| English | Russian |
| A regular polygon is a polygon that is both equilateral and equiangular | правильный многоугольник |
| 1. All mathematicians are antisocial. 2. There were some engineers and mathematicians in a | все математики |
| equations 2 and 3 are therefore complemented by the boundary conditions | таким образом, уравнения 2 и 3 дополняются граничными условиями |
| for a real understanding of these facts it must be emphasized once more that the rational numbers are our own creation and that the rules 1 are imposed at our volition | наложены по нашему желанию |
| for a real understanding of these facts it must be emphasized once more that the rational numbers are our own creation and that the rules 1 are imposed at our volition | для действительного понимания этих фактов необходимо подчеркнуть ещё раз, что |
| get a feel for this result and how it is proved we begin with the trivial case d=1 | чтобы прочувствовать этот результат ... |
| get a feel for this result and how it is proved we begin with the trivial case d=1 | чтобы понять этот результат ... |
| in the early 1960s the size and types of problems were limited both by the capacity of early computers and by the lack of algorithm technology for their solving | ограничивались отсутствием алгоритмов их решения |
| in the mid and late 1960's | в середине и конце ... годов |
| is limited between 10 and 20 m as a maximum | ограничен между 10 и 20 метрами, как максимум |
| likewise, P x, k is a polynomial in k of degree 3 and of the same form as | аналогично, P x, k есть полином по переменной k третьей степени |
| next, the differentiation formulas for the new functions are derived by separating the real and imaginary parts | далее, формулы дифференцирования новых функций выводят, разделяя действительную и мнимую части |
| next, the differentiation formulas for the new functions are derived by separating the real and imaginary parts | далее, формулы дифференцирования для этих новых функций выводятся разделением действительных и мнимых частей |
| similarity of triangles means that the three angles in one triangle are equal to the three angles of another triangle and, as a consequence, the corresponding sides are in the same ratio | подобие треугольников |
| since M1 and M2 are unit lower triangular, so is the product of their inverses | таким является и |
| supplementary adjacent angles have a common vertex and a common side and their sum is equal to 180 deg | смежные углы |
| suppose that N=z and z is large, say, z=50 | предположим, что N=z и z велико, например, z=50 |
| the absolute value of a real number is the distance between its corresponding point on the number line and the number 0 | расстояние между точками |
| the author uses the ideas and theoretical apparatus that were developed by W.A. Day 2 | которые были развиты Дэем 2 |
| the heart of these methods is the algorithm 2 and the a priori estimates in Theorem 2 | априорные оценки |
| the idea is to take advantage of the sparsity structure of the a matrix to reduce the time and storage requirements | разрежённость |
| the inertia of a symmetric matrix is the triple whose elements are the number of positive, negative, and zero eigenvalues, counted with multiplicities | инерция матрицы |
| the interior angle that is greater than n and whose apex faces into an irregular polygon is called a reentrant reentering angle | угол входа |
| the material can be brought to size and shape by conventional methods | доводить до заданных размера и формы |
| the plate is submitted to body forces f and the upper and lower surfaces to surface forces g1 and g2 | пластина подвержена действию массовых сил ... |
| the plate is submitted to body forces f and the upper and lower surfaces to surface forces g1 and g2 | пластина подвергается объёмной нагрузке ... , а верхняя и нижние её поверхности – поверхностным нагрузкам ... |
| the points 0 and 1 in 0,1 are not the centers of open intervals entirely contained in 0,1 | полностью содержащийся в |
| the problems that arise in ... are numerous and varied | проблемы, возникающие в ... многочисленны и разнообразны |
| there are an infinite number of points satisfying 3.6 and lying on distinct rays through 0 | на различных лучах, проходящих через точку 0 |
| there are vectors and scalars, not all zero, such that | не все равные нулю |
| where a and b are complex constants to be adjusted so that | где комплексные константы ... подбираются так, чтобы (2.12) can be combined into a single complex equation) |
