In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

* 1799: Doctoral dissertation on the Fundamental theorem of algebra, with the title: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (" New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors ( i. e., polynomials ) of the first or second degree ")

* Central composite design, an experimental design in response surface methodology for building a second order model for a response variable without a complete three level factorial

Most systems may be assumed to have a second order and single variable system response in the time domain ignoring multi-variable.

The output of op amp 0 will correspond to the x variable, the output of 1 will correspond to the first derivative of x and the output of 2 will correspond to the second derivative.

The second view is the probabilistic view: the random variable depends upon the random variable, which depends upon, which depends upon the random variable.

Also Meeus's formula uses a fractional variable to allow computation of the four main phases, and uses a second variable for the secular terms.

For example, is a polynomial, but is not, because its second term involves division by the variable x ( 4 / x ), and also because its third term contains an exponent that is not a non-negative integer ( 3 / 2 ).

His Cine-Kodak K-100 camera had markings on its continuously variable dial of 16, 24, 32, 48, and 64 frames per second and was capable of filming at any frame speed within this range.

" His second argument, which follows from the first, is that once the caricature of " constant speedism " is dismissed, we are left with one logical alternative, which Dawkins terms " variable speedism.

Until the standardization of the projection speed of 24 frames per second ( fps ) for sound films between 1926 and 1930, silent films were shot at variable speeds ( or " frame rates ") anywhere from 12 to 26 fps, depending on the year and studio.

The second shows the much more variable high and low tides that form a " mixed tide ".

While the first one may be seen as the variance of the sample considered as a population, the second one is the unbiased estimator of the population variance, meaning that its expected value E is equal to the true variance of the sampled random variable ; the use of the term n − 1 is called Bessel's correction.

This mechanism suffers from timing attacks on the second generator, since the speed of the output is variable in a manner that depends on the second generator's state.

In fact the Lunar Mechanism which is part of the Antikythera Mechanism depicts the motion of the Moon and its phase, for a given time, using a train of four gears with a pin and slot device which gives a variable lunar velocity that is very close to the second law of Kepler, i. e. it takes into account the fast motion of the Moon at perigee and slower motion at apogee.

But if we multiply all values of the first variable by 100, then the principal component will be almost the same as that variable, with a small contribution from the other variable, whereas the second component will be almost aligned with the second original variable.

Grant followed the album with her second Christmas album, Home For Christmas in 1992, which included the song " Breath of Heaven ( Mary's Song )", written by Chris Eaton and Grant, and would later be covered by many artists, including Donna Summer, Jessica Simpson ( who acknowledged Grant as one of her favorite artists ), Vince Gill, Sara Groves, Point of Grace, and Broadway star Barbara Cook.

One of the most famous involved star second baseman Napoleon Lajoie, who in 1901 went across town in Philadelphia from the National League Phillies to the American League Athletics.

* CS Cam is the second brightest star, though it has neither a Bayer nor a Flamsteed designation.

In addition to Alpha Centauri ( the 3rd brightest star in the sky ), a second first magnitude star, Beta Centauri, is part of Centaurus.

In 1901, Napoleon " Nap " Lajoie, the Philadelphia Phillies ' star second baseman, jumped to the A's after his contract was capped at $ 2, 400 per year — one of the highest-profile players to jump to the upstart AL.

The second one happens on the evening of 24 December ; gifts are placed under the Christmas tree, usually in the absence of Santa-believing children ( many of whom are occupied with watching the sky in search of the first star ) if there are any in the family.

The derivation must then have been secondary for the initial ayin to be confused with an aleph ( both represented by vowels in Akkadian ), and the second consonant descended as a / s / ( like in the Aramaic asthr " bright star "), rather than a / sh / as in Hebrew and most commonly in Akkadian.

Some countries ' top divisions feature highly paid star players ; in smaller countries and lower divisions, players may be part-timers with a second job, or amateurs.

The second cornerstone of the Fermi paradox is a rejoinder to the argument by scale: given intelligent life's ability to overcome scarcity, and its tendency to colonize new habitats, it seems likely that at least some civilizations would be technologically advanced, seek out new resources in space and then colonize first their own star system and subsequently the surrounding star systems.

By the end of 1917, Trotsky was unquestionably the second man in the Bolshevik Party after Lenin, overshadowing the ambitious Zinoviev, who had been Lenin's top lieutenant over the previous decade, but whose star appeared to be fading.

The Kingdom ( Riget ) was planned as a trilogy of three seasons with 13 episodes in total, but the third season was not filmed due to death of star Ernst-Hugo Järegård shortly after completion of the second season.

With an apparent brightness of 0. 03m, this is the second brightest star of the northern hemisphere ( after Arcturus ) and the fifth brightest star in all ; its spectral class is A0 V and it lies at a distance of only 25. 3 ly.

In astrophysics, mass transfer is the process by which matter gravitationally bound to a body, usually a star, fills its Roche lobe and becomes gravitationally bound to a second body, usually a compact object ( white dwarf, neutron star or black hole ), and is eventually accreted onto it.

At the toilet, the second most important star of the show, Harry, is feeling ill and asks himself what is happening to his body when he hears a voice from the toilet asking him if he does not feel well: It is the paparazzi F. W.

Alternatively, 5 ml from a neutron star of radius 20 km radius ( average density ) has a mass of about 400 million metric tons, or about the mass of all humans .</ ref > The resulting force of gravity is so strong that if an object were to fall from a height of one meter it would only take one microsecond to hit the surface of the neutron star, and would do so at around 2000 kilometers per second, or 7. 2 million kilometers per hour.

However, the second shell is twice as far away, so each star in it would appear four times dimmer than the first shell.

One possible explanation for the lack of white dwarfs is that when a red giant expels its outer layers to become a planetary nebula, a slight asymmetry in the loss of material could give the star a ' kick ' of a few kilometres per second, enough to eject it from the cluster.

He won 51 of the events, abandoned one race and lost two handicap races along with his final event ; a half-mile race at the Yankee Stadium, where he finished second to American track star Alan Helffrich.

The construction principle for these expressions is that expression is obtained by concatening two copies of, appropriately renaming the letters of the second copy using fresh alphabet symbols, concatenating the result with another fresh alphabet symbol, and then by surrounding the resulting expression with a Kleene star.

Numbers with a decimal point were used to insert new star systems for the second edition without destroying the desired order ( by right ascension ).

These began to be apparent in a press conference held during the second illness in order that the consulting specialists might clarify the President's condition for the nation.

Its second press release was on January 15, 1958, and it recommended that the secret papers be destroyed.

Upon second thought we were forced to realize that we have very few reliable historical benchmarks against which we might compare the present situation, and that conclusions that present-day students are `` more '' or `` less '' religious could not be defended on the basis of our data.

Even to be `` from hope and fear set free '' is at least better than to have lost the first without having got rid of the second.

So, all in all, the infield can't be expected to supply the added improvement to propel the Birds from second to first.

Hank Foiles, backed up by Frank House who will be within calling distance in the minors, make up better second line catching than the Birds had all last year, but Gus is still that big man you need when you start talking pennant.

When he came to Baltimore, he was leaving a team which was supposed to win the National League pennant, and he was joining what seemed to be a second division American League club.

Carvey considers that former Vice President Nixon would be Brown's most formidable foe, with ex-Gov. Knight a close second.

The 15th Street deposit is not to be confused with the nearby famous Mayflower Hotel cypress swamp on 17th Street reported in The Washington Post, August 2, 1955, which was probably formed during the second interglacial period and is therefore much younger.

It was evident that a second transfer had to be effected, and that it had to take place between the time the fille finished the doctor's room and the time she began Alex's.

However, the healthy inventory position of the textile industry lends support to the broadly expressed belief that improvement in that industry can be expected by the second half of 1961.

In the second, more shops, laboratories, and staff will be required.

Sweet-sour sauce can be kept warm over a second hibachi or chafing dish while charcoal in broiler is reaching glowing coal stage.

In a two-story house, one unit may be installed in the basement to serve the first floor, another in the attic to cool the second.

The expectation is that first-level supervisors will be selected in approximately equal numbers from the second and third engineering level, with very few coming from the first level.

She always let it be known that there was wine in the pot roast or that the chicken had been marinated in brandy, and that Koussevitzky's second cousin was an intimate of theirs.

This will be more or less our general method for the second problem.

Clearly, any line, l, of any bundle having one of these points of tangency, T, as vertex will be transformed into the entire pencil having the image of the second intersection of L and Q as vertex and lying in the plane determined by the image point and the generator of Af which is tangent to **zg at T.

the second requires that there be a line through P which meets **zg in Af points.

It is planned to double the number of teams and to make use of improved equipment in a second demographic inquiry in 1960, so that the inquiry can be carried through in one year and the results published more expeditiously.

Is George put the cat out, dominant stress will ordinarily be on the first complement, the cat, not the second complement out.

In the second sentence if drinking water is a gerundial clause and without drinking water is roughly equivalent in meaning to unless I drink water, there will be stronger stress on water than on drinking ; ;

These differences in turn result from the fact that my Yokuts vocabularies were built up of terms selected mainly to insure unambiguity of English meaning between illiterate informants and myself, within a compact and uniform territorial area, but that Hoijer's vocabulary is based on Swadesh's second glottochronological list which aims at eliminating all items which might be culturally or geographically determined.

This second conclusion, independently arrived at by independent study of material from two pairs of language families as different and remote from one another as these four are, cannot be ignored.

My guess would be that interest rates will decline moderately into the spring of 1961 and during the second half of the year will turn up gradually to recover the ground lost during the downturn.