Task 3. Translate the phrases from Text 1

Contunuous media; field theory; stability criteria; control theory; group representations; dynamics of particles; stimulated by Newton’s mechanics; other areas; one of the main problems; in another sense; more fundamental; any of the topics; most directly; starting with the creation of calculus.

This theory plays a crucial role in… We shall see… Mechanics played a key part in… We will return to… They are being applied to… The theory has attempted… It is based on… It is what is tied to… The student should not expect… It is what generalizes…

 

Word Formation

 

Task 1. Answer the following questions

 

1. Обратите внимание на соответствия между суффиксами данных существительных и их русских эквивалентов: competence, economics, capitalism, demonstration, culture, mentality, poetess, economist. Могут ли данные английские суффиксы иметь другие русские соответствия? Приведите примеры таких слов.

Выделите суффиксы в следующих словах. Какие из них относятся к абстрактным существительным, а какие – к конкретным: resistance, dictionary, freedom, slavery, employee, childhood, measurement, kindness, friendship, engineering, length?

Какие значения выражают суффиксы в следующих словах: handful, accountant, driver, editor, Chinese, academician?

 

2. Обратите внимание на соответствия между суффиксами данных прилагательных и их русских эквивалентов: comfortable, scalar, American, phonetic, active, astral. Могут ли данные английские суффиксы иметь другие русские соответствия? Приведите примеры таких слов.

Выделите суффиксы в следующих словах. К какой части речи они относятся: useful, dangerous, foolish, salty, Pythagorean, significant, lovely?

Какие значения выражают суффиксы в следующих словах: countable, divisible, Russian, useless, monthly, Turkish, yellowish, n-tuple?

От чего обычно образуются прилагательные с суффиксами –ed, –ing? Приведите примеры таких слов. Что они напоминают? Какие значения выражают данные суффиксы?

 

 

Task 2. Translate without a dictionary

 

Elegance, needless, achievement, worker, mathematical, mathematician, countable, richness, Newtonian, confused, lioness, shocking, Italian, Japanese, width, authorship, Irish, talkative, brotherhood, Portuguese, harmonic, partnership, weekly newspapers, to like fishing.

 

Task 3. Translate the words from Text 1

 

Lagrangian, structure, engineering, gravity, Hamiltonian, needless, electromagnetism, formalism, continuous, dynamics, fundamental, development, creation, exciting, interesting, physics, important, formulation, basic, application, stability, various, collection, subsequent, variational, relativistic, equivalent, general, relativity, outstanding, ingredient.

 

Words and Phrases

 

Task 1. Answer the following questions

 

1. Какие значения имеют следующие слова: since, sense, treat, turn, stage, detail, in detail, needless to say?

2. Какой суффикс чаще всего образует наречия от прилагательных? Всегда ли эти прилагательные и наречия точно соответствуют друг другу по значению?[1]

 

Task 2. Translate with a dictionary

 

Since 1980; many years since; a sense of humour; common sense; to make no sense; in a sense; in all senses; my sixth sense; to treat somebody for an illness; bad treatment; a new treatment; to treat a topic; to turn on/off the lights; to turn to Plato; in turn; an unexpected turn; to turn to the right; to turn black; to turn milk into butter; to stage a play; to stage a demonstration; to quit the stage; to remember all the details; to look closely at somebody; readily acceptable; mostly in France; nearly all the questions; shortly after the holiday.

Since he was there, we did it together. Since he went away, we are happy. She has not seen her parents since. I can’t sense it. He hurt his leg badly. It is likely to be true. She could hardly move. I have seen him lately.

 

Task 3. Translate the phrases from Text 1

 

Fairly rapidly; to understand perfectly at this stage; to see in detail.

It is more fundamental since it is based on… In one sense, …, in another sense, …. It treats a collection of topics… They in turn are being applied… Needless to say, it remains…

 

Speaking on the Text

 

Ask 5-7 questions on the text.

What are the key words in the text?

Give a short summary of the text using the key words.

 

Text 2. Nonlinear Stability

 

There are various meanings that can be given to the word "stability." In­tuitively, stability means that small disturbances do not grow large as time passes. Being more precise about this notion is not just capricious math­ematical nitpicking; indeed, different interpretations of the word stability can lead to different stability criteria. Examples like the double spherical pendulum and stratified shear flows, which are sometimes used to model oceanographic phenomena show that one can get different criteria if one uses linearized or nonlinear analyses (see Marsden and Scheurle [1993a] and Abarbanel, Holm, Marsden, and Ratiu [1986]).

Some History. The history of stability theory in mechanics is very com­plex, but certainly has its roots in the work of Riemann [1860, 1861], Routh [1877], Thomson and Tait [1879], Poincaré [1885, 1892], and Liapunov [1892, 1897].

Since these early references, the literature has become too vast to even survey roughly. We do mention, however, that a guide to the large Soviet literature may be found in Mikhailov and Parton [1990].

The basis of the nonlinear stability method discussed below was origi­nally given by Arnold [1965b, 1966b] and applied to two-dimensional ideal fluid flow, substantially augmenting the pioneering work of Rayleigh [1880]. Related methods were also found in the plasma physics literature, notably by Newcomb [1958], Fowler [1963], and Rosenbluth [1964]. However, these works did not provide a general setting or key convexity estimates needed to deal with the nonlinear nature of the problem. In retrospect, we may view other stability results, such as the stability of solitons in the Korteweg–de Vries (KdV) equation (Benjamin [1972] and Bona [1975]) as being instances of the same method used by Arnold. A crucial part of the method exploits the fact that the basic equations of nondissipative fluid and plasma dynam­ics are Hamiltonian in character. We shall explain below how the Hamiltonian structures discussed in the previous sections are used in the stability analysis.

 

Слова к тексту

 

intuitively	[ın´tju:ətıvlı]	интуитивно
disturbance	[dıs´tз:bəns]	возмущение
to grow	[grəυ]	расти; зд. становиться
precise	[prı´saız]	точный, определенный
notion	[´nəυ∫n]	понятие
capricious	[kə´prı∫əs]	капризный
nitpicking	[´nıtpıkıŋ]	придирки
pendulum	[´pendjυləm]	маятник
stratified	[´strætıfaıd]	расслоенный, слоистый
shear flow	[´∫ıə fləυ]	сдвиговое течение
phenomenon (pl phenomena)	[fı´nכmınən], [fı´nכmınə]	явление, феномен
linearized	[lınıə´raızd]	линеаризованный
nonlinear	[,nכn´lınıə]	нелинейный
to model	[´mכdl]	моделировать
reference	[´refrəns]	ссылка
to survey	[sə´veı]	обозревать, делать обзор
roughly	[´rΛflı]	грубо, приблизительно
originally	[ə´rıdζnəlı]	первоначально
two-dimensional	[´tu:d(a)ı´men∫ ə n ə l]	двумерный
substantially	[səb´stæn∫lı]	в значительной степени
augment	[כ:g´ment]	увеличивать, прибавлять, пополнять
pioneering	[,paıə´nıərıŋ]	первый, новаторский
related	[rı´leıtıd]	связанный
notably	[´nəυtəblı]	в особенности
provide	[prə´vaıd]	предоставлять, давать
setting	[´setıŋ]	установка, регулирование, пуск в ход
convexity	[kכn´veksıtı]	выпуклость
estimate, n	[´estımeıt]	оценка
in retrospect	[ın ´retrə υ spekt]	ретроспективно
to view	[vju:]	рассматривать, оценивать
instance	[´ınstəns]	пример, отдельный случай
to exploit	[ık´splכıt]	использовать в своих интересах
nondissipative	[,nכn´dısıpeıtıv]	недиссипативный
below	[bı´ləυ]	ниже
previous	[´pri:vıəs]	предыдущий

 

Letters and Sounds