward.
Another problem with the panorama was what it came to be associated with, namely, by redefining the sublime to incorporate the material.
Another and with
Another editor pointed despairingly at a bundle of letters that had accumulated for him, saying, `` But Mr. Hearst, what shall I do with this correspondence ''??
Another classic sight that gave us considerable pleasure was the Evzone sentry, in his ballet skirt with great pompons on his shoes, who was patrolling up and down in front of the palace.
Another remained when an American Army car was recovered but with a broken glass.
Another evidence of the spreading rule of reason was provided from Mexico City with the daily hijacking of an American plane by a demented Algerian with a gun.
Another example is the recent cancellation of the F-108, a long-range interceptor with a speed three times as great as the speed of sound, which was designed for use against manned bombers in the period of the mid-1960's.
Another growth factor is increased consumer demand for better quality and larger quantities of fabrics that go with a rising standard of living.
Another spot with an image-provoking name is the Black Hills where you can visit the old frontier mining town of Deadwood.
Another person inside with a weight against each batten will help in the fastening.
Another method of assuring a clean hole is to first drill a small pilot hole all the way through, then drill half way with the dimensional bit, turn the piece over, and finish from the other side.
Once there, the D.A. with devilish cleverness would provide Marshall with headlines: `` Viola's Multiple Romances '' `` Viola Lake an Addict '' `` Downfall of Another Film Idol ''!!
Another stock vaudeville gag ran: `` Mother is home sick in bed with the doctor ''.
Another cure for hydrophobia was to suck the wounds, then cauterize them with a hot knife or poker.
Another wart removal method was to rub each wart with a bean split open and then to bury the bean halves under the drip of the house for seven days.
Another neighbor, Mrs. Frank C. Smith, 2731 Pall Mall, Sterling Township, surprised Kowalski by coming to the home yesterday with $135 collected locally toward the $400 funeral costs.
Another speaker, William H. Draper, Jr., former Under Secretary of the Army and now with the Palo Alto venture capital firm of Draper, Gaither & Anderson, urged the U.S. to `` throw down the gauntlet of battle to communism and tell Moscow bluntly we won't be pushed around any more ''.
Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a place holder.
Another popular method of exploiting this bug was to simply use thrust to keep the ship in motion with 1 or 2 asteroids in the play field, allowing the player to pick off as many 1, 000 point UFOs as possible.
Another view defines anxiety as " a future-oriented mood state in which one is ready or prepared to attempt to cope with upcoming negative events ," suggesting that it is a distinction between future and present dangers which divides anxiety and fear.
Another advantage with analog signals is that their processing may be achieved more simply than with the digital equivalent.
Another place popular with children is the Parque Papagayo which is a large family park which has life-sized replicas of a Spanish galleon and the space shuttle Columbia, three artificial lakes, aviary, skating rink, rides, go-karts and more.
Another influence was Alexander Kikin, a high-placed official who had fallen out with the Tsar and had been deprived of his estates.
Another marriage alliance attempted to resolve the potential conflict with Serbia in Macedonia, as Andronikos II married off his five-year old daughter Simonis to King Stefan Milutin in 1298.
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