| (3) |
Если областью,1 в которой задана2 начальная температура t(x, y, z), является всё3 пространство, то4 решение может быть записано5 в замкнутой форме.
If the domain, in which the initial temperature t(x, y, z), is prescribed, is the whole space, then the solution can be written in closed form.
Notes
| 1. | Instrumental case with являться (to be). ↑ |
| 2. | Short form, feminine, of заданный; a predicative use is indicated here, and the passive participle gives the passive sense to the translation. ↑ |
| 3. | всё is an adjective, and its synonyms often give a smoother translation than "all." ↑ |
| 4. | The conjunction "then" rather than the neuter of тот. ↑ |
| 5. | The same use of the passive participle as in note 2; the link-verb быть must be used here following может. Note also that может быть as a phrase has the meaning "perhaps," but that the context rules out this possibility. See also Some Special Verbs below. ↑ |
| (4) |
Для того, чтобы1 этот процесс имел2 смысл, необходимо,3 чтобы4 он давал единственный результат.
In order that this process have meaning, it is necessary that it give a unique result.
Notes
| 1. | для того, чтобы is the usual phrase "in order that," and the verb to follow is always subjunctive or conditional. ↑ |
| 2. | The conditional or subjunctive mood of иметь (to have); the particle бы has been attached to the что (that) in the clause. ↑ |
| 3. | Note the short form and the implied predicative. ↑ |
| 4. | The conditional of давать (to give) is давал бы, and the particle бы usually combines with что. ↑ |
| (5) |
Повторяя1 это рассуждение, мы получим2 тот же3 результат для функции f (x).
By repeating this argument, we obtain the same result for the function f (x).
Notes
| 1. | Adverbial participle of повторить (to repeat); the translation of повторяя could have been rendered by "Repeating" or "If we repeat," to suit the taste of the translator. ↑ |
| 2. | Perfective form, and the future "we shall obtain" has the same sense, in the context, as "we obtain." ↑ |
| 3. | Note the pair тот же under тот or under же in the dictionary. ↑ |
| (6) |
Распределение, задаваемое1 функцией плотности2 sn(x) или функцией распределения2 Sn(x) известно под названием распределения Стьюдента или t-распределения; оно было впервые использовано3 в одной важной статистической проблеме В. Госсетом, писавшим4 под псевдонимом «Стьюдент» (Student).5
The distribution defined by the frequency function sn(x) or the distribution function Sn(x) is known under the name of Student's distribution or the t-distribution; it was first used in an important statistical problem by W. Gosset, writing under the pseudonym of "Student."