(Pythian ) chapter. 1 On the dating of the Pythian festivals, see references in n. above. According to schol. P. 4 Inscr.

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "(Pythian 4. 1-3) chapter. 1 On the dating of the Pythian festivals, see references in n. above. According to schol. P. 4 Inscr."

Transcript

1 Pythian 4 This poem celebrates, like Pythian 5, the chariot victory won at Delphi in 466 or 462 B. C. 1 by king Arcesilas of Cyrene. It seems to have been performed in the victor s home city. 2 Since the ode is much longer than all other preserved epinicians, some scholars assume that it was performed by a solo singer rather than by a chorus. 3 However, nothing precludes a choral performance. 4 In the last triad the narrator pleads with the king on behalf of the exiled Cyrenaean Demophilus for the latter s return. It has been suggested that Demophilus, who in the last line is said to have recently visited Thebes, where he learned immortal words (the present poem), commissioned the ode, and even that he himself performed it. (ref.) The song opens with an invocation of the Muse: Σάμερον μὲν χρή σε παρ ἀνδρὶ φίλῳ στᾶμεν, εὐίππου βασιλῆϊ Κυράνας, ὄφρα κωμάζοντι σὺν Ἀρκεσίλᾳ, Μοῖσα, Λατοίδαισιν ὀφειλόμενον Πυθῶνί τ αὔξῃς οὖρον ὕμνων, (Pythian ) (Today, Muse, you must stand beside a man who is a friend, the king of Kyrene with its fines horses, so that while Arkesilas is celebrating you may swell the breeze of hymns owed to Leto s children and to Pytho (Translation of Race)) As Braswell comments, comparing with Olympian 3. 4 and Bacchylides 11. 5, Greek παρά c. dat. used with ἵστημι (and esp. the compound παρίστημι), like English to stand by or beside (someone) can imply help as well as presence, even when (as here) it is not especially emphasized. 5 The request that the Muse stand beside Arcesilas thus combines [1] the hymnic summoning of the deity, [2] the notion, associated with the goddess of song, that she travels to her subject matter the enactment of the song is her arrival 6 and [3] the wish 1 On the dating of the Pythian festivals, see references in n. above. According to schol. P. 4 Inscr. a, b and schol. P. 5 Inscr. the victory was won in the 31st festival. 2 Cf. Neumann-Hartmann (2007) with ref. (performance at the court? Chek Neumann- Hartmann etc.) 3 Davies (1988) 56; Gentili et al. (1995) 103 (where it is suggested that a solo singer might have been accompanied by a mute chorus). Davies, M. (1988), Monody, Choral Lyric and the Tyranny of the Hand-Book CQ N. S. 38: Add Ferrari? 4 See Carey (1989) 564 n Braswell (1988) See further discussion below of the poem s concluding passage, and compare the discussion of N. 3 in the next chapter.

2 that she help the king. Furthermore, the prayer that the Muse swell the favourable wind of songs suggests the notion of the ode as a sea journey. 7 The first antistrophe then introduces, through the quotation of a prophecy uttered on Thera by Medea, the expedition of the Argonauts. One of these heroes is Euphamus, and Medea foretells how his descendants will eventually colonize Libya, having first migrated from Lemnos to Thera: < > ἀντὶ δελφίνων δ ἐλαχυπτερύγων ἵππους ἀμείψαντες θοάς, ἁνία τ ἀντ ἐρετμῶν δίφρους τε νωμάσοισιν ἀελλόποδας. (Pythian ) (In place of short-finned dolphins they will take swift horses and instead of oars they will ply reins and chariots that run like a storm. (Translation of Race.)) Through this description the recent chariot victory is presented as the fullfilment of Medea s prophecy, and Arcesilas as the successor not only of the Theran colonists but ultimately of the Argonauts, mythical oarsmen par excellence. Medea continues her prophecy, recalling how Euphamus was given a clod of earth by the sea god Triton in Libya, which the Argonauts visited before sailing to Thera. The clod is a sign that Euphamus descendant Battus Arcesilas forefather will found Cyrene: κεῖνος ὄρνις ἐκτελευτάσει μεγαλᾶν πολίων ματρόπολιν Θήραν γενέσθαι, τόν ποτε Τριτωνίδος ἐν προχοαῖς λίμνας θεῷ ἀνέρι εἰδομένῳ γαῖαν διδόντι ξείνια πρῴραθεν Εὔφαμος καταβαίς δέξατ αἰσίαν δ ἐπί οἱ Κρονίων Ζεὺς πατὴρ ἔκλαγξε βροντάν, <====> ἁνίκ ἄγκυραν ποτὶ χαλκόγενυν ναῒ κριμνάντων ἐπέτοσσε, θοᾶς Ἀργοῦς χαλινόν δώδεκα δὲ πρότερον ἁμέρας ἐξ Ὠκεανοῦ φέρομεν νώτων ὕπερ γαίας ἐρήμων ἐννάλιον δόρυ, μήδεσιν ἀνσπάσσαντες ἁμοῖς. τουτάκι δ οἰοπόλος δαίμων ἐπῆλθεν (Pythian ) 7 Cf. Gildersleeve (1881) 282; Becker (1937) 70; Silk (1974) 157; Braswell (1988) 64.

3 ( This sign will bring it to pass that Thera will become the mother-city of great cities the token which Euphamos once received at the ouflow of Lake Tritonis, when he descended from the prow and accepted earth proferred as a guest-present by a god in the guise of a man and father Zeus, son of Kronos, pealed for him an auspicious thunderclap when he came upon us hanging the bronze-jawed anchor, swift Argo s bridle, against the ship. Before that, we had drawn up the sea-faring bark from Okeanos in accordance with my instructions, and for twelve days had been carrying it across the desolate stretches of land. At that point the solitary god approached us (Race s translation)) The description of the anchor as a bridle suggests an analogy between the Argo and Arcesilas victorious horses. 8 Euphamus descendants gain a kind of hereditary right to Cyrene when he receives a clod of earth by the mythical Lake Tritonis, which must thus be located by Pindar in the same region as the city. 9 As it appears from ll. 25-8, and (see futher discussion below), Pindar follows the same tradition as the Hesiodic Catalogue, where the heroes travelled from Colchis, the location of the Golden Fleece at the eastern end of the Black Sea, up the River Phasis to the Oceanus (the stream encircling the world), continuing south to the outer coast of Libya (the Greek name for Africa), whence they carried the ship across the continent to the Mediterranean. 10 In Pindar s account, after marching across Libya the heroes reach Lake Tritonis, where they launch the Argo. As the disguised god Triton approaches they are about to leave the lake along a river that will take them to the Mediterranean. The departure at the beginning of the second triad of the Argo from Libya signalled by an auspicious thunderclap just like that of the same ship from Iolcus in ll reflects the narrator s departing on a poetic journey from Cyrene, the here and now of performance. After ending the quotation of Medea s prophecy in l. 56, subsequently telling of how Battus was greeted as the fated king of Cyrene by the Delphic Oracle, and how his dynasty continues to blossom through Arcesilas, the narrator returns, in the transition between the third and the fourth triad, to the myth of the Argonauts. A long narrative, the second in the poem, ensues, describing the events leading up to the expedition and the journey through the Clashing Rocks to Colchis, where in the eleventh triad king Aeëtes finally reveals to Jason the 8 Cf. Braswell (1988) ; Gentili et al. (1995) Other authors place it elsewhere: see Braswell (1988) 90 with ref.; Huß in Der neue Pauly s. v. Triton (2). (ref. to English version.) 10 Hes. fr. 241 MW = schol. Ap. Rhod (pp Wendel) and schol. Ap Rhod (p. 281 Wendel). The former scholion mentions that also Antimachus follows this version. Different authors versions of the return journey are listed and discussed in EGM ii Later sources, listed by Gentili et al. (1995) 435-6, describe how the Argonauts carry the ship through Libya on their shoulders. According to Hecataeus FGrH 1 F 18 the Argonauts sailed from Oceanus down the Nile.

4 location of the fleece. Introducing the second mythical narrative, the speaker states his intention to offer to the Muses not only Arcesilas but also the Golden Fleece (ll. 67-8). When the narrator comes to the fleece, he accordingly interrupts the account: αὐτίκα δ Ἀελίου θαυμαστὸς υἱὸς δέρμα λαμπρόν ἔννεπεν, ἔνθα νιν ἐκτάνυσαν Φρίξου μάχαιραι ἔλπετο δ οὐκέτι οἱ κεῖνόν γε πράξασθαι πόνον. κεῖτο γὰρ λόχμᾳ, δράκοντος δ εἴχετο λαβροτατᾶν γενύων, ὃς πάχει μάκει τε πεντηκόντερον ναῦν κράτει, τέλεσεν ἃν πλαγαὶ σιδάρου. < > μακρά μοι νεῖσθαι κατ ἀμαξιτόν ὥρα γὰρ συνάπτει καί τινα οἶμον ἴσαμι βραχύν πολλοῖσι δ ἅγημαι σοφίας ἑτέροις. κτεῖνε μὲν γλαυκῶπα τέχναις ποικιλόνωτον ὄφιν, ὦ Ἀρκεσίλα, κλέψεν τε Μήδειαν σὺν αὐτᾷ, τὰν Πελίαο φονόν ἔν τ Ὠκεανοῦ πελάγεσσι μίγεν πόντῳ τ ἐρυθρῷ Λαμνιᾶν τ ἔθνει γυναικῶν ἀνδροφόνων (Pythian ) (At once the wondrous son of Helios told him where Phrixos sacrificial knives had stretched out the shining hide, but he did not expect him to perform that further trial, because it lay in a thicket and was right by the ferocious jaws of a serpent, which exceeded in breadth and length a ship of fifty oars, which strokes of iron have fashioned. But it is too far for me to travel on the highway, because the hour is pressing and I know a short path and I lead the way in wise skill for many others. He cunningly slew the green-eyed snake with spotted back, O Arkesilas, and with her own help stole away Medea, the slayer of Pelias. They came to the expanses of Okeanos, to the Red Sea, and to the race of man-slaying Lemnian women. (Translation of Race)) The description of the snake as bigger than a ship of fifty oars, which strokes of iron have fashioned suggests the construction of the Argo. 11 Euripides Hypsipyle TrGF f 21 refers to the Argo as a πεντηκόντερον, as does also Apollodorus It is not clear whether Pythian is the origin of or just the earliest known allusion to this tradition. 12 The mythical narrative is introduced by the question about which danger bound [the heroes] with mighty nails of adamant (l. 71: τίς δὲ κίνδυνος κρατεροῖς ἀδάμαντος δῆσεν 11 Cf. Gildersleeve (1881) Cf. Braswell (1988) 338; EGM ii 207 n. 37 with ref. Check Silk (1974)

5 ἅλοις;), presenting the danger of the expedition as an irresistible challenge to the heroes 13 This question is answered through the reference (ll ) to the jaws of the serpent, bigger than a ship of fifty oars, which strokes of iron have fashioned, and the narrative is thereby interrupted. 14 Both descriptions (l. 71 and ll. 241 ff.) combine a reference to danger with an allusion to carpentry, suggesting the building of the Argo. According to Apollonius the Argo was built with the help of Athena; 15 that the tradition of divine assistance in the construction of the ship is presupposed by Pindar seems confirmed by his allusion to the speaking beam of Dodonian oak (see discussion below). The interruption of the Argonautic myth with the reference to a ship finished by strokes of iron (l. 246: τέλεσεν ἃν πλαγαὶ σιδάρου) seems to suggest an analogy between the construction of the Argo, built with the help of a goddess, and the enactment executed with the help of the Muse of the mythical narrative about the ship: the interruption of the narrative mirrors the completion of the ship. In addition, the journey of the Argo converges with the poetic enactment, as the narrator breaks off the myth of the journey by declaring that it is too far for him to return (νεῖσθαι often takes on this meaning 16 ) along the carriageway, but that he knows a short road. 17 This convergence of myth and poetic enactment is also indicated, as often in Pindar, through the intimation of danger with which the narrative is interrupted: the narrator shrinks back, as it were, from the serpent. The interruption suggests that the task of describing the serpent exceeds the poem s scope, and thereby another aspect of the analogy between song and ship: they are both surpassed by the serpent in size. Pindar may also be alluding to earlier epic treatments of the myth, 18 suggesting through the break-off the difference between lyric and epic poetry: the narrator has embarked in a lyric poem on an epic narrative, but now has to take a shortcut back to the encomiastic occasion since time is pressing (l. 247). The unity of poetic enactment and mythical journey may be further suggested by a play in the reference to the short οἶμον (l. 248: road ) on the similarity and assumed etymological connection between the words οἶμος and οἴμη (song) Braswell (1988) Cf. Gildersleeve (1881) 299. The question in l. 71 is recalled also by the description in ll of how Hera instils in the heroes a yearning for the ship Argo: see Schroeder (1922) 39; Burton (1962) 154; Braswell (1988) 163; Gentili et al. (1995) Apoll. Rhod , , 226 (with schol. 551, 721 (check)), ; cf. Schulten in RE ii s. v. Argo (1) Cf. Braswell (1988) 193-4, Cf. Braswell (1988) On which see Braswell (1988) 6-12; West (2005) with ref. 19 Cf. Felson (1999) Felson, N. (1999), Vicarious Transport: Fictive Deixis in Pindar s Pythian Four, HSCPh 99: 1-31.

6 The narrator resumes the story and tells of how Jason killed the serpent. He is said to have done it through τέχναις, through wiles or trickery. 20 This might be an allusion to the tradition that Medea charmed the serpent to sleep. 21 We would then have to assume that Jason subsequently killed it. The kill seems reflected in the description of the fifty-oar ship, to which the snake is compared, as completed with strokes of iron. The τέχναις may also allude to a version of the myth not mentioned by any written source but suriving in several pictorial representations, a version where Jason, seemingly with the aid of Athena, was swallowed and then disgorged by the serpent, perhaps killing it from the inside. 22 In any case, the hero then stole Medea (l. 250), and in the next two lines the journey of song continues into the Oceanus (via the River Phasis, mentioned in l. 211, as must be understood), south to the Red Sea (today referred to as the Indian Ocean, part of the Oceanus), 23 and then to Lemnos, where Euphamus became the progenitor of the Battiads. The migration of his descendants to Cyrene, via Sparta and Thera, is told of in the following twelfth strophe. The narrator has thereby manoeuvered, taking a short cut as he promised in l. 248, from Colchis and the jaws of the serpent in the mythical past to the here and now where Arcesilas is celebrated. Ll see the speaker moving from Colchis via the Oceanus to Lemnos. In later sources, as presumably also in earlier, the Argonauts visit Lemnos on their way to Colchis, 24 but Pindar lets the heroes stop by the island on their homeward journey, thus making an elegant transition to the praise of Arcesilas family and to the encomiastic present. The narrator introduces the mythical narrative by declaring that he will sing not only about Arcesilas but also about the Golden Fleece however, the story about the Golden Fleece turns out to be also about the king. The short road suggests not only the omission of the passages (alluded to earlier in the poem) to and from the Oceanus, but also the transposition of the Argonauts visit on Lemnus and the use of this visit as a bridge to the here and now. This innovation is perhaps indicated by the narrator s description of himself as a leader for many others in poetic skill (l. 248). The narrator in a way plays the role of Medea when he renders her prophecy in ll , and the short road later taken by the narrator reflects the short cut from the Oceanus to the Mediterranean shown to the Argonauts by Medea (l. 27). Mythical action and poetic enactment converge as often in the transition from 20 Cf. Braswell (1988) Thus Braswell (1988) This is the version followed by Antimachus (fr. 73 Matthews), Apollonius ( ), and others. 22 See LIMC s. v. Iason nos with commentary; Meyer (1980) 79-98; Simon, Hirmer and Hirmer (1981) ; EGM ii Meyer, H. (1980), Medeia und die Peliaden: Eine attische Novelle und ihre Entstehung (Rome). Simon, E., Hirmer, M. and Hirmer, A. (1981), Die griechischen Vasen 2 (Munich). 23 Thus Gentili et al. (1995) 497, who refer to Hdt and for the name. 24 See Braswell (1988)

7 mythical narrative and the world beyond that of mortals in this case the Oceanus to the here and now. The Argonauts short road leads to Lake Tritonis, that of the narrator to nearby Cyrene. The reference to the short road is perhaps ironic: at Odyssey the Argonauts are said to return from Aeëtes through the Clashing Rocks. 25 Sophocles (Scythians TrGF 4 547) and Euripides (Medea 434-5) let the Argonauts travel to and from Colchis along the same route. Sailing back through the Dardanelles would be shorter and less strenuous than the itinerary taken in the Hesiodic Catalogue as well as in Pythian 4, and no reason is given in the latter poem for not doing that (on the contrary, the rocks are in ll said to have been pacified when the Argonauts passed through them on the way to Colchis). Linking the myth of the Argonauts more closely to Cyrene is obviously the poet s reason for taking the route through Libya. Like the Argonauts short cut around half the world, the narrator s to the here and now is not necessarily short, as it continues subsequent to the journey described above from Colchis to Lemnos from the latter island to Sparta (l. 257), Thera (l. 258), and only thence to Libya (l. 259), a journey taking many generations. In the following, 12th antistrophe the Battiads are then praised as devising just counsel (l. 262: ὀρθόβουλον μῆτιν ἐφευρομένοις), and the narrator therefore it is implied asks Arcesilas to know the wisdom or skill of Oedipus (l. 263: γνῶθι νῦν τὰν Οἰδιπόδα σοφίαν), by which is probably meant to become acquainted with the kind of wisdom characteristic of Oedipus, 26 who solved the Sphinx riddle. 27 If this is the correct interpretation, the following parable is a riddle posed to Arcesilas: 28 εἰ γάρ τις ὄζους ὀξυτόμῳ πελέκει ἐξερείψειεν μεγάλας δρυός, αἰσχύνοι δέ οἱ θαητὸν εἶδος, καὶ φθινόκαρπος ἐοῖσα διδοῖ ψᾶφον περ αὐτᾶς, εἴ ποτε χειμέριον πῦρ ἐξίκηται λοίσθιον, ἢ σὺν ὀρθαῖς κιόνεσσιν δεσποσύναισιν ἐρειδομένα μόχθον ἄλλοις ἀμφέπει δύστανον ἐν τείχεσιν, ἑὸν ἐρημώσαισα χῶρον. 25 The identification of the Symplegades with the entrance to the Black Sea evident in Pindar and all later sources was not yet made by Homer (or the epic source on which he seems to have based himself): see West (2005) Braswell (1988) 362; Hummel (1993) Cf. sch. 467; Burton (1962) 168-9: Braswell (1988) Alternatively, the wisdom of Oedipus might refer to an otherwise unknown parable, attributed to the legendary Theban king, which Pindar goes on to cite: Gildersleeve (1880) 301; Gentili et al. (1995) 501. Check Carey in Maia

8 < > (Pythian ) ( if someone with a sharp-bladed axe should strip the boughs from the great oak tree and ruin its splendid appearance, although it cannot bear foliage, it gives an account of itself, if ever it comes at last to a winter s fire, or if, supported by upright columns belonging to a master, it performs a wretched labor within alien walls, having left its own place desolate. (Translation of Race)) The meaning of the parable is partly obscure, but as several scholars have argued, Damophilus, the exiled Cyrenaean whose plea follows in the last triad, seems to be likened to an oak tree which has left its own place desolate. 29 Damophilus and the oak tree resemble each other not just in having abandoned their own land. In l. 265 the expression διδοῖ ψᾶφον περ αὐτᾶς, by comparison with Aeschines 1. 77, seems to mean that [t]he tree submits itself to a vote in the sense that it gives an account of itself, i. e. of its positive qualities 30 Damophilus resembles the oak tree in that he too through the poem s last epode pleads his case. However, the parable also seems to be a further allusion to the ship Argo. According to a tradition attested by Aeschylus (TrGF 3 20), by Pherecydes (EGM fr. 111a), and by many later authors, the Argo had the power of speech and prophecy because of a beam joined into its hull. 31 That this beam was of Dodonian oak is first mentioned in Apollonius Argonautica, but is probably implied also by Aeschylus and Pherecydes. 32 The talking oak trees of Dodona, expressing the will of Zeus, are described in the Odyssey and many later sources. 33 The speaking beam is in the version of Apollonius Rhodius ( , ; cf. Apollodorus ) fitted into the ship by Athena, in that of Valerius Flaccus (1. 305) by Hera. The oak in the legend of the Argo, like that in Pindar s parable, is removed from its own land, and while the former is joined into the hull of the ship, the latter is joined into a city wall (l. 268; compare the analogy of ship and city in the following epode). 34 The Dodonian oak also, like the one described in the parable, has the ability to give an account of itself. The strokes of iron 29 Thus schol. 368a; Burton (1962) 169; Silk (1974) 144-5; Braswell (1988) 361. Gentili et al. (1988) 502 think the oak represents the city of Cyrene. 30 Braswell (1988) 365. Cf. Gildersleeve (1880) 300; Burton (1962) 169; Gentili et al. (1995) Cf. Jessen in RE ii s. v. Argo (1) ; Vian in Vian and Delage (1976) i 74 n. 4. Vian, F. and E. Delage ( ) (transl.), Apollonius de Rhodes: Argonautiques, i-iii (Paris). 32 Cf. Ap. Rh ; Wilamowitz (1962) ii 178; Parke (1967) 13; Dräger (1993) Wilamowitz-Moellendorff, U. von (1962), Hellenistische Dichtung in der Zeit des Kallimachos 2 (2 original volumes in 1) (Berlin). Dräger, P. (1993), Argo pasimelousa (Stuttgart). Parke, H. W. (1967), The Oracles of Zeus (Oxford). 33 Hom. Od ; Hes. fr , fr. 319; Aesch. PV 832; cf. Parke (1967) 12-33; Graf in The New Pauly iv 606-7, s. v. Dodona. 34 Cf. Braswell (1988) 368: ἄλλοις ἐν τείχεσιν: within other city-walls, i. e. city walls different from his own city walls.

9 (πλαγαὶ σιδάρου), mentioned in ll as an allusion to the building of the Argo, are echoed in the description of the oak tree being stripped of its branches by a sharp-cutting axe in ll The parable thus, by likening Damophilus to the oak tree, links him with the myth of Argo and the Dodonian oak. As proposed above, the ship Argo functions as a metaphor for the poem. Developing this metaphor, Pindar may thus suggest that, just as the Argo had a speaking beam, Demophilus is fitted into the song through which he pleads his case. The Argo s arrival in Libya where it is carried as an ἐννάλιον δόρυ ( a beam of the sea, l. 27, compare l. 38; δόρυ is a common pars pro toto for ship 35 but here perhaps suggests the speaking beam) reflects the return that Demophilus hopes for. The confluence of the mythical and the poetic journey extends into the penultimate epode, which praises Arcesilas, but also alludes to recent political unrest at Cyrene: 36 ῥᾴδιον μὲν γὰρ πόλιν σεῖσαι καὶ ἀφαυροτέροις ἀλλ ἐπὶ χώρας αὖτις ἕσσαι δυσπαλὲς δὴ γίνεται, ἐξαπίνας εἰ μὴ θεὸς ἁγεμόνεσσι κυβερνατὴρ γένηται. (Pythian ) [For easily can even weaklings shake a city; but to set it back in place again is a difficult struggle indeed, unless suddenly a god becomes a helmsman for the leaders. (Translation of Race)] The reference to the divine helmsman invokes the common image of the ship of state, and as Braswell suggests, comparing with Sophocles Antigone 162-3, it is possible that the preceding descriptions of the city being shaken and set back in place, while suggesting a building, could also have been applied to a ship (in which case πόλιν σεῖσαι would suggest rock the boat, and χώρας αὖτις ἕσσαι put on an even keel ). 37 The mention at the start of this epode (l. 270) of Apollo, to whom this song in l. 3 is presented as a hymn, makes it clear that he is the king s protective deity, and l. 274 then suggests the hope that he might act as a helmsman for Cyrene. The Muse, meanwhile, accompanies the narrator on his poetic sea voyage, and thus might be thought to act as his divine helmsman, although the notion is not made explicit in this poem, as it is in Bacchylides At the beginning of Pythian 4 the Muse is asked, moreover, not only to increase the wind of songs, and thereby to commence the poetic journey, but also to παρ στᾶμεν (ll. 1-2) which might mean aid as well as stand next to 35 Cf. Braswell (1988) Cf. Braswell (1988) Braswell (1988) 375. Cf. Gildersleeve (1888) 302; Gentili et al. (1995) 504.

10 (see discussion above) Arcesilas, thus also in a sense to serve as the king s helmsman. Finally, in the context of Argonautic myth, the reference to a god becoming helmsman suggests the tradition, alluded to at the Odyssey , that Hera conveyed the Argo past the Symplegades (although in Pythian 4 it is left unsaid how the Argonauts got through the Clashing Rocks). The poem s last triad opens with an allusion to Homer: <====> τῶν δ Ὁμήρου καὶ τόδε συνθέμενος ῥῆμα πόρσυν ἄγγελον ἐσλὸν ἔφα τιμὰν μεγίσταν πράγματι παντὶ φέρειν αὔξεται καὶ Μοῖσα δι ἀγγελίας ὀρθᾶς. (Pythian ) (And among the sayings of Homer, take this one to heart and heed it: he said that a good messenger brings the greatest honor to every affair. The Muse, too, is strengthened through true reporting. (Translation of Race, modified)) As the scholion 493 suggests, ll must refer to Iliad : 38 ἐσθλὸν καὶ τὸ τέτυκται ὅτ ἄγγελος αἴσιμα εἰδῇ. ( and it is good when a messenger knows what is right.) Poseidon speaks these words to Iris. She has come to deliver a message from Zeus, commanding the sea god to withdraw from the battle. At Pythian the good messenger perhaps suggests Pindar 39 but also in a context where she is introduced in the next line, and where an allusion is made to another goddess acting as a messenger the Muse. αὔξεται καὶ Μοῖσα δι ἀγγελίας ὀρθᾶς (l. 279) seems to mean that the Muse, too, and not just the affair on which she bestows honour by acting as a messenger, is strengthened through true reporting. Braswell suggests that in αὔξεται the literal sense is very much present: the Muse is not just metaphorically exalted, but literally increased in power. 40 He further refers to Theogony 28-9, which describes how the Muse does not necessarily speak the truth; Pindar suggests the idea that the goddess power, by which must here be understood her power of 38 Cf. Burton (1962) 170-1; Braswell (1988) 378; Gentili et al. (1995) That Pindar is the good messenger is assumed by the scholia 493; Burton (1962) 171; Braswell (1988) 379; Gentili et al. (1995) Braswell (1988) 379.

11 persuasion, grows if she does speak the truth. The reference to a messenger at the beginning of this final triad, devoted to praise of Damophilus and the conveyance (in the epode) of his plea, suggests that it is a message delivered to Arcesilas. In the following antistrophe, a description of Demophilus may reflect the narrator: οὐδὲ μακύνων τέλος οὐδέν. ὁ γὰρ καιρὸς πρὸς ἀνθρώπων βραχὺ μέτρον ἔχει. εὖ νιν ἔγνωκεν θεράπων δέ οἱ, οὐ δράστας ὀπαδεῖ. (Pythian ) ( nor delaying any accomplishment, since opportunity in men s affairs has a brief span. He has come to know it well; he serves it as an attendant, not a hireling. (Translation of Race)) Braswell suggests that τέλος here indicates the accomplishment of an action, 41 and this action, which Damophilus does not hesitate to perform, is asking the king to call him back to Cyrene. Braswell further comments that the implication of l. 286 is that Demophilus, as the narrator goes on to say (287), has recognized (εὖ νιν ἔγνωκεν) that it is a favourable moment to seek reconciliation with the king and has accordingly taken the necessary steps. 42 However, while describing Damophilus, οὐδὲ μακύνων τέλος οὐδέν reflects also the narrator, who is about to end the song τέλος can mean completion and simultaneously, in the concluding epode, put forward Damophilus plea, thereby not delaying the accomplishment of asking the king to recall the exiled Cyrenaean. In the gnomic statement of l. 286 καιρός, a difficult word which here may refer to something like the opportune moment, suggests the limited time during which the king may be willing to allow Damophilus to return to Cyrene. However, as Pfeijffer notes, in references to the poetic enactment, especially in so-called break off passages, καιρός describes what is expedient from the poet s point of view, the criterion being effectiveness in the light of the encomiastic aims of his odes. 43 Pythian indicates that the song itself is about to be broken off as soon as Damophilus plea, the message of the Muse, has been delivered. In the following lines the suffering exile, Damophilus, is likened to Atlas: 41 Braswell (1988) Braswell (1988) Pfeijffer (1999b) pocket ed. 390 ad P He cites O ; P , 9. 78, 10. 4; N On καιρός in Pindar, cf. Pfeijffer (1999b) with ref. on p. 392.

12 φαντὶ δ ἔμμεν τοῦτ ἀνιαρότατον, καλὰ γινώσκοντ ἀνάγκᾳ ἐκτὸς ἔχειν πόδα. καὶ μὰν κεῖνος Ἄτλας οὐρανῷ προσπαλαίει νῦν γε πατρῴας ἀπὸ γᾶς ἀπό τε κτεάνων λῦσε δὲ Ζεὺς ἄφθιτος Τιτᾶνας. ἐν δὲ χρόνῳ μεταβολαὶ λήξαντος οὔρου < > ἱστίων. (They say that the most distressing thing is to know the good, but to be forced to stay away. Yes, that Atlas is wrestling even now with the sky away from his homeland and his possessions; yet immortal Zeus released the Titans. In the course of time sails are changed when the wind dies down. (Translation of Race.)) As Gildersleeve and others have pointed out, the comparison of Damophilus to Atlas echoes the parable in the preceding triad of the oak, which supports the wall of a foreign city. 44 The likening of Damophilus to Atlas is followed by an implicit likening of Arcesilas to Zeus. The latter comparison seems to involve exceptionally high praise. Not counting the cases involving Heracles a man when he performed his exploits and only subsequently a god (see next chapter) the only other epinician honorand apart from Arcesilas to be compared to a god is another king, Hieron, whose rule also seems to be presented as analogous to that of Zeus in Pythian In the gnomic statement at the transition to the closing epode (ll ) what is implied by μεταβολαὶ ἱστίων ( change of the sails ) depends on the meaning of οὔρου. οὖρος usually means favourable breeze, but can also just mean wind, or even rough breeze, storm. 46 The change of the sails referred to here could imply if the wind that now drops has been strong enough to necessitate furling the sails and letting the ship be driven off course both that the sails are hoisted and that the course is set for the ship s destination. Alternatively, if the wind has not been strong enough for the ship to be blown off course, it would be enough to hoist the sails further. Independent of its context, then, the gnomic statement of ll is ambiguous. When considered in relation to the context, at least three different are possible. Gnomic statements forming part of break-offs are often applicable either to the honorand or to the narrator, but in this special case where the 44 Gildersleeve (1880) 303; Braswell (1988) 367, Cf. Race (1997) i See LSJ s. v.; Braswell (1988) 392; Gentili et al. (1995) 509.

13 statement introduces the plea of Damophilus, it may also be related to the latter s situation. Ll can thus firstly be taken to express the hope that Damophilus may now finally set course for Cyrene, after being driven by a storm in a different direction than toward the home he hopes as the following lines make clear to return to. On this interpretation, the methapor of turbulent sea for civil unrest seems to be picked up from ll Secondly, the gnome in ll might be addressed to Arcesilas: hoisting the sails is a metaphor for generosity found towards the end of other odes (Pythian and Isthmian (both passages refer to the generosity of the honorand); Nemean (referring to the generosity of the narrator in praising)), 47 and in the present context it may be understood as a plea that the king will show Damophilus the favour of allowing him to return now that the storm threatening Cyrene has abated the image of the ship of state from l. 274 is thus resumed. Thirdly, ll may apply to the poetic enactment: now that the οὖρος of songs, requested of the Muse at the beginning of the poem (ll. 1-3), dies down, the narrator must hoist his sails further to reach his destination. It may be relevant that Atlas, referred to in the lines leading up to this gnomic statement, according to Hesiod (Theogony 517-9, ) was located at the western edge of the the earth. 48 According to this tradition Atlas must be thought to stand by the Oceanus, beyond the Pillars of Heracles (see next chapter) and the world of mortals. This dangerous and distant location, we could understand, is where the narrator finds himself when the storm of song dies down and allows him to set sail for his destination. The storm has taken the narrator beyond the world accessible to mortals also in the sense that his implicit comparison of Arcesilas to Zeus the narrator may go beyond what can be said without provoking mortals and immortals. Again, it may be suggested that the narrator risks going too far in his plea, provoking Arcesilas in the same way that the likening of the latter to Zeus may provoke the gods. What is the narrator s destination? It is both Cyrene, which he refers to in the following, concluding epode as he puts forward Damophilus plea to be allowed to return, and it is also Thebes, the home of Pindar, which the narrator arrives at in the final line of the ode: ἀλλ εὔχεται οὐλομέναν νοῦσον διαντλήσαις ποτέ οἶκον ἰδεῖν, ἐπ Ἀπόλλωνός τε κράνᾳ συμποσίας ἐφέπων θυμὸν ἐκδόσθαι πρὸς ἥβαν πολλάκις, ἔν τε σοφοῖς δαιδαλέαν φόρμιγγα βαστάζων πολί- 47 Cf., in general, Pfeijffer (1999) (in pocket ed., that is on N ). 48 Cf. West (1966) 311, who discusses different locations given for Atlas.

14 ταις ἡσυχίᾳ θιγέμεν, μήτ ὦν τινι πῆμα πορών, ἀπαθὴς δ αὐτὸς πρὸς ἀστῶν καί κε μυθήσαιθ, ὁποίαν, Ἀρκεσίλα, εὗρε παγὰν ἀμβροσίων ἐπέων, πρόσφατον Θήβᾳ ξενωθείς. (But he prays that, having bailed out the bilge water of his wretched affliction, he may some day see his home; that he may join the symposia at Apollo s fountain, often give his heart over to youthful enjoyment, and, taking up the ornate lyre among his cultured citizens, may attain peace, neither doing harm to anyone, nor suffering it from his townsmen. And he would tell, Arkesilas, what a spring of ambrosial verses he hound, when he was recently a guest at Thebes. (Translation of Race, modified)) Damophilus request is presented as a prayer (l. 293: εὔχεται, he prays ), and the comparison of Arcesilas to Zeus is thus again suggested. 49 In a further development of the metaphor of the sea journey the image is suggested of Damophilus having to empty his ship of bilge water after the storm, before he can return home. 50 With the enactment in this final epode of Damophilus plea, the poetic messenger referred to at the beginning of the triad has arrived. As suggested above, the narrator seems to have been driven by the storm of song to the location of Atlas, and thus into the Oceanus, when a drop in the wind allows him to set sail for Cyrene. The Argonauts short cut, above presented as analogous to the poetic enactment, across Libya to Lake Tritonis, is similarly a journey from Oceanus to the area of Cyrene. The Argonauts reach Lake Tritonis on the thirteenh day after leaving the Oceanus (ll. 24-6), while the narrator arrives in Cyrene in the thirteenth triad. The bilge water, which it would be lethal to drink, suggested at the beginning of the epode, is contrasted to the symposia at the Spring of Apollo in Cyrene, and, at the end of the ode, to the Theban spring of ambrosial words a metaphor for the poem itself, which provides a form of immortality. This passage to life-giving water might reflect that of the Argonauts through the desert to Lake Tritonis (their desperate thirst is described by Apollonius ff.). Finally, the Argo s journey from Greece to Libya emulates that of the poem and perhaps also of the poet from Thebes to Cyrene. 49 Cf. Braswell (1988) 392 and schol Cf. Gentili et al. (1995) 509 on διαντλήσαις; Braswell (1988) 303 on νοῦσον.

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014 LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV 18 February 2014 Slowly/quietly Clear/clearly Clean Quickly/quick/fast Hurry (in a hurry) Driver Attention/caution/notice/care Dance Σιγά Καθαρά Καθαρός/η/ο

Διαβάστε περισσότερα

Concrete Mathematics Exercises from 30 September 2016

Concrete Mathematics Exercises from 30 September 2016 Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)

Διαβάστε περισσότερα

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΕΙΡΑΙΑ ΤΜΗΜΑ ΝΑΥΤΙΛΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ ΝΑΥΤΙΛΙΑ ΝΟΜΙΚΟ ΚΑΙ ΘΕΣΜΙΚΟ ΦΟΡΟΛΟΓΙΚΟ ΠΛΑΙΣΙΟ ΚΤΗΣΗΣ ΚΑΙ ΕΚΜΕΤΑΛΛΕΥΣΗΣ ΠΛΟΙΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που υποβλήθηκε στο

Διαβάστε περισσότερα

C.S. 430 Assignment 6, Sample Solutions

C.S. 430 Assignment 6, Sample Solutions C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * *

Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * Chapter 2 * * * * * * * Introduction to Verbs * * * * * * * In the first chapter, we practiced the skill of reading Greek words. Now we want to try to understand some parts of what we read. There are a

Διαβάστε περισσότερα

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple

7 Present PERFECT Simple. 8 Present PERFECT Continuous. 9 Past PERFECT Simple. 10 Past PERFECT Continuous. 11 Future PERFECT Simple A/ Ονόματα και ένα παράδειγμα 1 Present Simple 7 Present PERFECT Simple 2 Present Continuous 8 Present PERFECT Continuous 3 Past Simple (+ used to) 9 Past PERFECT Simple she eats she is eating she ate

Διαβάστε περισσότερα

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού)

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Προσδοκώμενα αποτελέσματα Περιεχόμενο Ενδεικτικές δραστηριότητες

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

Finite Field Problems: Solutions

Finite Field Problems: Solutions Finite Field Problems: Solutions 1. Let f = x 2 +1 Z 11 [x] and let F = Z 11 [x]/(f), a field. Let Solution: F =11 2 = 121, so F = 121 1 = 120. The possible orders are the divisors of 120. Solution: The

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

Every set of first-order formulas is equivalent to an independent set

Every set of first-order formulas is equivalent to an independent set Every set of first-order formulas is equivalent to an independent set May 6, 2008 Abstract A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent

Διαβάστε περισσότερα

Right Rear Door. Let's now finish the door hinge saga with the right rear door

Right Rear Door. Let's now finish the door hinge saga with the right rear door Right Rear Door Let's now finish the door hinge saga with the right rear door You may have been already guessed my steps, so there is not much to describe in detail. Old upper one file:///c /Documents

Διαβάστε περισσότερα

Συντακτικές λειτουργίες

Συντακτικές λειτουργίες 2 Συντακτικές λειτουργίες (Syntactic functions) A. Πτώσεις και συντακτικές λειτουργίες (Cases and syntactic functions) The subject can be identified by asking ποιος (who) or τι (what) the sentence is about.

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 11: The Unreal Past Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

Διαβάστε περισσότερα

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014

LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV. 4 February 2014 LESSON 12 (ΜΑΘΗΜΑ ΔΩΔΕΚΑ) REF : 202/055/32-ADV 4 February 2014 Somewhere κάπου (kapoo) Nowhere πουθενά (poothena) Elsewhere αλλού (aloo) Drawer το συρτάρι (sirtari) Page η σελίδα (selida) News τα νέα (nea)

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951)

Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951) 1 Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951) Αναγνώσματα από το βιβλίο Η Απόλαυση της Μουσικής (Machlis, Forney), για τους μαθητές που θα μελετήσουν το έργο: «Ο Σαίνμπεργκ

Διαβάστε περισσότερα

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

Διαβάστε περισσότερα

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live.

Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live. Topic 1: Describe yourself Write your name, your nationality, your hobby, your pet. Write where you live. Χρησιμοποίησε το and. WRITE your paragraph in 40-60 words... 1 Topic 2: Describe your room Χρησιμοποίησε

Διαβάστε περισσότερα

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015

Adjectives. Describing the Qualities of Things. A lesson for the Paideia web-app Ian W. Scott, 2015 Adjectives Describing the Qualities of Things A lesson for the Paideia web-app Ian W. Scott, 2015 Getting Started with Adjectives It's hard to say much using only nouns and pronouns Simon is a father.

Διαβάστε περισσότερα

2007 Classical Greek. Intermediate 2 Translation. Finalised Marking Instructions

2007 Classical Greek. Intermediate 2 Translation. Finalised Marking Instructions 2007 Classical Greek Intermediate 2 Translation Finalised Marking Instructions Scottish Qualifications Authority 2007 The information in this publication may be reproduced to support SQA qualifications

Διαβάστε περισσότερα

14 Lesson 2: The Omega Verb - Present Tense

14 Lesson 2: The Omega Verb - Present Tense Lesson 2: The Omega Verb - Present Tense Day one I. Word Study and Grammar 1. Most Greek verbs end in in the first person singular. 2. The present tense is formed by adding endings to the present stem.

Διαβάστε περισσότερα

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι

department listing department name αχχουντσ ϕανε βαλικτ δδσϕηασδδη σδηφγ ασκϕηλκ τεχηνιχαλ αλαν ϕουν διξ τεχηνιχαλ ϕοην µαριανι She selects the option. Jenny starts with the al listing. This has employees listed within She drills down through the employee. The inferred ER sttricture relates this to the redcords in the databasee

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ

Διαβάστε περισσότερα

Chapter 29. Adjectival Participle

Chapter 29. Adjectival Participle Chapter 29 Adjectival Participle Overview (29.3-5) Definition: Verbal adjective Function: they may function adverbially or adjectivally Forms: No new forms because adverbial and adjectival participles

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?

ANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =? Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least

Διαβάστε περισσότερα

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013

LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013 LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV 10 December 2013 I get up/i stand up I wash myself I shave myself I comb myself I dress myself Once (one time) Twice (two times) Three times Salary/wage/pay Alone/only

Διαβάστε περισσότερα

Συστήματα Διαχείρισης Βάσεων Δεδομένων

Συστήματα Διαχείρισης Βάσεων Δεδομένων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Συστήματα Διαχείρισης Βάσεων Δεδομένων Φροντιστήριο 9: Transactions - part 1 Δημήτρης Πλεξουσάκης Τμήμα Επιστήμης Υπολογιστών Tutorial on Undo, Redo and Undo/Redo

Διαβάστε περισσότερα

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ

ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ ΣΕ ΕΙΔΙΚΑ ΘΕΜΑΤΑ ΔΙΕΘΝΩΝ ΣΧΕΣΕΩΝ & ΟΙΚΟΝΟΜΙΑΣ Ενότητα 1β: Principles of PS Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης

Διαβάστε περισσότερα

FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17

FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17 FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17 Name: Surname: Date: Class: 1. Write these words in the correct order. /Γράψε αυτέσ τισ λέξεισ ςτη ςωςτή ςειρά. 1) playing / his / not /

Διαβάστε περισσότερα

Code Breaker. TEACHER s NOTES

Code Breaker. TEACHER s NOTES TEACHER s NOTES Time: 50 minutes Learning Outcomes: To relate the genetic code to the assembly of proteins To summarize factors that lead to different types of mutations To distinguish among positive,

Διαβάστε περισσότερα

TMA4115 Matematikk 3

TMA4115 Matematikk 3 TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ

Διαβάστε περισσότερα

Assalamu `alaikum wr. wb.

Assalamu `alaikum wr. wb. LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump

Διαβάστε περισσότερα

Example Sheet 3 Solutions

Example Sheet 3 Solutions Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note

Διαβάστε περισσότερα

The Simply Typed Lambda Calculus

The Simply Typed Lambda Calculus Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

Example of the Baum-Welch Algorithm

Example of the Baum-Welch Algorithm Example of the Baum-Welch Algorithm Larry Moss Q520, Spring 2008 1 Our corpus c We start with a very simple corpus. We take the set Y of unanalyzed words to be {ABBA, BAB}, and c to be given by c(abba)

Διαβάστε περισσότερα

ICTR 2017 Congress evaluation A. General assessment

ICTR 2017 Congress evaluation A. General assessment ICTR 2017 Congress evaluation A. General assessment -1- B. Content - 2 - - 3 - - 4 - - 5 - C. Speakers/ Presentations/ Sessions - 6 - - 7 - D. Posters/ Poster sessions E. Organisation and coordination

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

Αναερόβια Φυσική Κατάσταση

Αναερόβια Φυσική Κατάσταση Αναερόβια Φυσική Κατάσταση Γιάννης Κουτεντάκης, BSc, MA. PhD Αναπληρωτής Καθηγητής ΤΕΦΑΑ, Πανεπιστήµιο Θεσσαλίας Περιεχόµενο Μαθήµατος Ορισµός της αναερόβιας φυσικής κατάστασης Σχέσης µε µηχανισµούς παραγωγής

Διαβάστε περισσότερα

ΕΡΙΤΟΡΕΣ ΚΑΙ ΑΝΘΩΡΟΙ ΚΛΕΙΔΙΑ ΑΝΑΘΕΣΘ ΑΓΩΝΑ ΓΑΦΕΙΟ ΑΓΩΝΩΝ ΟΓΑΝΩΤΙΚΘ ΕΡΙΤΟΡΘ. ζεκηλαρηο 1 ΡΑΓΚΟΣΜΙΑ ΟΜΟΣΡΟΝΔΙΑ (ISAF) ΕΛΛΘΝΙΚΘ ΟΜΟΣΡΟΝΔΙΑ (Ε.Ι.Ο.

ΕΡΙΤΟΡΕΣ ΚΑΙ ΑΝΘΩΡΟΙ ΚΛΕΙΔΙΑ ΑΝΑΘΕΣΘ ΑΓΩΝΑ ΓΑΦΕΙΟ ΑΓΩΝΩΝ ΟΓΑΝΩΤΙΚΘ ΕΡΙΤΟΡΘ. ζεκηλαρηο 1 ΡΑΓΚΟΣΜΙΑ ΟΜΟΣΡΟΝΔΙΑ (ISAF) ΕΛΛΘΝΙΚΘ ΟΜΟΣΡΟΝΔΙΑ (Ε.Ι.Ο. ΑΝΑΘΕΣΘ ΑΓΩΝΑ ΕΡΙΤΟΡΕΣ ΚΑΙ ΑΝΘΩΡΟΙ ΚΛΕΙΔΙΑ ΡΑΓΚΟΣΜΙΑ ΟΜΟΣΡΟΝΔΙΑ (ISAF) ΕΛΛΘΝΙΚΘ ΟΜΟΣΡΟΝΔΙΑ (Ε.Ι.Ο.) ΚΛΑΣΘ 6/6/2009 1 ΟΡΓΑΝΩΣΙΚΗ ΕΠΙΣΡΟΠΗ ΓΡΑΦΕΙΟ ΑΓΩΝΩΝ ΕΠΙΣΡΟΠΗ ΑΓΩΝΩΝ ΕΠΙΣΡΟΠΗ ΕΝΣΑΕΩΝ ΕΠΙΣΡΟΠΗ ΚΑΣΑΜΕΣΡΗΕΩΝ

Διαβάστε περισσότερα

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG. 4 March 2014

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG. 4 March 2014 LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG 4 March 2014 Family η οικογένεια a/one(fem.) μία a/one(masc.) ένας father ο πατέρας mother η μητέρα man/male/husband ο άντρας letter το γράμμα brother ο

Διαβάστε περισσότερα

Section 7.6 Double and Half Angle Formulas

Section 7.6 Double and Half Angle Formulas 09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)

Διαβάστε περισσότερα

Policy Coherence. JEL Classification : J12, J13, J21 Key words :

Policy Coherence. JEL Classification : J12, J13, J21 Key words : ** 80%1.89 2005 7 35 Policy Coherence JEL Classification : J12, J13, J21 Key words : ** Family Life and Family Policy in France and Germany: Implications for Japan By Tomoko Hayashi and Rieko Tamefuji

Διαβάστε περισσότερα

Math221: HW# 1 solutions

Math221: HW# 1 solutions Math: HW# solutions Andy Royston October, 5 7.5.7, 3 rd Ed. We have a n = b n = a = fxdx = xdx =, x cos nxdx = x sin nx n sin nxdx n = cos nx n = n n, x sin nxdx = x cos nx n + cos nxdx n cos n = + sin

Διαβάστε περισσότερα

Business English. Ενότητα # 9: Financial Planning. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων

Business English. Ενότητα # 9: Financial Planning. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα Business English Ενότητα # 9: Financial Planning Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων Άδειες Χρήσης Το παρόν εκπαιδευτικό

Διαβάστε περισσότερα

6.1. Dirac Equation. Hamiltonian. Dirac Eq.

6.1. Dirac Equation. Hamiltonian. Dirac Eq. 6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2

Διαβάστε περισσότερα

ΑΓΓΛΙΚΑ ΙΙΙ. Ενότητα 12b: The Little Prince. Ζωή Κανταρίδου Τμήμα Εφαρμοσμένης Πληροφορικής

ΑΓΓΛΙΚΑ ΙΙΙ. Ενότητα 12b: The Little Prince. Ζωή Κανταρίδου Τμήμα Εφαρμοσμένης Πληροφορικής Ενότητα 12b: The Little Prince Τμήμα Εφαρμοσμένης Πληροφορικής Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό, όπως εικόνες, που υπόκειται

Διαβάστε περισσότερα

The challenges of non-stable predicates

The challenges of non-stable predicates The challenges of non-stable predicates Consider a non-stable predicate Φ encoding, say, a safety property. We want to determine whether Φ holds for our program. The challenges of non-stable predicates

Διαβάστε περισσότερα

Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in

Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in : tail in X, head in A nowhere-zero Γ-flow is a Γ-circulation such that

Διαβάστε περισσότερα

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Centre No. Candidate No. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Materials required for examination Nil Paper Reference

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011 Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

Ακαδημαϊκός Λόγος Εισαγωγή

Ακαδημαϊκός Λόγος Εισαγωγή - In this essay/paper/thesis I shall examine/investigate/evaluate/analyze Γενική εισαγωγή για μια εργασία/διατριβή Σε αυτήν την εργασία/διατριβή θα αναλύσω/εξετάσω/διερευνήσω/αξιολογήσω... To answer this

Διαβάστε περισσότερα

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014

LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014 LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26 18 November 2014 But Weekend I love The song I sing I smile I laugh Greek (thing) Greek(people) Greek (man) αλλά (το) Σαββατοκύριακο αγαπώ (το) τραγούδι τραγουδώ

Διαβάστε περισσότερα

Solutions to Exercise Sheet 5

Solutions to Exercise Sheet 5 Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X

Διαβάστε περισσότερα

Srednicki Chapter 55

Srednicki Chapter 55 Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third

Διαβάστε περισσότερα

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013 Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering

Διαβάστε περισσότερα

2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, EVALUATION REPORT

2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, EVALUATION REPORT 2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, 26-6-2016 Can anyone hear me? The participation of juveniles in juvenile justice. EVALUATION REPORT 80 professionals

Διαβάστε περισσότερα

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ting Zhang Stanford May 11, 2001 Stanford, 5/11/2001 1 Outline Ordinal Classification Ordinal Addition Ordinal Multiplication Ordinal

Διαβάστε περισσότερα

Calculating the propagation delay of coaxial cable

Calculating the propagation delay of coaxial cable Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric

Διαβάστε περισσότερα

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α. Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:.

ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α.  Διαβάστε τις ειδήσεις και εν συνεχεία σημειώστε. Οπτική γωνία είδησης 1:. ΦΥΛΛΟ ΕΡΓΑΣΙΑΣ Α 2 ειδήσεις από ελληνικές εφημερίδες: 1. Τα Νέα, 13-4-2010, Σε ανθρώπινο λάθος αποδίδουν τη συντριβή του αεροσκάφους, http://www.tanea.gr/default.asp?pid=2&artid=4569526&ct=2 2. Τα Νέα,

Διαβάστε περισσότερα

On a four-dimensional hyperbolic manifold with finite volume

On a four-dimensional hyperbolic manifold with finite volume BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Numbers 2(72) 3(73), 2013, Pages 80 89 ISSN 1024 7696 On a four-dimensional hyperbolic manifold with finite volume I.S.Gutsul Abstract. In

Διαβάστε περισσότερα

ΙΑΤΡΟΦΙΚΗ ΦΡΟΝΤΙ Α ΓΙΑ ΤΑΞΙ ΙΩΤΕΣ ΣΥΝΤΟΜΗΣ ΚΑΙ ΜΑΚΡΑΣ ΙΑΡΚΕΙΑΣ

ΙΑΤΡΟΦΙΚΗ ΦΡΟΝΤΙ Α ΓΙΑ ΤΑΞΙ ΙΩΤΕΣ ΣΥΝΤΟΜΗΣ ΚΑΙ ΜΑΚΡΑΣ ΙΑΡΚΕΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΜΗΜΑ ΙΑΤΡΟΦΗΣ ΚΑΙ ΙΑΙΤΟΛΟΓΙΑΣ, ΤΕΙ ΚΡΗΤΗΣ ΙΑΤΡΟΦΙΚΗ ΦΡΟΝΤΙ Α ΓΙΑ ΤΑΞΙ ΙΩΤΕΣ ΣΥΝΤΟΜΗΣ ΚΑΙ ΜΑΚΡΑΣ ΙΑΡΚΕΙΑΣ ΕΠΙΜΕΛΕΙΑ: ΑΛΕΞΙΑ ΤΣΕΡΛΙΓΚΑ ΥΠΕΥΘΥΝΟΣ ΚΑΘΗΓΗΤΗΣ: Γ. Α. ΦΡΑΓΚΙΑ ΑΚΗΣ. 2012 σελ.

Διαβάστε περισσότερα

ΑΓΓΛΙΚΑ IV. Ενότητα 6: Analysis of Greece: Your Strategic Partner in Southeast Europe. Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών

ΑΓΓΛΙΚΑ IV. Ενότητα 6: Analysis of Greece: Your Strategic Partner in Southeast Europe. Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών Ενότητα 6: Analysis of Greece: Your Strategic Partner in Southeast Europe Ιφιγένεια Μαχίλη Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό,

Διαβάστε περισσότερα

1999 MODERN GREEK 2 UNIT Z

1999 MODERN GREEK 2 UNIT Z STUDENT NUMBER CENTRE NUMBER HIGHER SCHOOL CERTIFICATE EXAMINATION 1999 MODERN GREEK 2 UNIT Z (55 Marks) Time allowed Two hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Write your Student

Διαβάστε περισσότερα

CRASH COURSE IN PRECALCULUS

CRASH COURSE IN PRECALCULUS CRASH COURSE IN PRECALCULUS Shiah-Sen Wang The graphs are prepared by Chien-Lun Lai Based on : Precalculus: Mathematics for Calculus by J. Stuwart, L. Redin & S. Watson, 6th edition, 01, Brooks/Cole Chapter

Διαβάστε περισσότερα

Ακαδημαϊκός Λόγος Εισαγωγή

Ακαδημαϊκός Λόγος Εισαγωγή - Σε αυτήν την εργασία/διατριβή θα αναλύσω/εξετάσω/διερευνήσω/αξιολογήσω... Γενική εισαγωγή για μια εργασία/διατριβή In this essay/paper/thesis I shall examine/investigate/evaluate/analyze Για να απαντήσουμε

Διαβάστε περισσότερα

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ. Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action

Διαβάστε περισσότερα

1) Formulation of the Problem as a Linear Programming Model

1) Formulation of the Problem as a Linear Programming Model 1) Formulation of the Problem as a Linear Programming Model Let xi = the amount of money invested in each of the potential investments in, where (i=1,2, ) x1 = the amount of money invested in Savings Account

Διαβάστε περισσότερα

ΔΙΑΘΕΜΑΤΙΚΟ ΠΑΡΑΜΥΘΙ ΧΑΜΕΝΟΙ ΗΡΩΕΣ THE LOST HEROES

ΔΙΑΘΕΜΑΤΙΚΟ ΠΑΡΑΜΥΘΙ ΧΑΜΕΝΟΙ ΗΡΩΕΣ THE LOST HEROES ΔΙΑΘΕΜΑΤΙΚΟ ΠΑΡΑΜΥΘΙ ΧΑΜΕΝΟΙ ΗΡΩΕΣ THE LOST HEROES Μια φορά κι έναν καιρό σε τόπους μακρινούς συναντήθηκαν Once upon a time in far away places οι παλιοί φίλοι φίλοι ο Μπόλεκ, ο Λόλεκ, ο Αστερίξ, ο the

Διαβάστε περισσότερα

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

Διαβάστε περισσότερα

ΟΔΗΓΙΕΣ ΕΓΚΑΤΑΣTΑΣΗΣ ΓΙΑ ΠΑΤΩΜΑ WPC INSTALLATION GUIDE FOR WPC DECKING

ΟΔΗΓΙΕΣ ΕΓΚΑΤΑΣTΑΣΗΣ ΓΙΑ ΠΑΤΩΜΑ WPC INSTALLATION GUIDE FOR WPC DECKING 1/12 ΟΔΗΓΙΕΣ ΕΓΚΑΤΑΣTΑΣΗΣ ΓΙΑ ΠΑΤΩΜΑ WPC INSTALLATION GUIDE FOR WPC DECKING Ανοίγουμε τρύπες Ø8 x 80mm στο σημείο κατασκευής, με τρυπάνι. To προτεινόμενο πλάτος και μήκος μεταξύ των 2 οπών να είναι 30-35εκ.,

Διαβάστε περισσότερα

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3) Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 4: English a Language of Economy Το περιεχόμενο του μαθήματος διατίθεται με άδεια

Διαβάστε περισσότερα

Door Hinge replacement (Rear Left Door)

Door Hinge replacement (Rear Left Door) Door Hinge replacement (Rear Left Door) We will continue the previous article by replacing the hinges of the rear left hand side door. I will use again the same procedure and means I employed during the

Διαβάστε περισσότερα

Other Test Constructions: Likelihood Ratio & Bayes Tests

Other Test Constructions: Likelihood Ratio & Bayes Tests Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :

Διαβάστε περισσότερα

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Section 1: Listening and Responding/ Aκουστική εξέταση Στο πρώτο μέρος της

Διαβάστε περισσότερα

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο Δρ. Παναγιώτης Πεντάρης - University of Greenwich - Association for the Study of Death and Society (ASDS) Περιεχόµενα Εννοιολογικές

Διαβάστε περισσότερα

forms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with

forms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with Week 03: C lassification of S econd- Order L inear Equations In last week s lectures we have illustrated how to obtain the general solutions of first order PDEs using the method of characteristics. We

Διαβάστε περισσότερα

Δίκτυα Δακτυλίου. Token Ring - Polling

Δίκτυα Δακτυλίου. Token Ring - Polling Δίκτυα Δακτυλίου Token Ring - Polling Όλοι οι κόμβοι είναι τοποθετημένοι σε ένα δακτύλιο. Εκπέμπει μόνο ο κόμβος ο οποίος έχει τη σκυτάλη (token). The token consists of a number of octets in a specific

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: Understanding and Written Response

Advanced Subsidiary Unit 1: Understanding and Written Response Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes

Διαβάστε περισσότερα

Στην παθητική φωνή η έμφαση δίνεται στην πράξη όχι στο ποιος την διέπραξε.

Στην παθητική φωνή η έμφαση δίνεται στην πράξη όχι στο ποιος την διέπραξε. THE PASSIVE VOICE ΠΑΘΗΤΙΚΗ ΦΩΝΗ Στην παθητική φωνή η έμφαση δίνεται στην πράξη όχι στο ποιος την διέπραξε. Είναι επίσης πιθανό είτε κάποιος να αγνοεί το άτομο που έκανε κάτι (το ποιητικό αίτιο agent) είτε

Διαβάστε περισσότερα

Démographie spatiale/spatial Demography

Démographie spatiale/spatial Demography ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΙΑΣ Démographie spatiale/spatial Demography Session 1: Introduction to spatial demography Basic concepts Michail Agorastakis Department of Planning & Regional Development Άδειες Χρήσης

Διαβάστε περισσότερα