| Some Comments on the Translation of Verb Forms |
The difference in the sense of the imperfective and perfective can be emphasized by exhibiting both aspects of the same verb in one sentence. (It is recommended that each word in the sentence be looked up in the dictionary; the superscripts refer to the comments immediately following the translation.)
| (1) |
Прежде чем1 доказывать,2 что все собственные значения матрицы A удовлетворяют3 уравнению (4), мы докажем,4 что если h(λ) — общий наибольший делитель5 элементов присоединённой к A – λI матрицы,6 то7 φ(λ) = h(λ)ψ(λ).
Before we go on to prove (or, Before we prove) that all the eigenvalues of the matrix A satisfy equation (4), we shall prove that if h(λ) is the highest common divisor of the elements of the matrix (which is) adjoint to A – λI, then φ(λ) = h(λ)ψ(λ).
Notes
| 1. | Under the entry прежде appears the phrase прежде чем as a conjunction, meaning before, which is usually followed by an infinitive. ↑ |
| 2. | The infinitive here can be rendered in many ways, the simplest and most usual way being "Before proving that..."; the less common English expression in the translation has been used to emphasize the use of the imperfective aspect which must be explicit in Russian. ↑ |
| 3. | Imperfective infinitive is удовлетворять; the conjugation is like выполнять in Appendix D. ↑ |
| 4. | Perfective form доказать from the imperfective infinitive доказывать (see Appendix D). Although докажем is first-person plural, future indicative, the translation "we prove" is as correct as "we shall prove," since the two renderings are fully equivalent in the context of the sentence. ↑ |
| 5. | The expression общий наибольший делитель will be found listed in the dictionary after each of the three words in the phrase, since a literal rendering with the same word-order could conceivably lead to confusion, particularly since общий has other meanings. ↑ |
| 6. | The phrase присоединённой к A–λI матрицы is literally "of the adjoint to A–λI matrix" and is somewhat reminiscent of a construction in German. Note that the – between A and λI cannot be misinterpreted as a substitute for the verb to be, since Soviet mathematical writers are quite careful not to use the dash or hyphen for the verb to be whenever there is any possibility of confusion. ↑ |
| 7. | The word то is the conjunction then, not the demonstrative pronoun. ↑ |
| (2) |
Для каждой строго возрастающей1 последовательности σ индексов множество Aσ открыто2 в Ln+1,p+1 и насыщено2 по Δn,p, поэтому его3 канонический образ Cσ в Pn,p, является открытым множеством,4 гомеоморфным фактормножеству множества Aσ по отношению эквивалентности5 θσ, индуцируемому6 в Aσ отношением Δn,p.
For every strictly increasing sequence of indices σ, the set Aσ is open in Ln+1,p+1 and saturated for Δn,p; hence its canonical image Cσ in Pn,p is an open set (which is)7 homeomorphic to the quotient of the set Aσ by the equivalence relation θσ induced in Aσ by the relation Δn,p.
Notes
| 1. | Present participle, having the form of an adjective; this form is listed as an adjective in the dictionary. ↑ |
| 2. | Short form, neuter, of открытый (open) indicates a predicative use with the verb "to be" omitted; note the short form, neuter, of насыщенный (saturated). ↑ |
| 3. | Note that его is not declined, even though it is linked to образ. ↑ |
| 4. | The verb являться (to be) is followed by the instrumental case. ↑ |
| 5. | отношение эквивалентности (lit. relation of equivalence) is the usual way of expressing the English phrase equivalence relation. In Russian, the noun "equivalence" cannot be used as an adjective without adding an adjectival ending. It is quite possible to form the adjective эквивалентностный (equivalence, pert. to an equivalence) and write эквивалентностное отношение (equivalence relation), but it lacks one essential ingredient: it is not the idiomatic expression for "equivalence relation" in Russian. ↑ |
| 6. | This is the present passive participle индуцируемый of индуцировать (to induce) and has a second meaning "inducible"; both meanings are given in the dictionary. ↑ |
| 7. | This phrase in parentheses may or may not be inserted, at the discretion of the translator. ↑ |