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21 Отсутствие артиклей перед существительными, которые снабжены ссылками
It follows from Theorem 1 that $x=1$Section 2 of this paper gives (contains) a concise presentation of the notation to be used belowProperty 1 is called (known as) the triangle inequalityThis assertion (statement, proposition) has been proved in part 1 (part (a)) of the (our) proofAlgorithm 1 (с большой буквы) defines elementary permutations and elementary triangle matrices of index 2Equation (1) ((the) inequality (1)) can thus be written in the (артикль обязателен) form (2)In the language of our notation, algorithm (1) (с маленькой буквы) is a stable way of computing the inner productThe only place where the algorithm can break down is in statement 3 (in Statement 3)We combine Exercises 1 and 2 to construct an algorithm for finding an approximate eigenvectorThis case is illustrated in (но не on) Figure 1The asymptotic formula (1) was proved in Example 1Corollary 1 can be used to estimate the error in the inverse of a perturbed matrixBy property 1 (by Theorem 1), this function is positive except at the zero vectorA less trivial example is given in Appendix 3Step 1 in Example 1 and steps 2 and 3 in Example 2The idea of a norm will be introduced in Chapter 4Now from statements 2 and 3 of (1), we have...All the drivers for solving linear systems are listed in Table 1 (are illustrated in Figure 1)If Algorithm 1 in four-digit arithmetic is applied to refine $x$, then we obtain...Assertion (ii) is nothing but the statement that one natural way of extending these ideas to $R^n$ is to generalize formula (1) to obtain a Euclidean length of a vectorBy property 1, this function is positive except at the zero vectorWe have seen on page 3 that set of matrices is a vector space which is essentially identical with...Equation (1) effectively gives an algorithm for using the output of Algorithm 1 to solve...Русско-английский словарь по прикладной математике и механике > Отсутствие артиклей перед существительными, которые снабжены ссылками
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22 эффективно непостоянная функция
Mathematics: effectively variable functionУниверсальный русско-английский словарь > эффективно непостоянная функция
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23 эффективно постоянная функция
Mathematics: effectively constant functionУниверсальный русско-английский словарь > эффективно постоянная функция
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24 эффективно разрешимая функция
Mathematics: effectively decidable functionУниверсальный русско-английский словарь > эффективно разрешимая функция
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25 действовать
act, operate, function, work, run, affect, hold, hold good, be valid• В свою очередь, он (этот оператор и т. п.) действует как... - This in turn acts as...• Данные две силы действуют в противоположных направлениях. - The two forces act in opposite directions.• Дистанция, на которой действует данная сила... - The distance through which this force acts...• Оба изменения действуют в одном направлении. - Both changes operate in the same direction.• Чтобы эффективно действовать в подобной ситуации, мы должны... - In order to deal effectively with circumstances of this kind, we must... -
26 οἰκοδομέω
οἰκοδομέω (οἰκοδόμος; Hdt.; ins, pap, LXX, En, EpArist, Philo, Joseph., Test12Patr) impf. ᾠκοδόμουν; fut. οἰκοδομήσω; 1 aor. ᾠκοδόμησα also without augment οἰκοδόμησα (ApcMos 40; on the augment s. W-S. §12, 5a; Mlt-H. 191); pf. ᾠκοδόμηκα LXX; plpf. 3 sg. ᾠκοδομήκει (Just., D. 127, 3). Pass.: impf. 3 sg. ᾠκοδομεῖτο; 1 fut. οἰκοδομηθήσομαι; 1 aor. ᾠκοδομήθην (v.l.) or οἰκοδομήθην (other edd., J 2:20); perf. inf. ᾠκοδομῆσθαι (οἰ-Lk 6:48b); ptc. οἰκοδομημένος (Ox 1 recto, 15f [GTh 32]); ᾠκοδομημένος Hv 3, 2, 6; plpf. 3 sg. ᾠκοδόμητο.① to construct a building, buildⓐ w. obj. acc. build, erect (oft. pap [Mayser II/2 p. 315, 30ff]; Jos., Ant. 15, 403 al.; Did., Gen 29, 7) οἰκίαν (Diod S 14, 116, 8; Lucian, Charon 17) Lk 6:48a. τὰς οἰκοδομάς GJs 9:3; pass. (Sb 5104, 2 [163 B.C.] οἰκία ᾠκοδομημένη; PAmh 51, 11; 23) Lk 6:48b. πύργον (Is 5:2) Mt 21:33; Mk 12:1; Lk 14:28; Hs 9, 3, 1; 4; 9, 12, 6; pass. Hv 3, 2, 4ff; 3, 3, 3; 3, 5, 5; 3, 8, 9; Hs 9, 3, 2; 9, 5, 2; 9, 9, 7; cp. 9, 9, 4. ναόν Mk 14:58; 16:3 (Is 49:17); pass. J 2:20 (Heliodorus Periegeta of Athens [II B.C.]: 373 Fgm. 1 Jac. says of the Acropolis: ἐν ἔτεσι ε̄ παντελῶς ἐξεποιήθη; Orig., C. Cels. 5, 33, 13); 16:6 (cp. below; the ‘scripture’ pass. is interpreted spiritually). ἀποθήκας Lk 12:18 (opp. καθαιρεῖν; s. this 2aα). τοὺς τάφους τῶν προφητῶν the tombs of the prophets Mt 23:29 (s. EKlosterman2 ad loc.). τὰ μνημεῖα τῶν προφητῶν the monuments for the prophets Lk 11:47 (μνημεῖον 1).—οἰκ. τινί τι build someth. for someone (Gen 8:20; Ex 1:11; Ezk 16:24) συναγωγὴν οἰκ. τινί Lk 7:5. οἰκ. τινὶ οἶκον Ac 7:47, 49; 16:2 (the last two Is 66:1).—W. the obj. acc. and foll. by ἐπί w. acc. or w. gen: τὴν οἰκίαν ἐπὶ τὴν πέτραν build the house on the rock Mt 7:24. ἐπὶ τὴν ἄμμον on the sand vs. 26 (proverbial: Plut. VII p. 463, 10 Bern. εἰς ψάμμον οἰκοδομεῖς). πόλις ἐπὶ τ. ὄρους Lk 4:29 (cp. Jos., Ant. 8, 97). ἐπὶ τὴν γῆν 6:49. πόλις οἰκοδομημένη ἐπʼ ἄκρον ὄρους ὑψηλοῦ a city that is built on the top of a high mountain Ox 1 recto, 15f (GTh 32). πύργος ἐπὶ ὑδάτων Hv 3, 3, 5; ἐπὶ τὴν πέτραν Hs 9, 14, 4 (opp. χαμαὶ οὐκ ᾠκοδόμηται).ⓑ abs.α. when the obj. can be supplied fr. the context (Did., Gen. 33, 27) Lk 11:48; 14:30.—Cp. Hv 3, 1, 7; 3, 4, 1a; 3, 10, 1; Hs 9, 4, 1.β. but also entirely without an obj. (Theoph. Ant. 2, 13 [p. 132, 4f]) ᾠκοδόμουν they erected buildings Lk 17:28. οἱ οἰκοδομοῦντες the builders, the masons (after Ps 117:22) Mt 21:42; Mk 12:10; Lk 20:17; Ac 4:11 v.l.; 1 Pt 2:7; 6:4. Also with no ref. to the Ps passage: Hs 9, 4, 4; 9, 6, 6.γ. οἱ λίθοι οἱ ἤδη ᾠκοδομημένοι the stones already used in the building Hv 3, 5, 2; cp. Hs 9, 6, 3.ⓒ build up again, restore, a sense that οἰκ. can receive fr. the context (Josh 6:26; Ps 50:20; 68:36) Mt 26:61; 27:40; Mk 15:29; 16:3 (Is 49:17).—S. also 2.② to construct in a transcendent sense (as in Hermas passages given under 1, where the tower is a symbol of the church) build: of the building up of the Christian congregation/church (cp. Ruth 4:11; θεμελιώσαντες καὶ οἰκοδομήσαντες οἱ μακάριοι ἀπόστολοι τὴν ἐκκλησίαν Iren. 3, 3, 3 [Harv. II 10, 1]) ἐπὶ ταύτῃ τῇ πέτρᾳ οἰκοδομήσω μου τὴν ἐκκλησίαν on this rock I will build my congregation/church Mt 16:18. ὡς λίθοι ζῶντες οἰκοδομεῖσθε οἶκος πνευματικός like living stones let yourselves be built up (pass.) or build yourselves up (mid., so Goodsp., Probs. 194f) into a spiritual house 1 Pt 2:5. Paul refers to missionary work where another Christian has begun activities as ἐπʼ ἀλλότριον θεμέλιον οἰκ. building on another’s foundation Ro 15:20. He also refers to his negative view of law in relation to the Christ-event as a building, and speaks of its refutation as a tearing down (καταλύειν), and of returning to it as a rebuilding (s. 1c above) Gal 2:18. This is prob. where 11:1 belongs, where (followed by citations of Scripture) it is said of the Israelites that they do not accept the baptism that removes sin, but ἑαυτοῖς οἰκοδομήσουσιν will build up someth. for themselves. In another pass. B calls the believer a πνευματικὸς ναὸς οἰκοδομούμενος τῷ κυρίῳ a spiritual temple built for the Lord 16:10; cp. vs. 6f.—Hermas’ temple-building discourse mentions angels entrusted by God with οἰκοδομεῖν building up or completion of his whole creation Hv 3, 4, 1b.—(In this connection cp. Orig., C. Cels. 4, 38, 16 γυνὴ οἰκοδομηθεῖσα ὑπὸ τοῦ θεοῦ [of Eve]).③ to help improve ability to function in living responsibly and effectively, strengthen, build up, make more able. οἰκ. is thus used in a nonliteral sense and oft. without consciousness of its basic mng. (Straub p. 27), somewhat like edify in our moral parlance (this extended use is found as early as X., Cyr. 8, 7, 15 and in LXX: Ps 27:5; Jer 40:7. Also TestBenj 8:3.—JWeiss on 1 Cor 8:1). Of the Lord, who is able to strengthen the believers Ac 20:32. Of the congregation, which was being built up 9:31.—Esp. in Paul: ἡ ἀγάπη οἰκοδομεῖ love builds up (in contrast to γνῶσις, which ‘puffs up’) 1 Cor 8:1 (=Dg 12:5). πάντα ἔξεστιν, ἀλλʼ οὐ πάντα οἰκοδομεῖ everything is permitted, but not everything is beneficial 10:23. ὁ λαλῶν γλώσσῃ ἑαυτὸν οἰκοδομεῖ• ὁ δὲ προφητεύων ἐκκλησίαν οἰκοδομεῖ 14:4; cp. vs. 17. οἰκοδομεῖτε εἷς τὸν ἕνα strengthen one another 1 Th 5:11. In 1 Cor 8:10 the apostle is prob. speaking ironically, w. ref. to the ‘strong’ party at Corinth, who declare that by their example they are benefiting the ‘weak’: οὐχὶ ἡ συνείδησις αὐτοῦ οἰκοδομηθήσεται εἰς τὸ τὰ εἰδωλόθυτα ἐσθίειν; will not his conscience be ‘strengthened’ so that he will eat meat offered to idols? (difft. MargaretThrall, TU 102, ’68, 468–72).—Of Paul’s letters, by which δυνηθήσεσθε οἰκοδομεῖσθαι εἰς τὴν δοθεῖσαν ὑμῖν πίστιν you will be able to build yourselves up in the faith that has been given you Pol 3:2.—HCremer, Über den bibl. Begriff der Erbauung 1863; HScott, The Place of οἰκοδομή in the NT: PT 2, 1904, 402–24; HBassermann, Über den Begriff ‘Erbauung’: Zeitschr. für prakt. Theol. 4 1882, 1–22; CTrossen, Erbauen: ThGl 6, 1914, 804ff; PVielhauer, Oikodome (d. Bild vom Bau vom NT bis Clem. Alex.), diss. Hdlbg. ’39; PBonnard, Jésus-Christ édifiant son Église ’48.—B. 590. DELG s.v. δέμω. M-M. TW. Sv. -
27 ἀσθένεια
ἀσθένεια, ας, ἡ (σθένος ‘strength’, s. next entry; Hdt., Thu.+)① a state of debilitating illness, sickness, disease (X., Mem. 4, 2, 32; Appian, Bell. Civ. 5, 16 §65; Herodian 1, 4, 7; pap; 2 Macc 9:21f; Jos., Bell. 1, 76, Ant. 15, 359) Ac 5:15 D; w. νόσος Mt 8:17; ἔχειν ἀ. be ill Ac 28:9; ἀσθένειαν τῇ σαρκὶ αὐτῶν ἐπισπῶνται Hv 3, 9, 3; θεραπεύεσθαι ἀπὸ τῶν ἀ. Lk 5:15. For this ἀπολύεσθαι τῆς ἀ. 13:12; ἔτη ἔχειν ἐν ἀ. (s. ἔτος end) J 5:5, cp. 11:4; Hs 6, 3, 4. διʼ ἀσθένειαν τῆς σαρκός because of a bodily ailment (Persaeus [III B.C.]: 584 Fgm. 3a Jac. διὰ τὴν τοῦ σώματος ἀσθένειαν; Dio Chrys. 28 [45], 1 σώματος ἀσθ., likew. Ael. Aristid. 27, 2 K.=16 p. 382 D.—PLond III, 971, 4 p. 128 [III/IV A.D.] ἀδύνατος γάρ ἐστιν ἡ γυνὴ διὰ ἀσθένιαν τῆς φύσεως, cp. also PFlor 51, 5 σωματικῆς ἀσθενείας) Gal 4:13. ἀσθένειαι (pl., as 2 Cor 12:5, 9f) times of weakness, weaknesses 1 Ti 5:23. Caused by hostile spirits, the πνεύματα ἀσθενείας Lk 8:2; 13:11.② incapacity for someth. or experience of limitation, weaknessⓐ gener., Hv 3, 11, 4; 3, 12, 2. Opp. δύναμις (Diod S 4, 8, 3: many do not believe the writers of history when they relate the marvelous deeds of one like Heracles, because they judge the δύναμις of the divine hero in comparison with the ἀσθένεια of contemporary pers.) of inability to function as effectively as one might wish 1 Cor 15:43. δυναμοῦσθαι ἀπὸ ἀ. come out of weakness to strength Hb 11:34. In Paul’s ἀ., which appears in τὰ τῆς ἀ. μου 2 Cor 11:30 or αἱ ἀσθένειαι (s. 1 above) 12:5, 9f, all of which suggest ineffectualness, God’s δύναμις manifests itself 12:9 (s. τελέω 1 end), thus in effect converting displays of weakness into heroic performance.ⓑ gener., of the frailty to which all human flesh is heir (Pla., Leg. 854a ἀ. τ. ἀνθρωπίνης φύσεως; Diod S 1, 2, 3 ἡ τῆς φύσεως ἀ.; 13, 24, 4 and 6; Orig., C. Cels. 3, 42, 11; Did., Gen. 55, 19) of Christ (Orig., C. Cels. 3, 42, 11) ἐσταυρώθη ἐξ ἀ. (opp. ἐκ δυνάμεως θεοῦ) he was crucified as a result of his weakness (his vulnerability as a human being) 2 Cor 13:4. περίκειται ἀσθένειαν Hb 5:2. For this ἀ. ἔχειν 7:28.③ lack of confidence or feeling of inadequacy, weakness. Of Paul’s self-effacement, timidity (w. φόβος and τρόμος) 1 Cor 2:3. Of a sense of helplessness (Paul’s friends wish that Paul would remain with them ‘because of their weakness’, i.e. they cannot get along without him) AcPl Ha 6, 36. Of weakness in judgment (cp. Orig., C. Cels. 1, 9, 22) τῆς σαρκός Ro 6:19. Of lack of spiritual insight 8:26. Of moral deficiency 1 Cl 36:1; Hm 4, 3, 4. συμπαθῆσαι ταῖς ἀ. sympathize w. weaknesses Hb 4:15.—MBarré, CBQ 42, ’80, 216–27 (background of persecution in Qumran).—DELG s.v. σθένος. M-M. TW.
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