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1 ряд с конечным числом членов
конечный ряд; ряд с конечным числом членов — finite series
Русско-английский большой базовый словарь > ряд с конечным числом членов
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2 низший член ряда
Chemistry: lower member of the series -
3 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 -
4 rang
rang [ʀɑ̃]masculine noun• en rang par deux/quatre two/four abreast• se mettre en rangs par quatre [élèves] to line up in fours• plusieurs personnes se sont mises sur les rangs pour l'acheter several people have indicated an interest in buying it• servir dans les rangs de [soldat] to serve in the ranks ofc. ( = condition) station• de haut rang ( = noble) noble• tenir or garder son rang to maintain one's rankd. (hiérarchique = grade, place) rank• ce pays se situe au troisième rang mondial des exportateurs de pétrole this country is the third largest oil exporter in the world━━━━━━━━━━━━━━━━━In Quebec, rural areas are divided into districts known as rangs. The word rang refers to a series of rectangular fields (each known as a « lot »), usually laid out between a river and a road (the road itself also being called a rang). The rangs are numbered or given names so that they can be easily identified and used in addresses (eg « le deuxième rang », « le rang Saint-Claude »). In Quebec, the expression « dans les rangs » means « in the countryside ».* * *ʀɑ̃nom masculin1) ( rangée) (de personnes, chaises, légumes) row; ( de collier) strandse mettre en rangs — [enfants] to get into (a) line
2) Armée rankrompre les rangs — ( sur ordre) to fall out; ( sans ordre) to break ranks
sortir du rang — Armée, fig to rise ou come up through the ranks
serrer les rangs — Armée, fig to close ranks
rentrer dans le rang — lit to fall into line; fig to toe the line
les rangs des mécontents — fig the ranks of the discontented
3) ( place)arriver au 20e rang mondial — to rank 20th in the world
être au 5e rang mondial des exportateurs — to be the 5th largest exporter in the world
4) ( ordre) order5) ( dans une hiérarchie) rank6) ( au tricot) row* * *ʀɑ̃1. nm1) (= rangée) rowse mettre sur un rang — to get into a line, to form a line
se mettre en rangs par 4 — to get into fours, to get into rows of 4
2) (= grade, condition, classement) rankau rang de — among, among the ranks of
3) [perles] row, string2. rangs nmplMILITAIRE ranks* * *rang nm1 ( rangée) (de personnes, chaises, légumes) row; ( de collier) strand; les enfants étaient en rangs the children were in rows; mettre les enfants en rangs to make the children line up; se mettre en rangs [enfants] to get into (a) line; (mettez-vous) en rangs deux par deux/trois par trois line up in twos/threes; Paul est au premier/dernier rang Paul is in the first/last row;2 Mil rank; placer des soldats sur deux rangs to draw up soldiers in two ranks; silence dans les rangs! silence in the ranks!; les rangs d'une armée the rank and file, the ranks; rompre les rangs ( sur ordre) to fall out; ( sans ordre) to break ranks; servir dans le rang to serve in the ranks; sortir du rang Mil, fig to rise ou come up through the ranks; serrer les rangs Mil to close ranks; Scol [élèves] to crowd together; fig ( être solidaires) to close ranks; ramener qn dans le rang fig to bring sb into line, to make sb toe the line; rentrer dans le rang lit to fall into line; fig to toe the line; rejoindre les rangs de l'opposition fig to join the ranks of the opposition; venir grossir les rangs des mécontents fig to swell the ranks of the discontented;3 ( place) arriver au 20e rang mondial des exportations de café to rank 20th in the world for coffee exports; être au 5e rang mondial des exportateurs de coton to be the 5th largest exporter of cotton in the world; ce problème vient au premier/dernier rang des préoccupations du gouvernement the problem is at the top/bottom of the government's list of priorities ; reléguer qn/qch au rang de to relegate sb/sth to the rank of; être sur les rangs pour un poste to be in the running for a job; acteur/auteur de second rang second-rate actor/author;4 ( ordre) order; par rang d'ancienneté/de taille in order of seniority/of height;5 ( dans une hiérarchie) rank; rang inférieur, rang subalterne lower rank; avoir rang de to have the rank of; accéder au rang de to rise to ou to attain the rank of; élevé au rang de promoted to the rank of; fonction de très haut rang high-ranking post; ne fréquenter que des personnes de son rang to mix only with people of one's own station; garder or tenir son rang to behave in a way appropriate to one's position; mettre sur le même rang que to put in the same class as;6 ( au tricot) row; un rang à l'endroit/l'envers one row knit/purl.[rɑ̃] nom masculin1. [rangée - de personnes] row, line ; [ - de fauteuils] row ; [ - de crochet, de tricot] row (of stitches)2. [dans une hiérarchie] rankce problème devrait être au premier rang de nos préoccupations this problem should be at the top of our list of prioritiesvenir au deuxième/troisième rang to rank second/thirdde premier rang high ranking, first-class, top-class3. [condition sociale] (social) standing4. MILITAIREb. (figuré) to give in, to submit————————rangs nom masculin plurielêtre ou se mettre sur les rangs to line upservir dans les rangs d'un parti/syndicat to be a member ou to serve in the ranks of a party/union————————au rang de locution prépositionnelle1. [dans la catégorie de]une habitude élevée ou passée au rang de rite sacré a habit which has been raised to the status of a sacred rite2. [au nombre de]3. [à la fonction de]élever quelqu'un au rang de ministre to raise ou to promote somebody to the rank of minister————————de rang locution adverbiale————————en rang locution adverbialein a line ou rowentrez/sortez en rang go in/out in single filese mettre en rang to line up, to form a lineen rang d'oignons in a line ou row
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