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1 компактное в нормированной топологии множество
Mathematics: norm compact setУниверсальный русско-английский словарь > компактное в нормированной топологии множество
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2 Для того чтобы
In order that $f^*$ be (но не is) a good approximation to a given function $f$, we require the error function $f-f^*$ to be small in some senseFor a function $f$ to be continuous it is necessary that...A necessary and sufficient condition for a matrix to be nonsingular is that its determinant be nonzeroIn order that this process have (но не has) meaning, it is necessary that it give (но не gives) a unique resultFormula (1) is applied to study the above case (to derive the theorem below, to obtain an $x$ with norm not exceeding 1)Let us consider some examples to show how this function decreases at infinityThis approach is too complicated to be used in the above caseThis particular case is important enough to be considered separatelyWe now apply (use) Theorem 1 to obtain $x=y$Insert (1) into (2) (substitute (1) into (2)) to find that...We partially order $Z$ by declaring $X<Y$ to mean that...For this to happen (in order that this happens), this set must be compactFor the second estimate to hold, it is enough to assume that...Then for such a map to exist, we should assume that...One must use basis functions of degree at least two in order for $x$ to be nonzeroРусско-английский словарь по прикладной математике и механике > Для того чтобы
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