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1 method of expansion into series
- method of expansion into series
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Англо-русский строительный словарь. — М.: Русский Язык. С.Н.Корчемкина, С.К.Кашкина, С.В.Курбатова. 1995.
Англо-русский словарь строительных терминов > method of expansion into series
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2 method of expansion into series
Строительство: метод разложения в рядУниверсальный англо-русский словарь > method of expansion into series
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3 method of expansion into series
Англо-русский строительный словарь > method of expansion into series
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4 method
- method
- nметод, способ; система; порядок; методика; технология
- method of analysis
- method of application
- method of attack
- method of bearing and distances
- method of bipolar coordinates
- method of calculation
- method of design
- method of detail survey
- method of elastic weights
- method of electric needles
- method of expansion into series
- method of fixed points
- method of intersection
- method of joint isolation
- method of least work
- methods of manufacture
- method of minimum strain energy
- method of moment distribution
- method of radiation
- method of redistribution of pressure
- method of sections
- method of steam jet
- methods of structural analysis
- method of successive approximations
- methods of testing
- method of water needles
- accepted method of building
- accepted method of house construction
- accurate method of analysis
- adhesive nail-on method
- admittance method
- advanced methods of concreting
- advance slope method
- aggregate exposure method
- air permeability method
- alternate methods
- American method
- analytical method of determining reactions
- API method of pile design
- approximate method
- approximation method
- area method
- area-moment method
- assembly methods
- Austrian method
- autogenous curing method
- balanced cantilever method
- Belgian method
- Benoto method
- bentonite method
- Billner method
- "bin" method
- boiling water method
- boom placement concreting method
- bricklaying methods
- building method
- building block module method
- cable method of rock stressing
- calculation method
- cantilever method
- Chicago method
- circular-arc method
- Coast-Survey method
- collapse method of structural design
- combined finite strip-finite element method
- compaction methods of clays
- conjugate beam method
- consistency measurement method
- construction methods
- construction and erection methods
- contiguous pile method
- continuous-flight augers method
- continuous-sample method of advance
- convergence method
- critical method
- critical path method
- Cross moment distribution method
- Cross method
- cross-section method
- current design methods
- cut-and-cover method
- dampproofing methods
- displacement method
- displacement method of advance
- dual-rail method
- dummy unit-load method
- dust-spot method
- Dutch cone method
- earth pressure balanced tunneling method
- elastic center method
- elastic weights method
- electric analogy method
- electric resisting method
- energy method
- equal friction method of duct sizing
- equal friction method
- equivalent load method
- erection method
- fast track construction methods
- fatigue test method
- finite difference method
- finite element method
- finite strip method
- flight auger method
- flotation caisson method
- flue loss method
- folded plate method of analysis
- force method
- free cantilever method of construction
- general method of analysis
- Glotzl hydraulic cell method
- Gow method
- Hardy Cross method
- housing appraisal method
- in-duct method
- industrialized methods of construction
- iterative method
- jack method
- jacking method
- lacquer curtain coating method
- laser beam method
- leap-frog method
- limit equilibrium method
- limit state method
- listening methods
- load factor design method
- mandrel method
- mathematical method of design
- matrix method of structural analysis
- maturity method
- measuring method
- mixed-mode method
- mix-in-place method
- modern building methods
- modular ratio method
- moiré fringe method
- moment-balance method
- nondestructive methods of tests
- normal method of quality control
- null method
- numerical method
- one-rail method
- optical square method
- permissible stress method
- phototheodolite method
- plastic methods of structural analysis
- plate count method
- precast concrete manufacturing methods
- pressuremeter method
- proven construction methods
- p-y method of pile design
- rapid test method
- ratio method of balancing
- rebound hammer method
- reference point method
- relaxation method
- reproducible methods
- resistivity method
- resonant-frequency method
- reverberant field method
- Rockwell method of hardness testing
- safe method
- safe working methods
- secant interlocking pile method
- secant pile method
- seismic method of surveying
- seismic reflection method
- seismic refraction method
- semiprobabilistic design method
- shear transfer method
- shock response method of pile testing
- sliding-wedge method
- slope deflection method
- solar radiation method
- sonic method
- special method of quality control
- standard test method
- static regain method of duct sizing
- static regain method
- statistical design method
- step-by-step method
- strength design method
- strength evaluation method
- successive approximations method
- suspended cantilever method
- swamp shooting method
- Tagg method
- tangent modulus method
- test methods
- Theis method
- thixotropic liquid method
- three-point method
- tilt-up method
- time-saving method of construction
- TNO method of analysis
- TNO method of pile testing
- transit and stadia method
- tremie method
- truss analogy method
- turn-of-nut method
- ultrasonic pulse velocity method
- vacuum concrete method of bridge construction
- valveless pulse-jet method
- vane shear method
- velocity reduction method of duct sizing
- velocity reduction method
- vibratory method
- Vickers method of hardness testing
- volume method of measuring aggregates
- warm water method
- water fog spray method
- western bricklaying method
- western method
- working-stress design method
Англо-русский строительный словарь. — М.: Русский Язык. С.Н.Корчемкина, С.К.Кашкина, С.В.Курбатова. 1995.
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5 method
1) метод; способ; средство2) система; порядок3) технология4) методика•- method of applying liquid lubrication - method of calculation - method of column analogy - method of comparison - method of connecting - method of determining bending moments by fixed points - method of directions - method of elastic arch - method of elastic weights - method of electric needles - method of exchange of members - method of firing - method of fixed points - method of images - method of initial parameters - method of joints - method of least squares - method of least work - method of limit equilibrium - method of minimum strain energy - method of moments - method of movement - method of operation - method of payment - method of planning - method of production - method of redundant reactions - method of rotations - method of sections - method of separate joint displacement - method of slopes - method of stowage - method of strain measurement method - method of substitute redundant members - method of successive approximations - method of successive corrections - method of training - method of transportation - method of working - method of zero moment points - methods of network planning and control - ad hoc method - advertising method - aero-projection method - air-permeability method - airslide method - approximation method - arbitrary proportions method - area moment method - artificial islands method - ball method of testing - bench method - bidding methods - brush method of treatment timber - building methods - caisson method - cantilever method of design - cassette method of production of thin-slab structures - central mixing method - centre drift method - centrifuge method - centroidal method of design - change-in-stress method - chemical injection method - closed building method - column analogy method of design - compressed-air method of tunnelling - concrete testing method - cone method - construction works quality control method - core-drill method - correlation method - cut-and-cover method - cut-and-try method - cylinder method - deflection method - design methods - development method - dip method - dipping method of treatment timber - effective method - electrolytic method - emulsified-asphalt penetration method - energy method - equal load increments method - equal strain method - error method - fabrication method - fixing method - float and chains method - flow-line conveyer method - force method - graphical method - heading method of tunnelling - hot-air heating standpipe method - hot penetration method - hydraulic fill method - impact method - kinematic method - lacquer film method - land-assembly methods - lift-slab method - limit equilibrium method - limit stage design method - line production method - loading method - magnaflux method - mechanical method by pumps - membrane method of waterproofing - mixed-in-place method - mock-up methods of design - modular ratio method - moire fringe method - moment area method - moment-distribution method - moment-of-inertia method of designing - mud-jack method - mulch method - near end moment distribution method - neutral-points method - non-destructive testing methods - normal method - packing methods - patented method of construction - penetration method - percussive pneumatic method of riveting - photo-elastic method of stress-determination - photo-elasticity method - pilot method - pilot tunnel method - pin-and-string method - pipe-bridge method - plastic method of design - plastic theory method - polarized light method - portal method of design - pounding method of curing concrete - production line method of construction - qualitative methods - quantitative methods - relaxation method - ring-and-ball method - rolled-on method - safe method of heat insulation - safety methods - sampling method - sand-bearing method of testing clay pipes - sand-island method - scheduling method - seismic method of prospecting - simultaneous construction method - slope deflection method - spatial self-fixation erection method - statistical analysis method - stovepipe pipe-laying method - strain-energy method - successive construction method - surface-coating method of waterproofing - synthetic method of restoration - thixotropic liquid method - tilt-up method - top-heading method - transfiguration method - trial-load method - turnover method - ultimate-strength method - ultrasonic pulse velocity method - void method of proportioning - volume method of concrete mix design - volumetric method - water-jet method of pile-driving - weight method - well-point method of excavation - work method - working stress method of design* * *метод, способ; система; порядок; методика; технология- method of analysis
- method of application
- method of attack
- method of bearing and distances
- method of bipolar coordinates
- method of calculation
- method of design
- method of detail survey
- method of elastic weights
- method of electric needles
- method of expansion into series
- method of fixed points
- method of intersection
- method of joint isolation
- method of least work
- methods of manufacture
- method of minimum strain energy
- method of moment distribution
- method of radiation
- method of redistribution of pressure
- method of sections
- method of steam jet
- methods of structural analysis
- method of successive approximations
- methods of testing
- method of water needles
- accepted method of building
- accepted method of house construction
- accurate method of analysis
- adhesive nail-on method
- admittance method
- advanced methods of concreting
- advance slope method
- aggregate exposure method
- air permeability method
- alternate methods
- American method
- analytical method of determining reactions
- API method of pile design
- approximate method
- approximation method
- area method
- area-moment method
- assembly methods
- Austrian method
- autogenous curing method
- balanced cantilever method
- Belgian method
- Benoto method
- bentonite method
- Billner method
- "bin" method
- boiling water method
- boom placement concreting method
- bricklaying methods
- building method
- building block module method
- cable method of rock stressing
- calculation method
- cantilever method
- Chicago method
- circular-arc method
- Coast-Survey method
- collapse method of structural design
- combined finite strip-finite element method
- compaction methods of clays
- conjugate beam method
- consistency measurement method
- construction methods
- construction and erection methods
- contiguous pile method
- continuous-flight augers method
- continuous-sample method of advance
- convergence method
- critical method
- critical path method
- Cross moment distribution method
- Cross method
- cross-section method
- current design methods
- cut-and-cover method
- dampproofing methods
- displacement method
- displacement method of advance
- dual-rail method
- dummy unit-load method
- dust-spot method
- Dutch cone method
- earth pressure balanced tunneling method
- elastic center method
- elastic weights method
- electric analogy method
- electric resisting method
- energy method
- equal friction method of duct sizing
- equal friction method
- equivalent load method
- erection method
- fast track construction methods
- fatigue test method
- finite difference method
- finite element method
- finite strip method
- flight auger method
- flotation caisson method
- flue loss method
- folded plate method of analysis
- force method
- free cantilever method of construction
- general method of analysis
- Glotzl hydraulic cell method
- Gow method
- Hardy Cross method
- housing appraisal method
- in-duct method
- industrialized methods of construction
- iterative method
- jack method
- jacking method
- lacquer curtain coating method
- laser beam method
- leap-frog method
- limit equilibrium method
- limit state method
- listening methods
- load factor design method
- mandrel method
- mathematical method of design
- matrix method of structural analysis
- maturity method
- measuring method
- mixed-mode method
- mix-in-place method
- modern building methods
- modular ratio method
- moiré fringe method
- moment-balance method
- nondestructive methods of tests
- normal method of quality control
- null method
- numerical method
- one-rail method
- optical square method
- permissible stress method
- phototheodolite method
- plastic methods of structural analysis
- plate count method
- precast concrete manufacturing methods
- pressuremeter method
- proven construction methods
- p-y method of pile design
- rapid test method
- ratio method of balancing
- rebound hammer method
- reference point method
- relaxation method
- reproducible methods
- resistivity method
- resonant-frequency method
- reverberant field method
- Rockwell method of hardness testing
- safe method
- safe working methods
- secant interlocking pile method
- secant pile method
- seismic method of surveying
- seismic reflection method
- seismic refraction method
- semiprobabilistic design method
- shear transfer method
- shock response method of pile testing
- sliding-wedge method
- slope deflection method
- solar radiation method
- sonic method
- special method of quality control
- standard test method
- static regain method of duct sizing
- static regain method
- statistical design method
- step-by-step method
- strength design method
- strength evaluation method
- successive approximations method
- suspended cantilever method
- swamp shooting method
- Tagg method
- tangent modulus method
- test methods
- Theis method
- thixotropic liquid method
- three-point method
- tilt-up method
- time-saving method of construction
- TNO method of analysis
- TNO method of pile testing
- transit and stadia method
- tremie method
- truss analogy method
- turn-of-nut method
- ultrasonic pulse velocity method
- vacuum concrete method of bridge construction
- valveless pulse-jet method
- vane shear method
- velocity reduction method of duct sizing
- velocity reduction method
- vibratory method
- Vickers method of hardness testing
- volume method of measuring aggregates
- warm water method
- water fog spray method
- western bricklaying method
- western method
- working-stress design method -
6 expansion
1. n рост, развитие, распространение2. n расширение, растяжение, растяжка; увеличение3. n пространство, протяжение; простор4. n экспансия5. n подробное изложение; детализация6. n мат. раскрытие; разложение7. n тех. раскатка, развальцовка8. n геол. распространение на большую поверхностьСинонимический ряд:1. expanse (noun) amplitude; breadth; distance; expanse; space; stretch2. increasing in size (noun) amplification; augmentation; development; enlargement; extension; growth; increase; increasing in size; magnification; spreadАнтонимический ряд: -
7 метод разложения в ряд
1) Construction: method of expansion into series2) Mathematics: expansion methodУниверсальный русско-английский словарь > метод разложения в ряд
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8 метод разложения в ряд
разложение в ряд по … — expansion in terms of …
разложение в ряд — expansion into a series; expansion
Авиация и космонавтика. Русско-английский словарь > метод разложения в ряд
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9 разложение в асимптотический ряд
разложение в ряд по … — expansion in terms of …
разложение в ряд — expansion into a series; expansion
Авиация и космонавтика. Русско-английский словарь > разложение в асимптотический ряд
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10 Chevenard, Pierre Antoine Jean Sylvestre
SUBJECT AREA: Metallurgy[br]b. 31 December 1888 Thizy, Rhône, Franced. 15 August 1960 Fontenoy-aux-Roses, France[br]French metallurgist, inventor of the alloys Elinvar and Platinite and of the method of strengthening nickel-chromium alloys by a precipitate ofNi3Al which provided the basis of all later super-alloy development.[br]Soon after graduating from the Ecole des Mines at St-Etienne in 1910, Chevenard joined the Société de Commentry Fourchambault et Decazeville at their steelworks at Imphy, where he remained for the whole of his career. Imphy had for some years specialized in the production of nickel steels. From this venture emerged the first austenitic nickel-chromium steel, containing 6 per cent chromium and 22–4 per cent nickel and produced commercially in 1895. Most of the alloys required by Guillaume in his search for the low-expansion alloy Invar were made at Imphy. At the Imphy Research Laboratory, established in 1911, Chevenard conducted research into the development of specialized nickel-based alloys. His first success followed from an observation that some of the ferro-nickels were free from the low-temperature brittleness exhibited by conventional steels. To satisfy the technical requirements of Georges Claude, the French cryogenic pioneer, Chevenard was then able in 1912 to develop an alloy containing 55–60 per cent nickel, 1–3 per cent manganese and 0.2–0.4 per cent carbon. This was ductile down to −190°C, at which temperature carbon steel was very brittle.By 1916 Elinvar, a nickel-iron-chromium alloy with an elastic modulus that did not vary appreciably with changes in ambient temperature, had been identified. This found extensive use in horology and instrument manufacture, and even for the production of high-quality tuning forks. Another very popular alloy was Platinite, which had the same coefficient of thermal expansion as platinum and soda glass. It was used in considerable quantities by incandescent-lamp manufacturers for lead-in wires. Other materials developed by Chevenard at this stage to satisfy the requirements of the electrical industry included resistance alloys, base-metal thermocouple combinations, magnetically soft high-permeability alloys, and nickel-aluminium permanent magnet steels of very high coercivity which greatly improved the power and reliability of car magnetos. Thermostatic bimetals of all varieties soon became an important branch of manufacture at Imphy.During the remainder of his career at Imphy, Chevenard brilliantly elaborated the work on nickel-chromium-tungsten alloys to make stronger pressure vessels for the Haber and other chemical processes. Another famous alloy that he developed, ATV, contained 35 per cent nickel and 11 per cent chromium and was free from the problem of stress-induced cracking in steam that had hitherto inhibited the development of high-power steam turbines. Between 1912 and 1917, Chevenard recognized the harmful effects of traces of carbon on this type of alloy, and in the immediate postwar years he found efficient methods of scavenging the residual carbon by controlled additions of reactive metals. This led to the development of a range of stabilized austenitic stainless steels which were free from the problems of intercrystalline corrosion and weld decay that then caused so much difficulty to the manufacturers of chemical plant.Chevenard soon concluded that only the nickel-chromium system could provide a satisfactory basis for the subsequent development of high-temperature alloys. The first published reference to the strengthening of such materials by additions of aluminium and/or titanium occurs in his UK patent of 1929. This strengthening approach was adopted in the later wartime development in Britain of the Nimonic series of alloys, all of which depended for their high-temperature strength upon the precipitated compound Ni3Al.In 1936 he was studying the effect of what is now known as "thermal fatigue", which contributes to the eventual failure of both gas and steam turbines. He then published details of equipment for assessing the susceptibility of nickel-chromium alloys to this type of breakdown by a process of repeated quenching. Around this time he began to make systematic use of the thermo-gravimetrie balance for high-temperature oxidation studies.[br]Principal Honours and DistinctionsPresident, Société de Physique. Commandeur de la Légion d'honneur.Bibliography1929, Analyse dilatométrique des matériaux, with a preface be C.E.Guillaume, Paris: Dunod (still regarded as the definitive work on this subject).The Dictionary of Scientific Biography lists around thirty of his more important publications between 1914 and 1943.Further Reading"Chevenard, a great French metallurgist", 1960, Acier Fins (Spec.) 36:92–100.L.Valluz, 1961, "Notice sur les travaux de Pierre Chevenard, 1888–1960", Paris: Institut de France, Académie des Sciences.ASDBiographical history of technology > Chevenard, Pierre Antoine Jean Sylvestre
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11 показать
(= показывать) show, register, read, exhibit, reveal, depict, display, illustrate, indicate• Анализ этих уравнений показывает, что... - Inspection of these equations shows that...• Более совершенным рассуждением можно показать, что... - By a more refined argument it can be shown that...• Более того, данное обсуждение показывает, что... - The discussion shows, moreover, that...• Более точное вычисление показывает, что... - A more exact calculation shows that...• Быстро покажем, что... - It will be shown in a moment that...• В главе 2 мы вернемся к этому вопросу и попытаемся показать, что... - In Chapter 2 we shall return to this question and try to show that...• В предыдущем параграфе мы уже показали, как исследовать... - In the preceding section we have shown how to investigate...• Важно, что исследование также показывает, что... - Importantly, the study also shows that...• Нам остается лишь показать, что... - All that remains is to show that...• Вычисления показали, что... - Computations have shown that...• Далее будет показано, что... - It will be shown in the sequel that...• Далее можно показать, что... - It can further be shown that...• Далее, легко показать, что... - It is easy to show, furthermore, that...• Далее, мы показываем, что существуют функции, нарушающие это неравенство при к > 2... - Next, we show that there are functions which violate this inequality for к > 2.• Дальнейшее исследование, однако, показало, что... - Further investigation, however, has shown that...• Дальнейшее применение соотношения (1) показывает, что... - Further application of (1) shows that...• Данная формулировка показывает сразу несколько аспектов. - The formulation reveals several things.• Данные примеры должны показать, что... - These examples should make it clear that...• Данный подход показывает, что... - The present approach shows that...• Данный результат следует немедленно, если мы можем показать, что... - The result will follow immediately if we can show that...• Действительно, в этом случае мы могли бы показать, что... - Indeed, in this case, we may show that...• Довольно громоздкое вычисление показывает, что... - A somewhat lengthy computation shows that...• Еще более удивительным является пример, найденный Смитом [11], который показывает, что... - Even more startling is an example due to Smith [11], which shows that...• Еще раз, это показывает зависимость... - Again, this demonstrates the dependence of...• Здесь мы можем только показать, что... - We can show here only that...• Изучение... показывает, что... - Studies of... indicate that...• Используя определения F и G, легко показать, что... - It is a simple matter, using the definitions of F and G, to show that...• Используя эти соотношения, мы легко можем показать по индукции, что... - From these relations we can easily show by induction that...• Исследование уравнения (4) показывает, что... - An examination of (4) shows that...• Исследования показали важность... - The studies demonstrated the importance of...• Видимо, все это показывает, что... - All this seems to show that...• Как легко показать, используя..., этим можно полностью пренебречь. - It is utterly negligible, as we can easily show by...• Как показывает следующий пример, это не обязательно выполняется. - This is not necessarily the case, as the following example illustrates.• Как приложение данного результата, мы покажем, что... - As an application of this result, we show that...• Количественный анализ этих результатов показывает, что... - A quantitative analysis of these results shows that...• Легко показать, что... - It is easily shown that...• Легкое изменение приведенного выше рассуждения показывает, что... - A slight modification of the above reasoning shows that...• Метод анализа, намеченный в предыдущем абзаце, показывает... - The method of analysis outlined in the last paragraph shows...• Многие годы экспериментов показали, что... - Many years of experimentation have shown that...• Можно показать, что в целом это заключение является справедливым. - It can be shown that this conclusion is generally valid.• Можно показать, что они являются как достаточными, так и необходимыми. - It may be shown that they are sufficient as well as necessary.• Можно показать, что это эквивалентно условию... - This can be shown to be equivalent to the condition that...• Мы должны показать, что... - We have to show that...• Мы можем показать это на простом примере. - We can demonstrate this with a simple example.• Мы оставляем для самостоятельного решения задачу показать, что... - We leave it as a problem to show that...• Мы покажем теперь, что это не справедливо. - We shall now show that this is not the case.• Мы хотим явно показать, что... - We wish to show explicitly that...• На самом деле мы лишь показали, что... - We have in fact only shown that...• На самом деле мы можем показать, что... - We can show, in fact, that...• На самом деле, его исследование, похоже, показывает, что... - Actually his investigation seemed to show that...• Нам остается показать, что... - We need only to show that...; It remains for us to show that...• Намеченные выше вычисления показывают, что... - The calculations outlined above show that...• Например, мы покажем, что... - We shall show, for example, that...• Например, не слишком трудно показать, что... - For example, it is not too difficult to show that...• Например, экспериментально было показано, что... - For example, it has been shown experimentally that...• Наш простой пример показывает, что... - Our simple example demonstrates that...• Наши цифры показывают, что... - Our figures show that...• Небольшое изменение этого доказательства показывает, что... - A minor modification of the proof shows that...• Небольшое размышление показывает, что... - A moment's reflection will indicate that...• Недавние эксперименты показали, что... - Recent experiments have shown that...• Недавняя работа показала, что... - Recent work has shown that...• Недолгое размышление покажет, что... - A moment's thought will show that...• Несколько иное рассуждение показывает, что... - A slightly different argument shows that...• Общие наблюдения показывают... - It is a matter of common observation that...• Один тип... показан на рис. 2. - One type of... is shown in Figure 2.• Однако, мы хотим показать, что... - We wish to show, however, that...• Однако мы уже показали, что... - But we have already shown that...• Однако следующая теорема показывает, что... - The next theorem shows, however, that...• Он показал существование глобального по времени решения. - Не showed existence of a global-in-time weak solution.• Описанные здесь исследования показывают, что... - The studies described here show that...• Исторический опыт показывает, что... - Historical experience shows that...• Остается показать, что... - It remains to be shown that...• Оценка показывает, что... - It is estimated that...• Подобное же рассуждение показывает нам... - A similar argument will show that...• Подобные вычисления показывают, что... - Similar computations reveal that...• Подобным образом можно показать, что... - In like manner it can be shown that...• Подробный вывод показал бы, что... - A detailed derivation would show that...• Подстановка этой величины в уравнение (1) показывает, что... - Insertion of this value into equation (1) shows that...• Полная теория показывает, что... - Detailed theory shows that...• Помимо всего, нам необходимо показать, что... - Above all, we need to show that...• Помимо прочих следствий, данный результат показывает, что... - Among other things, this result shows that...• Последнее разложение показывает, что... - The latter expansion shows that...• Это может быть трудно показать на практике. - In practice this may be difficult to demonstrate.• Предварительные результаты показывают, что... - The preliminary results suggest that...• Пренебрегая этими эффектами, легко показать, что... - Neglecting these effects it is easy to show that...• Приведенный выше пример 2 показывает, что... - Example 2 above shows that...• Придерживаясь тех же обозначений, что и в первом параграфе, мы покажем, что... - With the same notation as in Section 1, we shall show that...• Применение данного метода показывает... - An application of this process shows...• Продолжая действовать так же, как в параграфе 1, мы можем показать, что... - Proceeding as in Section 1, we may show that...• Ранее мы показывали, что... - Earlier we showed that...• Рассуждение, приведенное в конце последней главы, показывает, что... - The argument at the end of the last chapter shows that...• Рассуждения Гильберта относительно этого уравнения показывают, что... - Hilbert's discussion of this equation shows that...• Реальные вычисления, однако, показывают, что... - Actual computations show, however, that...• Результат показан ниже. - The result is recorded below.• С другой стороны, эксперименты показывают, что... - On the other hand, experiments show that...• Следующая серия примеров (= иллюстраций) показывает... - The following series of illustrations shows...• Следующая теорема позволяет нам показать, что... - The following theorem enables us to show that...• Следующие задачи помогут показать, что важность... - The following problems will help show that importance of...• Следующие примеры покажут важность данного определения. - Examples will bring out the significance of this definition.• Следующий пример показывает, что... - The following example shows that...• Следующим шагом мы покажем, что... - Next it will be shown that...• Совершенно аналогичным образом можно показать, что... - It can be shown by an exactly similar process that...• Сравнение с точным результатом (2) показывает, что... - A comparison with the exact result (2) shows that...• Ссылка на уравнение (6) показывает, что... - Reference to equation (6) shows that...• Стандартные вычисления показывают, что... - A routine calculation shows that...• Таблицы данных показывают, что... - The tables show that...• Теоретические соображения показывают, что... - Theoretical considerations show that...• Теперь мы покажем, что допустимо (предполагать и т. п.)... - We shall now show that it is permissible to...• Термометр показывает 20 градусов ниже нуля. - The thermometer shows/reads 20 degrees below zero.• Типичный... показан на рис. 2. - A typical... is shown in Figure 2.• То же самое рассуждение показывает, что... - The same reasoning shows that...• То же самое рассуждение четко показывает, что... - The same reasoning evidently shows that...• То же самое рассуждение, что и выше, показывает, что... - The same argument as above shows that...• То, что мы показали, это... - What we have shown is that...• Только что проделанные вычисления показывают нам, что... - The result just calculated shows us that...• Рис. 2 показывает результаты, полученные... - Fig. 2 shows results obtained for Equation (2.8).• Цель заключается в том, чтобы показать, что... - The aim is to show that...• Чтобы доказать теорему, достаточно показать, что... - То prove the theorem it is sufficient to show that...• Чтобы завершить доказательство, нам остается показать, что... - То complete the proof, we need to demonstrate that...• Чтобы показать, что обратное несправедливо, мы должны... - То show that the converse is false, we must...• Чтобы показать, что это невозможно, давайте... - То show that this is not possible, let...• Чтобы это доказать, нам остается лишь показать, что... - То prove this we need only show that...• Эксперимент подтверждает это, однако также(= одновременно) показывает, что... - Experiment confirms this but also shows that...• Эксперимент показывает, что... - Experiment shows that...; Experiment tells us that...• Эксперименты с полупроводниками показывают, что... - Experiments with semiconductors show that...• Эти и многие другие примеры показывают, что... - These and many other examples show that...• Эти равенства позволяют нам показать, что... - These identities enable us to show that...• Эти рассуждения показывают нам, что... - These considerations show us that...• Эти результаты ясно показывают, что... - These results clearly show that...• Это доказательство легко переделывается для того, чтобы показать, что... - The proof is easily adapted to show that...• Это могло бы быть легко показано при использовании условия... - This may be shown readily by employing the condition that...• Это можно показать двумя методами. - This can be seen in two ways.• Это показывает (одно) важное ограничение (чего-л). - This demonstrates an important limitation of...• Это показывает еще раз, что... - This shows once more that...• Это показывает, что невозможно... - This shows that it is impossible to...• Это простое соотношение немедленно показывает, что... - This simple relation shows immediately that...• Это соотношение также показывает, что... - This relation also shows that...• Это ясно показано на рис. 1, которая представляет результаты (чего-л). - This is clearly demonstrated in Figure 1 which shows the results of...• Этот пример показывает, что может быть необходимым... - This example shows that it may be necessary to...• Этот рисунок четко показывает принципиальные различия между... - This figure clearly illustrates the basic differences between...• Этот эффект будет обсуждаться в главе 2, где будет показано, что... - This effect will be discussed in Chapter 2, where it will be shown that... -
12 Wöhler, August
SUBJECT AREA: Metallurgy[br]b. 22 June 1819 Soltau, Germanyd. 21 June 1914 Hannover, Germany[br]German railway engineer who first established the fatigue fracture of metals.[br]Wöhler, the son of a schoolteacher, was born at Soltau on the Luneburg Heath and received his early education at his father's school, where his mathematical abilities soon became apparent. He completed his studies at the Technical High School, Hannover.In 1840 he obtained a position at the Borsig Engineering Works in Berlin and acquired there much valuable experience in railway technology. He trained as an engine driver in Belgium and in 1843 was appointed as an engineer to the first Hannoverian Railway, then being constructed between Hannover and Lehrte. In 1847 he became Chief Superintendent of rolling stock on the Lower Silesian-Brandenhurg Railway, where his technical abilities influenced the Prussian Minister of Commerce to appoint him to a commission set up to investigate the reasons for the unusually high incidence of axle failures then being encountered on the railways. This was in 1852, and by 1854, when the Brandenburg line had been nationalized, Wöhler had already embarked on the long, systematic programme of mechanical testing which eventually provided him with a clear insight into the process of what is now referred to as "fatigue failure". He concentrated initially on the behaviour of machined iron and steel specimens subjected to fluctuating direct, bending and torsional stresses that were imposed by testing machines of his own design.Although Wöhler was not the first investigator in this area, he was the first to recognize the state of "fatigue" induced in metals by the repeated application of cycles of stress at levels well below those that would cause immediate failure. His method of plotting the fatigue stress amplitude "S" against the number of stress cycles necessary to cause failure "N" yielded the well-known S-N curve which described very precisely the susceptibility to fatigue failure of the material concerned. Engineers were thus provided with an invaluable testing technique that is still widely used in the 1990s.Between 1851 and 1898 Wöhler published forty-two papers in German technical journals, although the importance of his work was not initially fully appreciated in other countries. A display of some of his fracture fatigue specimens at the Paris Exposition in 1867, however, stimulated a short review of his work in Engineering in London. Four years later, in 1871, Engineering published a series of nine articles which described Wöhler's findings in considerable detail and brought them to the attention of engineers. Wöhler became a member of the newly created management board of the Imperial German Railways in 1874, an appointment that he retained until 1889. He is also remembered for his derivation in 1855 of a formula for calculating the deflections under load of lattice girders, plate girders, and other continuous beams resting on more than two supports. This "Three Moments" theorem appeared two years before Clapeyron independently advanced the same expression. Wöhler's other major contribution to bridge design was to use rollers at one end to allow for thermal expansion and contraction.[br]Bibliography1855, "Theorie rechteckiger eiserner Brückenbalken", Zeitschrift für Bauwesen 5:122–66. 1870, "Über die Festigkeitversuche mit Eisen und Stahl", Zeitschrift für Bauwesen 20:73– 106.Wöhler's experiments on the fatigue of metals were reported in Engineering (1867) 2:160; (1871) 11:199–200, 222, 243–4, 261, 299–300, 326–7, 349–50, 397, 439–41.Further ReadingR.Blaum, 1918, "August Wöhler", Beiträge zur Geschichte der Technik und Industrie 8:35–55.——1925, "August Wöhler", Deutsches biographisches Jahrbuch, Vol. I, Stuttgart, pp. 103–7.K.Pearson, 1890, "On Wöhler's experiments on alternating stress", Messeng. Math.20:21–37.J.Gilchrist, 1900, "On Wöhler's Laws", Engineer 90:203–4.ASD
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