| English | Russian |
| A corresponding limitation on the number of negative roots can be obtained by | соответствующее ограничение на число отрицательных корней может быть получено путём ... |
| a drift component in a vibratory gyroscope is caused by the anisoelasticity of its rotor support | неравножёсткость |
| A is defined by the formula | а определяется формулой |
| a method for determining the shapes of pulses caused by the impact of bullets at one end of a long rod | на одном конце |
| a particular space of piecewise polynomials is selected by the choice of the polynomial degree and the degree of continuity across element boundaries | степень непрерывности |
| a particular space of piecewise polynomials is selected by the choice of the polynomial degree and the degree of continuity across element boundaries | степень многочлена |
| a pursuer approaches a target by the method of proportional navigation | пропорциональное наведение |
| A relationship between k and m is given by the formula | соотношение между k и m даётся формулой |
| all metals are affected to some extent by the atmosphere | подвергаться воздействию |
| angle is a figure formed by two rays going out of the same point | исходящий из |
| angle is a figure formed by two rays going out of the same point | выходящий из |
| as time goes on the place occupied by P generally will vary | в общем случае положение, занимаемое частицей P, будет изменяться со временем |
| be also known by the name | быть также известным под названием |
| be complicated by the fact that | осложняться тем, что |
| be described by the equation | описываться уравнением |
| be given by the equation | описываться уравнением |
| be hampered by the fact that | затрудняться вследствие того, что |
| be symbolized by the Greek letters | обозначать греческими буквами |
| it soon became obvious that for some materials; the foundations subjected to loads behaved differently than predicted by the theory | вели себя отлично от того, что было предсказано теорией (of elastic isotropic solids) |
| better understanding of the meaning of these operations can sometimes be gained by studying them from a different viewpoint | добиться лучшего понимания |
| better understanding of the meaning of these operations can sometimes be gained by studying them from a different viewpoint | лучшее понимание |
| by a slight change in the method of 3 | немного изменив метод, изложенный в 3 ... |
| by a slight change in the method of 3 | несколько изменив метод, излагаемый в 3 ... |
| by a slight change in the method of 3 | несколько изменив метод, изложенный в 3 ... |
| by A we denote the maximum of the moduli of the absolute values of the eigenvalues of this matrix | абсолютное значение (модуль) |
| by A we denote the maximum of the moduli of the absolute values of the eigenvalues of this matrix | абсолютное значение (модуль) |
| by A we shall mean the first term of the expansion | первый член этого разложения мы назовём A |
| by applying the principle | используя принцип (of virtual work we ...) |
| by dividing the equation 3 through by the highest power of z we can | деля все уравнение 3 на старшую степень z, мы можем |
| by dividing the equation 3 through by the highest power of z we may | деля все уравнение на старшую степень z, мы можем |
| by dividing the equation throughout | деля всё уравнение целиком (by the highest power of z which occurs in all Laurent expansions of the Bn around z=1, we may assume ...) |
| by dividing the equation throughout | деля все уравнение целиком (by the highest power of z which occurs in all Laurent expansions of the Bn around z=1, we may assume ...; ...) |
| by igniting the mixture | при помощи |
| by putting the equation in the form | путём приведения уравнения к виду |
| by the addition of | путём добавления |
| by the addition of | присоединением |
| by the construction of | по построению |
| by the data | по условию |
| by the directives | согласно указаниям |
| by the early 1980s | к началу 1980-х годов |
| by the early 20th century | к началу 20-го века |
| by the end of the 1980s | в конце 1980-х годов |
| by the example of | на примере |
| by the implicit function theorem | по теореме о неявной функции (the first equation may be solved for y in terms of z: y=y (z)) |
| by the induction assumption | по предположению индукции (by the induction hypothesis (assumption), the matrix A is positive definite for n = 2) |
| by the induction hypothesis | по предположению индукции (by the induction hypothesis (assumption), the matrix A is positive definite for n = 2) |
| by the instruction | согласно указаниям |
| by the joint action of | совместным взаимо- действием |
| by the kilogram | на килограммы |
| by the late 1980s | к концу 80-х годов |
| by the most conservative estimate | по самым скромным подсчётам |
| by the passage to | путём перехода |
| by the preceding | согласно предыдущему |
| by the preceding, we obtain | согласно предыдущему |
| by the procedure | по методике |
| by the same principle | по тому же принципу |
| by the same procedure | таким же образом |
| by the same reasoning | по тем же соображениям |
| by the same reasoning as for | по тем же соображениям, что и в отношении |
| by the thousands | тысячами |
| by the time | к моменту |
| by the time of | ко времени (by the time of publishing this book) |
| by the triangle inequality | по неравенству треугольника (F (x) is integrable) |
| by the way | попутно |
| by virtue of the fact that | в силу того, что (в силу того, что • The detached electron will conduct electricity by virtue of the fact that it carries a negative charge. Zimmerman Alexander Demidov) |
| by virtue of the fact that | так как |
| by virtue of the fact that | поскольку |
| by virtue of the same reasoning as was used for | по той же самой причине, которая использовалась для ... |
| By virtue of the sign constancy of | В силу знакопостоянства (s0me_0ne) |
| by Weyl's criterion this is equivalent to the requirement that | по критерию Вейля это эквивалентно требованию, что |
| it can be approximated by the equation | можно приближённо выразить соотношением |
| completing the triangle by points | заполнение |
| connected by the relation | связанный посредством соотношения |
| correct by the factor | вводить поправочный множитель |
| correct by the factor n | исправлять умножением на n |
| correct by the factor n | вводить поправочный множитель n |
| corrosion by the atmosphere and by water | коррозия под действием воздуха и воды |
| damage wrought by the explosion is | нанесённое взрывом повреждение |
| definition 2.1 given by Wiener allow us to convert the general control problem of the form 2.7 to a problem of the form | свести общую задачу теории управления к задаче ... (2.8) |
| next, the differentiation formulas for the new functions are derived by separating the real and imaginary parts | вывести разделением действительной и мнимой частей |
| Descartes' idea of translating geometry into algebra by associating with each point of the plane an ordered pair of real numbers | соответствие |
| differ by the value of R | отличаться на величину R |
| different methods will differ only by how at each stage they choose the next direction | различные методы будут отличаться только тем, как |
| different methods will differ only by how at each stage they choose the next direction | различные методы будут отличаться лишь тем, как ... |
| divide the number by six | разделить на число |
| dividing by 5 is the inverse of multiplying by 5 | обратная операция по отношению к |
| division of the first expression by the second gives | деление первого выражения на второе даёт |
| equations 2 and 3 are therefore complemented by the boundary conditions | таким образом, уравнения 2 и 3 дополняются граничными условиями |
| extension of the map M by the identity to | продолжение отображения на (до) |
| extension of the mapping M by the identity to | продолжение отображения на (до) |
| follow the method given by | осуществляться по методу |
| given by the equation | заданный уравнением |
| given by the equation | задан уравнением |
| half the unknowns are eliminated by taking certain linear combinations of equations | некоторый |
| here V is the volume swept by the moving object | заметанный |
| if the matrix is symmetric, then the work can further be reduced by one-half | наполовину (на половину) |
| in general, the Dirichlet problem for the equilibrium equations cannot be solved by the boundary integral equation method both inside and outside a bounded domain | как внутри, так и вне ограниченной области |
| in the attempt to make this text usable by nonspecialists, including graduate students | для того, чтобы попытаться сделать этот текст понятным для неспециалистов, включая студентов (, we have provided Parts A and B) |
| in the attempt to make this text usable by nonspecialists, including graduate students | для того, чтобы попытаться сделать этот текст понятным для неспециалистов, включая студентов (, we have provided Parts A and B; ...) |
| in the case of linear convergence, in each step the error is multiplied by an almost constant convergence factor whose absolute value is less than 1 | множитель сходимости |
| 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 |
| inside the area enclosed by these two curves | внутри области, заключённой между этими двумя кривыми (each point corresponds to ...) |
| inside the area enclosed by these two curves each point corresponds to | ограниченный |
| integrate the power series term by term | интегрировать степенной ряд почленно |
| is calculated by the following formula | рассчитывается по следующей формуле (Ремедиос_П) |
| is just the one predicted by | как раз такой, какой предсказывался |
| is offset to the left by | сдвинут влево |
| is specified by the expression | заданный уравнением |
| is specified by the expression | задан уравнением |
| it can be approximated by the equation | можно приближённо выразить соотношением |
| it follows by the Riesz theory of compact operators that | следует по теории Рисса |
| it follows by the Riesz theory that | из теории Рисса следует, что |
| it has been necessary to amplify the wave theory of radiation by the quantum theory | расширить теорию |
| it has been necessary to amplify the wave theory of radiation by the quantum theory | дополнить теорию |
| it is possible for two entirely different systems to be represented by the same block diagram | могут быть представлены |
| it was shown by the method considered above | методом, рассмотренным выше |
| judge by the picture | судить по рисунку |
| judge by the results obtained | судя по полученным результатам |
| kinetic energy is the product of mass by velocity squared, whereas momentum known as quantity of movement (motion) is the product of mass by speed | произведение (velocity) |
| miss the target by a certain distance | промахнуться мимо цели на некоторое расстояние |
| multiplying the first equation by | умножая первое уравнение на (p, the second by q; adding the relating equations and integrating; we obtain, after simplifying the right-hand term in the same way as in Sect.3) |
| multiplying the first relation by 2 followed by summation, we come to the concise form of the above equation | последующее суммирование |
| multiplying the first relation in 1 by x and the second one by y, followed by summation, we come to the concise form the above equations | с последующим суммированием |
| never before has the imagination of mankind been captivated so much by the concept of space | никогда ранее |
| new general formula for the pull-back of cycle by a monoidal transformation | новая общая формула для обратного образа цикла при моноидальном преобразовании (ssn) |
| 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 |
| non-linear system analysis by the perturbation method | анализ проведённый методом |
| numerical solution of Helmholtz's equation by (the) use of the a capacitance matrix method | метод ёмкости |
| occupation of the levels by electrons | заполнение |
| it soon became obvious that for some materials, the foundations subjected to loads behaved differently than predicted by the theory of elastic isotropic solids | предсказанный по теории твёрдых изотропных тел |
| review by the author | автореферат |
| root mean square average is by definition the root of the average of the squares of the deviations from the average | среднее квадратичное |
| rotation by the angle n/2 | поворот на |
| scattered by the quartz | рассеянный на кварце |
| since the early 1960s several generalized theories of differentiation have been proposed by different authors | с начала |
| suppose that the shell is acted on by a body force | на оболочку действует |
| that period was the first and by far the largest interval in | намного более продолжительный, чем другие |
| the above phenomena is illustrated by this and all examples to follow | приведённый ниже |
| the above theory was tested by results of a series of experiments | вышеуказанная теория была проверена результатами серии экспериментов |
| the additive inverse of a is denoted by | обратная величина относительно сложения |
| the analysis was inspired by experimental observations made by | этот анализ был продиктован экспериментальными результатами, полученными ... |
| the angle is subtended by the arc | угол стягивается дугой |
| the angles subtended by an arc of a circle at the circle are equal | углы, стягиваемые одной и той же дугой окружности, равны между собой |
| the approximations used by discretization modules are more accurate with the constraints of machine arithmetic | ограничение |
| the area fraction occupied by transparency zones | доля пространства |
| the articles by Bauer give | в статьях Бауэра приводится (extensive lists of references) |
| the articles by Bauer 1970, 1971 give extensive lists of references | обширные списки цитированной литературы |
| the articles by Bauer 1970, 1971 give extensive lists of references | дают обширные ссылки на литературу |
| the author uses the ideas and theoretical apparatus that were developed by W.A. Day 2 | которые были развиты Дэем 2 |
| the bar is suspended from the top by steel wires | подвешен |
| the book contains papers by the authors listed below | указанные ниже |
| the bound provided by i is of limited use because it involves the unknowns | ограничено для использования |
| the bound provided by 3 is of limited use because it involves the unknowns | ограниченное применение (иметь ограниченное применение) |
| the center of gravity of a the triangle divides each median by ratio 2:1, considering from a vertex | делить в отношении |
| the change of the particle velocities is estimated by solving the above impulse equations | с импульсными правыми частями уравнения |
| the characteristic values of A are uniquely determined by Eq. | однозначно определёны (3.3) |
| the characteristic values of A are uniquely determined by Eq. | характеристические значения A однозначно определяются уравнением (3.2) |
| the classification of ... by | классификация по |
| the components unaffected by corrosion are | не затронутые коррозией |
| the convergence of series 3 is caused by the rapid decrease in the Fourier coefficients | сходимость ряда 3 определяется скоростью убывания коэффициентов Фурье |
| the convergence of series 3 is caused by the rapid decrease in the Fourier coefficients | сходимость ряда 3 обусловлена ... |
| the current induced by a magnetic field is | ток, создаваемый магнитным полем |
| the data can be approximated better by | данные могут быть лучше аппроксимированы с помощью ... |
| the degree of occupation of the surface by adsorbed particles is | степень заполнения |
| the degree of P exceeds is less than that of Q by at least at most 2 | на... больше меньше |
| the degree of P exceeds is less than that of Q by at least at most 2 | на ... больше (меньше) |
| the difficulty is eliminated by employing | затруднение устраняется путём |
| the distance d traveled by a given particle | расстояние d, проходимое точкой |
| the elastic medium fills a region of space given by | упругая среда занимает область |
| the element is flexed to a predetermined curve by adjusting screws | изогнут по заранее заданной кривой |
| the elements of the matrix A are uniquely determined by formulas 1 and | однозначно определён (2) |
| the energies required by the various studies of nuclei are in the 1 to 20 MeV range | в диапазоне |
| the energy is measured by the ionization potential | измеряться по |
| the energy released by explosive is | освобождённая энергия взрывом |
| the engine increased its power by 5% | рост мощности на 5% |
| the equations are defined by | уравнения определяются из соотношения (1.2) |
| the error exceeds this value by 50 % | превосходить на (by mere than 100 %, by at least 50%, by greater than three times, by a factor of 3, by almost a factor of 2, by 4 times, by about a factor of 5, by approximately 20%) |
| the exclusion of x=0 is necessary because division by zero is undefined | исключение точки х=0 необходимо, так как деление на ноль не определено |
| the existence time the lifetime is sharply reduced by two orders of magnitude | на ... порядков |
| the field is given by the following expression | поле задаётся следующим уравнением |
| the force exerted by ... on | усилие прилагаемое со стороны ... к ... |
| the functional to be analyzed is given by | подлежать анализу |
| the graph of this function may be found approximately by plotting points on the graph | график данной функции мог бы быть построен приближённо путём нанесения точек ... (and drawing a smooth curve through them) |
| the integral converges by the Lebesgue theorem | по теореме Лебега |
| the inverse of the matrix A is denoted by A-1 | обратное |
| the least remainder on dividing a by b | наименьший остаток от деления |
| the long term response of the material is given by | длительный отклик материала даётся |
| the machine occupies a floor space of 3 by 4 m | занимать площадь |
| the material can be brought to size and shape by conventional methods | доводить до заданных размера и формы |
| the maximizing sequence xn is bounded from above majorized by the number x | ограничена сверху |
| the measurements were unaffected by changes in | изменения в ... не оказывали влияния на измерения |
| the minimizing sequence xn is bounded from below by the number x | ограничена снизу |
| the motion of charged particles is governed described by the above equation of equilibrium | описываться уравнением |
| the multiplicative inverse of a is denoted by | обратная величина относительно умножения |
| the one exception to many of these drawbacks is represented by | одно исключение из |
| the optimum protection is afforded by the addition of | оптимальная защита обеспечивается добавочным устройством ... |
| the orders placed by are | размещённые заказы |
| the overhead storage requirements imposed by sparse matrix methods are still substantial | издержки накладные расходы по памяти |
| the part of the line intercepted by the half-circle is | отрезок прямой, отсекаемый полуокружностью |
| the plate is assumed bent by | пластина предполагается изогнутой под действием ... |
| the plate is blown over by a gaseous flow | обдувать |
| the point-by-point measurements | измерение по точкам |
| the points are obtained by solving | эти точки на графике получаются решением (the points are obtained by solving Eqs. (2.6) , (2.8) simultaneously with (2.10)) |
| the polynomial, call it R t, corresponding to this function by 2.1, is almost everywhere nonzero | этот многочлен, обозначаемый далее R t, который соответствует данной функции по формуле 2.1, почти всюду равен нулю |
| the pressure is delivered by a compressor | подавать давление |
| the problem can be forestalled by | трудность может быть предотвращена путём (the problem can be forestalled by using a direct-current link to tie) |
| he studied the problem of reduction of elastic moduli by | задача уменьшения упругих модулей путём (regarding ...) |
| the process of occupation of the surface by adsorbed particles is steady | заполнение поверхности |
| the product of a by b | произведение a на b |
| the product of ... by | умножение ... на |
| the proof has been rediscovered by many later writers | это доказательство позднее было переоткрыто многими авторами |
| the proof is by induction on п | индукция по п |
| the proof method is analogous to the method used by | метод доказательства является аналогичным методу, использованному |
| the properties of the material are controlled by at least three major factors | зависеть от трёх основных факторов |
| the purpose of the book is in part to discuss the validity of the upper bound work method in a form that can be appreciated by a practicing soil engineer | целью этой книги частично является обсуждение справедливости |
| the real process is well represented by this equation | действительный процесс весьма хорошо отражается этим уравнением |
| the region of interest is prescribed by this condition | задан |
| the regulations set up by the commission | привила, установленные комиссией |
| the relevance of the theory to gels has been discussed by Chandler 1 | пригодность данной теории для гелей обсуждалась Чендлером 1 |
| the rest of Lemma 2 follows by a very easy calculation | остальная часть Леммы 2 следует из весьма простых вычислений |
| the rest of the lemma follows by a very easy calculation | остаток леммы |
| the rest of the lemma follows by a very easy calculation | оставшаяся часть леммы |
| the rise in bacterial numbers is followed by a sudden drop | за увеличением |
| the rocket is by no means a modern development | отнюдь не |
| the routine abc.c passes its first argument by value and the second argument by reference | по значению и ссылке |
| the routine abc.c passes its first argument by value and the second argument by reference | передавать |
| the sedimentation velocity of particles can be described by the formula | скорость оседания частиц |
| the separation condition is ensured by the possibility of satisfying the strict inequalities | разделение этих условий обеспечивается возможностью удовлетворения строгих неравенств (2.3) |
| the separation condition is ensured by the possibility of satisfying the strict inequalities | гарантировано возможностью (2.3) |
| the separation condition is ensured by the possibility of satisfying the strict inequality | условие разделения гарантируется возможностью удовлетворения строгого неравенства |
| the set of real numbers can be pictorially represented by the real number line | графически представимо в виде |
| the set X is mapped by the function f to the set Y | отображаться |
| the solution may have been found by | возможно, что решение было получено |
| the solution of the problem is summarized by three main theorems | полное решение проблемы собрано здесь в виде трёх основных теорем |
| the solution of the problem is summarized by three main theorems | решение проблемы состоит из трёх основных теорем |
| the solution sought is given by | искомое решение даётся формулой |
| the stability of the steady solutions is studied by introducing linear perturbations | устойчивость стационарных решений изучается путём введения линейных возмущений |
| the stress experienced by the plate | напряжения, испытываемые пластиной |
| the stress experienced by the plate is | напряжения, испытываемые пластиной |
| the substitution of ... by | замена (первого вторым; ...) |
| the sun radiates as mach energy every second as would be released by the explosion of several billion atomic bombs | столько ... сколько ... бы |
| the surface generated by the rays ... is called | образованная лучами ... поверхность |
| the tangential projection is defined by this third-order tensor being expressed in terms of strains | выражаемый |
| the temperature is at least by several orders of magnitude lower than | порядок величины |
| the term ... was coined by | термин ... был создан |
| the theorem was first proved by | теорема была впервые доказана |
| the velocity can be found by substituting | его скорость может быть найдена подстановкой ... |
| the velocity is determined by averaging the above equation with respects to x | осреднением по |
| the vertical velocity jump across at the interface is numerically evaluated by the above formula | на границе раздела |
| the work done by pressure in virtual displacements | работа давления на возможных перемещениях |
| the work done by the force F | работа, произведённая силой F |
| then a repeated integration by parts leads to the formula | повторное интегрирование |
| there is some concern whether a strain pulse measured by a gauge on the surface of a bar rod is representative of the wave travelling down its interior | внутри |
| these two expressions differ from one another by a quantity of the order of h2 | на величину порядка |
| this approach can improve the overall process by an order of magnitude | на порядок |
| this can be depicted by the following equations | это может быть описано следующими уравнениями |
| this device may exceed the transmission rate by one or two orders of magnitude | на один-два порядка |
| this discrepancy is accounted for by the difference in | расхождение объясняется разностью в |
| this discrepancy is accounted for by the difference in | расхождение объясняется разностью в |
| this is by no means always the case | это далеко не всегда так |
| this is done by bridging the gap between these two dates | заполнение пробела между |
| this is favored by the following data | это предпочитается по следующим соображениям |
| this step is preceded by the lemma | данный шаг предваряется следующей леммой |
| this subroutine multiplies a general matrix by the orthogonal transformation matrix from a reduction to без артикля Hessenberg form | матрица ортогонального преобразования |
| this vector is multiplied from left by the reflection matrix A | слева |
| this was proved shown by rutherford to exits at the center of the atoms of all substances | доказано существование |
| to tighten from the inside by bolts with tapered heads | коническая головка (болта) |
| Trends normally introduced by the coupling of a relatively slow and uncontrolled variation in the extraneous variables with a sequential application in values of the independent variable applied will be broken up | Тренды, обычно привносимые сочетанием относительно медленной и неконтролируемой вариацией во внешних переменных и последовательным использованием значений рассматриваемой независимой переменной, будут компенсироваться (ssn) |
| we can achieve this by corresponding replacement (of the argument x by y of the form | мы можем достичь этого заменой ... |
| we can avoid the difficulty by making an a posteriori analysis which | мы можем избежать эту трудность, проведя апостериорный анализ, который |
| we can avoid the difficulty by making an a posteriori analysis which | мы можем избежать эту трудность, проведя апостериорный анализ |
| we define a random test by a measurement matrix that sets a random order to the change in the value of the independent variable applied | мы определяем случайный опыт при помощи матрицы измерений, которая устанавливает некоторый случайный порядок в изменение значения рассматриваемой независимой переменной |
| we denote by P the projector in H onto the space spanned by n first eigenvectors of A | пространство, натянутое на n первых собственных векторов A |
| we extend calculations made for the annular plate by Koenig 5 | мы распространяем вычисления, проделанные для круглой пластины Кёнигом 5 |
| we shall define the circumference as the perimeter of the circle, in other words, as the measure of the entire path formed by the circle | весь путь |
| we turn first to the solution of the triangular systems by | сначала (вначале) |
| we will simplify the proof of theorem slightly by working with the subspaces | мы упростим слегка доказательство теоремы, используя подпространства |
| we will simplify the proof of theorem slightly by working with the subspaces | мы слегка упростим доказательство теоремы, используя подпространства |
| the 10 specimens tested were manufactured by the electroplating technique | были изготовлены с использованием техники гальванопокрытия |
| whenever possible, we shall attempt to represent the components of a vector by the corresponding Greek letters | там, где это возможно |
| ... with characteristics differing from the characteristics of f z by a quantity g | отличающийся на величину |
