Sometimes this theorem is stated as follows: every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity.

Sometimes, reduced homology groups of a chain complex C ( X ) are defined as homologies of the augmented complex

Sometimes a single calculation can be achieved in several ways, all of which are algebraically equivalent in terms of ideal real or complex numbers, but in practice when performed on digital computers yield different results.

Sometimes the term face is used to refer to a simplex of a complex, not to be confused with a face of a simplex.

Sometimes, if the dispute is more complex, the ombudsman must mediate.

Sometimes formulas cannot be understood without a written or spoken explanation, but often they are sufficient by themselves, and sometimes they are difficult to read aloud or information is lost in the translation to words, as when several parenthetical factors are involved or when a complex structure like a matrix is manipulated.

* Sometimes the rules of correspondence are more complex and depend on adjacent letters, often as a result of historical sound changes ( as with the rules for the pronunciation of c and ci in Italian, and the silent e in English ).

Some phytochemicals with physiological properties may be elements rather than complex organic molecules. Sometimes they can be harmful and sometimes they can be very helpful, as far as concerned they are responsible for the color in vegetables or fruits.

Sometimes patterns are more complex:

Sometimes, newly built replicas and reproductions of vintage aircraft are called " warbirds ," such as Allison V-1710-powered Yakovlev Yak-9s from Yakovlev, Messerschmitt Me 262s built by the Me 262 Project and Focke-Wulf Fw 190s by Flug Werk ; this can include any one of a large number of different aircraft designs from between World War I the late 1930s, when military aircraft design was less complex.

Sometimes these maps are just static images allowing simple panning and zooming, while others are more complex pages.

Sometimes intricate, complex music was made using the possibilities of 4 or 5 players.

Sometimes the pattern takes the shape of a grid or other array formation and complex beamforming signal processing is used to transcend the capabilities of single, or limited numbers of, hydrophones.

Sometimes, poltergeist classes are created because the programmer anticipated the need for a more complex architecture.

Sometimes a such function is referred as n-harmonic function, where n ≥ 2 is the dimension of the complex domain where the function is defined.

Sometimes, Be stars will form multiple gas rings or " decretion disks ", each with its own evolution, creating complex circumstellar dynamics.

Penelope Farmer's Charlotte Sometimes ( 1969 ) was a darker, more complex novel about the way time slip ( back to 1918 ) could threaten the main character's very identity.

Sometimes, the degree of uncommonalities would lead some to perceive the group's bond as being ordinarily unlikely ; here it can indicate the fact the historical ties may no longer be in operation, and the coalition members, instead, are joined by a new intention, not necessarily prior bonds.

Sometimes eutectic was sprinkled between the layers to increase the bond.

Sometimes, CDs that are indexed to the stock market, the bond market, or other indices are introduced.

Sometimes, they bond over a mutual sentiment towards an unpleasant experience and their attacking each other is more play than serious attacks.

Sometimes he did this three or four times a day, for this Woman was almost always with him.

Sometimes they get their initial experience in church haflis, conducted by Lebanese and Syrians in the U.S., where they dance with just as few veils across their bodies as in nightclubs.

Sometimes it is necessary to roughly calculate the square inch area of the opening but the calculation can usually be made with sufficient accuracy that it won't affect the final computation.

Sometimes she even wore the uniform in solid, unrelieved black, and with her blonde hair cut so closely, wearing this uniform, she strongly resembled a member of the SS..

Sometimes, he coincided with my father's being at home.

Sometimes these servants wrote or dictated for enclosure with the letters of their soldier-masters messages to their relatives and to members of their owners' families.

`` Sometimes we'd have trouble persuading her to make tax-exempt charitable contributions, and I've known her to quarrel with a plumber over a bill for fixing a faucet ; ;

Sometimes, countries have the written language undergo a spelling reform to realign the writing with the contemporary spoken language.

Sometimes our perceptions and our languages actually mislead us as to the " facts " with which we must deal.

Sometimes slightly stronger theories such as Morse-Kelley set theory or set theory with a strongly inaccessible cardinal allowing the use of a Grothendieck universe are used, but in fact most mathematicians can actually prove all they need in systems weaker than ZFC, such as second-order arithmetic.

Sometimes the whole space is taken up with the inscription.

Sometimes, Roman numerals are still used for enumeration of lists ( as an alternative to alphabetical enumeration ), for sequential volumes, to differentiate monarchs or family members with the same first names, and ( in lower case ) to number pages in prefatory material in books.

Sometimes the garment and the shield are merged, with a small version of the shield appearing on the garment.

Sometimes medication is combined with psychotherapy but research has found that there is no benefit of combined pharmacotherapy and psychotherapy versus monotherapy.

Sometimes they are also outfitted with irrigation systems or heat sink-systems which can respectively irrigate the plants or help to store energy from the sun and redistribute it at night ( when the greenhouses starts to cool down ).

Sometimes they wanted a little alteration, sometimes none ; sometimes the lines needed in order to make a complete poem would come later, spontaneously or with ' a little coaxing '; sometimes he had to sit down and finish the poem with his head.

Sometimes in series with this rule an exception is made for religious materials such as the Bible, Torah or Qur ' an.

Sometimes vinegar is added, but only after the beans are cooked as vinegar interferes with the beans ' softening.

Sometimes, disciplines within BME are classified by their association ( s ) with other, more established engineering fields, which can include:

Sometimes the term includes data that has not traditionally been associated with computers, such as film, tapes, and records.

Sometimes the term includes data that has not traditionally been associated with computers, such as film, tapes, and records.

Sometimes applications are bundled with the computer, but that does not change the fact that they run as independent applications.

Sometimes, EVPs report to the Vice Chair who in turn reports directly to the CEO ( so Vice Chairs in effect constitute an additional layer of management ), other Vice Chairs have more responsibilities but are otherwise on an equal tier with EVPs.

Sometimes, even the non-bonding valence shell electrons ( with the two-dimensional approximate directions ) are marked, i. e. for elemental carbon < sub >.</ sub >< sup >'</ sup > C < sup >'</ sup >.