A. J. Lohwater's Russian-English Dictionary of the Mathematical Sciences

Notice that the imperfective future tense is compound, while the perfective future is simple. The first component of the compound future construction, буду of буду читать, is the future tense of the verb "to be" and is used to form all imperfective future tenses. The following sentence illustrates the imperfective future tense:

Мы будем называть функцию  f (z) непрерывной, если ... . → We will call a function  f (z) continuous if ... .

Although a great number of imperfective and perfective verb pairs may be derived from each other by affixation (adding or removing a prefix, suffix, or infix), not all pairs are easily recognized as pairs by their form. In the dictionary, the imperfective verb is listed with its definition, with the perfective form given in parentheses. The perfective form may be listed with or without a definition, but is usually referenced to its imperfective. When no perfective form is indicated, this is not necessarily an oversight: some verbs do not have a perfective aspect, some have only the perfective, and many, especially verbs adopted from other languages, have the same form in both aspects. (These special situations are not usually mentioned in the dictionary, since nonexistent forms do not have to be translated.) The definition may be repeated for the perfective form when the imperfective and perfective are widely separated in the dictionary. The perfective forms of reflexive or passive verbs are not usually mentioned if the corresponding active forms are given.

A. The Verb "To Be"

The verb "to be" (быть) is very important in Russian, as in all languages. Following is the conjugation of быть:

present tense 2
он, она, оно есть		he, she, it is		они суть		they are
future tense
я буду		I will be		мы будем		we will be
ты будешь		you will be		вы будете		you will be
он, она, оно будет		he, she, it will be		они будут		they will be
past tense был, была, было, были
я был, была		I was		мы были		we were
ты был, была		you were		вы были		you were
он был она была оно было		he, it was she, it was it was		они были		they were

1. It has already been illustrated that the present tense of быть is usually omitted in Russian sentences. Review the following sentence:

Неравенство (11) слабее чем неравенство (12). → The inequality (11) is weaker than the inequality (12).

Consider also the following sentence:

Предложение P эквивалентно Q. → Proposition P is equivalent to Q.

The present tense of быть, "to be," is omitted in both sentences. However, often a dash (—) is used in place of the omitted verb, as in the following example:

Если E — некоторое множество точек комплексной плоскости, ... → If E is a set of points of the complex plane, ...

Occasionally, the forms есть and суть, from быть, are used:

Граница этой области есть окружность K

_r, где r — постоянная. → The frontier of this domain is the circle K_r, where r is a constant.

Матрицы суть спиновые матрицы Паули. → The matrices are the Pauli spin matrices.

2. Unlike the present tense, the future and past tenses of быть are never omitted. Furthermore, when быть is used in the future or the past, the predicate is often in the instrumental case:

Если α алгебраическая величина относительно Σ, a Σ — алгебраическое поле относительно Δ, то α будет алгебраическим относительно Δ. → If α is algebraic with respect to Σ, and Σ is algebraic with respect to Δ, then α will be algebraic with respect to Δ.

3. The verb являться. The verb являться (to appear, to present oneself) is often used to replace the present tense of "to be" in sentences which would be confusing if lacking a verb. In such instances, the verb is translated as the appropriate form of "to be." The third-person singular and plural forms are, respectively: является, являются. The predicate of these verb forms is always in the instrumental case. The following sentences illustrate this construction:

Такая функция существует и является единственной. → Such a function exists and is unique.

Единственными изоморфизмами топологической группы T в себя являются тождественное отображение и симметрия X→–X. → The only isomorphisms of the topoiogical group T into itseif are the identity map and the symmetry X→–X.

Вероятность P будет являться абстрактной копией эмпирической частоты. → The probability P will be an abstract counterpart of the empirical frequency ratio.

В. Verb Conjugations