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

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 ? алгебраическая величина относительно ?, a ? — алгебраическое поле относительно ?, то ? будет алгебраическим относительно ?. > If ? is algebraic with respect to ?, and ? is algebraic with respect to ?, then ? will be algebraic with respect to ?.

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

Russian verbs are classified as members of either the first or second conjugation, according to their nonpast personal endings. It is possible, however, for a verb to exhibit a mixed conjugation; that is, some of its endings are those of the first conjugation, while the rest are from the second. The following chart shows the endings of the two conjugations:

	First Conjugation		Second Conjugation
	Singular		Plural		Singular		Plural
1st person	-ю (-у)		-ем		-ю (-у)		-им
2nd person	-ешь