JOSHUA D. SOSIN NOTES ON INSCRIPTIONS. aus: Zeitschrift für Papyrologie und Epigraphik 186 (2013) Dr. Rudolf Habelt GmbH, Bonn

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "JOSHUA D. SOSIN NOTES ON INSCRIPTIONS. aus: Zeitschrift für Papyrologie und Epigraphik 186 (2013) 163 170. Dr. Rudolf Habelt GmbH, Bonn"

Transcript

1 JOSHUA D. SOSIN NOTES ON INSCRIPTIONS aus: Zeitschrift für Papyrologie und Epigraphik 186 (2013) Dr. Rudolf Habelt GmbH, Bonn

2

3 163 NOTES ON INSCRIPTIONS Honors at Didyma I.Didyma 176 records honors for a victor, name now lost, in the boy s pankration at the Didymeia: 1.. Kοΐ ν [του.... ] ου Αὐρʹ Πρ.... ν ικήσαντα ιδ[ύ]- 4 μεια παίδω[ν] παγκράτιο[ν] προφητεύον - τος Μάρκου 8 Ἀντωνίου Πολέμωνος. These honorary inscriptions are formulaic: ἡ βουλὴ καὶ ὁ δῆμος ἐτίμησεν, name of honorand in the accusative, patronym in the genitive, νικήσαντα τὰ Μεγάλα ιδύμεια, event in the accusative. What appears before νικήσαντα is either the honorand in the accusative or his patronym in the genitive, occasionally a papponym, 2 or in rare instances some other distinction. 3 For the name Πρ - Rehm suggested, quite reasonably, Πρι [μου, Πρε [ίμου, or Πρε [ίσκου. This must be a patronym; were it a papponym we would expect a preceding τοῦ. Reasoning further, we can conclude that Αὐρ cannot be the honorand, since the preceding -ου precludes an accusative Αὐρ(ήλιον). Three genitives in a row, then: -ου Αὐρ(ηλίου) Πρ..ο υ, a good Roman name. The council and people honored Name son of -os Aurelios Pr..os. Thus, the genitive, Kοΐ ν [του, cannot be right; this person must be the victor, the honorand, and in the accusative. And, we do not expect a bare praenomen, Kοΐ ν [τον, here. A problem, then. We also do not expect him to have won the boy s pankration at the Didymeia. Rather, the Great Didymeia. Another problem. While the text has drawn scant scholarly attention since its publication, being entirely absent from the indices of both Bulletin épigraphique and SEG, tourists know it. A visitor to Didyma on 22 August 2010 took an excellent photograph of the stone (along with I.Didyma 178, and 504) and posted it to Flickr. 4 The image is helpful in a number of places. In line 1 the kappa of Kοΐ ν [του can be read only with considerable faith; the omicron is perhaps plausible, but if the trace of a hasta after, and close to, the omicron is an iota, then traces of two descenders following it may be spaced too far apart to be the remains of a nu. Whatever Rehm was able to see, KOIN[ seems a stretch, not impossible but not compelling either; if he saw more than we can, then perhaps something like Kοΐ ν [τιον. The start of line 2 might have held one letter, now missing. At the end of line 2 the pi is plausible enough, but the rho seems to me dubious, and Rehm s four illegible characters are in fact altogether missing. More important, line 3 very clearly does not read NΙΚΗΣΑΝΤΑ Ι, but rather NΙΚΗΣΑΝΤΑ[ ]. It is also clear that the fourth of the extant lines has been omitted altogether; it reads ΜΕΓΑΛΑ Ι [ ]. Perhaps the visual similarity ΜΕΓΑΛΑ and ΜΕΙΑΠΑΙ, the one atop the other, tripped up the editor, or the typesetter. 1 PHI Greek Inscriptions, in line 2, expands to Αὐρ(ηλίου), represents the unconstrued letter fragment after Πρ as simply illegible, and brackets Rehm s four illegible letters at the end of line: Πρ.[...]: oi?ikey=247246&bookid=489&region=8&subregion=29. 2 E.g. I.Didyma : ἐτείμησεν Αὐρ(ήλιον) Ζ ωπυριανὸν ιονυσίου τοῦ Ζωπυριανοῦ νι κήσαντα; or : ἐτί μησεν Αὐρ(ήλιον) Συνέγδη μον βʹ νικήσαντα. 3 E.g. I.Didyma : ἐτείμ[η] σαν Μᾶρκον [Αἴ] λιον Αὐρήλι[ον] όμνον τὸν [χο] ρηγὸν καὶ ἀμ[φι] θαλῆ, νικήσα[ν] τα. 4 G. Dere, Apollon Tapınağı Yazıtlar (Didyma, Temple of Apollon, Inscriptions) Didim, Aydin, Turkey, flickr.com/photos/guraydere/ , accessed 3 December 2012.

4 164 J. D. Sosin Thus, lines 1 5 should read: [..].ο..[...] [.?]ου Αὐρ(ηλίου) Π.[..ου] ν ικήσαντα [τὰ] 4 Μεγάλα ιδ[ύ]- μεια παίδω[ν] παγκράτιο[ν] The identity of our victor in the boy s pankration is lost, but his father may have had a good Roman name and that was something to boast. 5 *** Honors at Olympia IvO 464 records honors awarded to T. Flavius Phylax, son of T. Flavius Alexander, a Thessalian from Hypata and, according to Philostratos, among those better called laughing-stocks than sophists worthy of note. 6 His brother Phoinix, rated little better, deserving neither admiration nor total contempt, rhythmless, and suited to teaching young, ignorant beginners, prominently entombed at Athens though he was. 7 Philostratos does not even mention their father, T. Flavius Alexander, who apparently plied the same trade: the two brothers honored him with a statue at Delphi (now gone), calling him in the inscribed base their father and teacher, and a σύνεδρος of the Thessalians. 8 Whatever the cause of Philostratos disdain, and however clear the prosopography may be, 9 the epigraphic footprint of this little family of sophists is muddy. The composition of the text on their father s Delphic statue base was a mess. CID IV 158 gives: 5 Or, if a space is missing at the start of line two then [.?]ου Αὐρ(ηλίου) Πρ.[..ου] could be [τ]οῦ Αὐρ(ηλίου) Πρ.[..ου] and possibly a papponym. 6 Phil. VS II 604: Ἄγει με ὁ λόγος ἐπ ἄνδρα ἐλλογιμώτατον αμιανὸν τὸν ἐκ τῆς Ἐφέσου, ὅθεν ἐξῃρήσθων Σώτηροί τε καὶ Σῶσοι καὶ Νίκανδροι καὶ Φαῖδροι Κῦροί τε καὶ Φύλακες, ἀθύρματα γὰρ τῶν Ἑλλήνων μᾶλλον οὗτοι προσρηθεῖεν ἂν ἢ σοφισταὶ λόγου ἄξιοι. Ἄθυρμα is an ugly word in Philostratus. The sophist Favorinus kept an ἄθυρμα called Autolekythos, an Indian whose faltering and barbarous tongue was a source of (obviously derisive) enjoyment to him and Herodes: ἦν δὲ οὗτος Ἰνδὸς μὲν καὶ ἱκανῶς μέλας, ἄθυρμα δὲ Ἡρώδου τε καὶ Φαβωρίνου, ξυμπίνοντας γὰρ αὐτοὺς διῆγεν ἐγκαταμιγνὺς Ἰνδικοῖς Ἀττικὰ καὶ πεπλανημένῃ τῇ γλώττῃ βαρβαρίζων (Phil. VS I 490). Perhaps other enjoyments as well; on the sexual connotations of αὐτολήκυθος see A. Steiner, Private and Public: Links Between Symposion and Syssition in Fifth-Century Athens, ClAnt 21 (2002) , ; L. Holford-Strevens, Aulus Gellius: An Antonine Scholar and his Achievement 2 (Oxford 2003) 438; E. K. Borthwick, Autolekythos and Lekythion in Demosthenes and Aristophanes, LCM 18 (1993) 34 37; G. Anderson, ΛΗΚΥΘΙΟΝ and ΑΥΤΟΛΗΚΥΘΟΣ, JHS 101 (1981) The claim at VS II 557, that Herodes Atticus called off mourning for Regilla, whom he was alleged to have murdered, after hearing a joke aimed at himself and involving radishes, lest he become a laughing-stock of decent (σπουδαῖοι) men, is harder to unpack. For possible sexual undertones see S. B. Pomeroy, The Murder of Regilla: A Case of Domestic Violence in Antiquity (Cambridge, MA 2007) 131; but see L. Holford- Strevens, BMCR n. 8, for doubts. 7 Phil. VS II 604: Φοῖνιξ δὲ ὁ Θετταλὸς οὐδὲ θαυμάσαι ἄξιος, οὐδὲ αὖ διαβαλεῖν πάντα. ἦν μὲν γὰρ τῶν Φιλάγρῳ πεφοιτηκότων, γνῶναι δὲ ἀμείνων ἢ ἑρμηνεῦσαι, τάξιν τε γὰρ τὸ νοηθὲν εἶχε καὶ οὐθὲν ἔξω καιροῦ ἐνοεῖτο, ἡ δὲ ἑρμηνεία διεσπάσθαι τε ἐδόκει καὶ ῥυθμοῦ ἀφεστηκέναι. ἐδόκει δὲ ἐπιτηδειότερος γεγονέναι τοῖς ἀρχομένοις τῶν νέων ἢ τοῖς ἕξιν τινὰ ἤδη κεκτημένοις, τὰ γὰρ πράγματα γυμνὰ ἐξέκειτο καὶ οὐ περιήμπισχεν αὐτὰ ἡ λέξις. ἑβδομηκοντούτης δὲ ἀποθανὼν Ἀθήνησιν ἐτάφη οὐκ ἀφανῶς, κεῖται γὰρ πρὸς τοῖς ἐκ τῶν πολέμων ἐν δεξιᾷ τῆς Ἀκαδημίανδε καθόδου. 8 CID IV 158 = FD III = B. Puech, Orateurs et sophistes grecs dans les inscriptions d époque impériale (Paris 2002) no C. P. Jones, Two Friends of Plutarch, BCH 96 (1972) , , well argues that this was not the Epicurean Alexander who was friends with Plutarch; J. Pouilloux, Une famille de sophistes thessaliens à Delphes au II e siè cle ap. J.-C., REG 80 (1967) , and FD III p. 157, that he almost certainly was. B. Puech, Prosopographie des amis de Plutarque, ANRW 33.6 (1992) , , and ead., Orateurs et sophistes no. 3 p. 45, is uncommitted, emphasizing, however, Jones observation (p. 267) that an Epicurean is not likely to have thought much of sophists. S. Follet, Bull.épigr. (1988) 110, has identified the eponymous magistrate of the Thessalian koinon, attested in a manumission from Thessalian Echinos dated to 133/4 ca.150 AD, as T. Flavius Alexander: SEG XXXVI 545. Even if he was as old as 60 when he held this position, and if his magistracy fell at the earliest end of the spectrum, he would have been a full 30 years younger than Plutarch. The later his magistracy and birth, the less likely the relationship with Plutarch. Thus, chronology seems to weigh heavily in favor of Jones

5 Notes on Inscriptions 165 Ἀμφικτυόνων δόγματι Τίτ Φλάβιον Ἀλέ- 4 ξανδρον τὸν σοφιστὴν Φλά Φοῖνιξ καὶ Φύλαξ τὸν πατέρα καὶ διδάσκαλον, 8 σύνεδρον Θεσσαλῶν, Ὑπαταῖον. But this representation does not reflect the full complexity of the text. At 4 6 Homolle had read ϹΟ ΦΙϹΤΗΝΙΦΛΑ ͻ ΦΟΙΝΙ ΚΗ, on which Bourguet clearly improved by suggesting, Les traces que l on voit après la fin de ϹΟΦΙϹΤΗΝ sont celles de deux lettres qui ont été effacées: Τί(τος). Ensuite venait le nom de ΦΛΑΒΙΟϹ écrit en entier, puis à la ligne suivante ΦΥΛΑΞ. Οn a effacé, outre ΤΙ, ΒΙΟϹ de Φλάβιος et ajouté en surcharge Φοῖνιξ καὶ. Le Φ occupe la place de l Ι de ΒΙΟϹ. 10 But Pouilloux observed, and the photographs published by Bousquet and at FD III.4 pl.26a support, On avait effectivement gravé Τι- mais ensuite la pierre n a jamais porté que Φλα; les traces de martelage affectent seulement l emplacement de Τι et l interligne au-dessous de Φλα, and that at 5 6 Φοῖνιξ καὶ was inscribed after the fact, smaller, faster, and squeezed into the margins. 11 FD III.4 plate 26A shows this clearly: To this we may add that the plate also shows quite clearly that in line 3, the ΤΙ of Τίτ(ον) stands out in the left margin, and awkwardly distant from the second Τ; the balance of the text, by contrast, shows for the most part a tidy respect for the left margin. Autopsy might tell for sure, but it appears that the mason inscribed Τ ͻ for Τ(ίτον), and that he, or another correcting hand, subsequently changed this to ΤΙΤ ͻ for Τίτ(ον): But of the hundreds of epigraphic witnesses to an abbreviated instance of the name Τίτος, the overwhelming majority show Τ(ίτος), and while Τί(τος) is not terribly common perhaps a few dozen instances Τίτ(ος) is extremely rare. 12 And so, to inscribe ΤΙΤ ͻ in the first place would have been odd, but to correct argument. The philosophical inclination of Plutarch s friend is perhaps slightly less probative: some Epicureans showed civic and religious engagements beyond what we might have expected: e.g. R. Koch-Piettre, Des Épicuriens entre la vie retirée et les honneurs publics, in V. Dasen and M. Piérart (eds.), Ἰδίᾳ καὶ δημοσίᾳ: les cadres «privés» et «publics» de la religion grecque antique: Actes du IX e colloque du Centre international d étude de la religion grecque antique (CIERGA), tenu à Fribourg du 8 au 10 septembre 2003 (Liège 2005) [= Kernos suppl. 15] ; M. F. Smith, An Epicurean Priest from Apamea in Syria, ZPE 112 (1996) T. Homolle, BCH 21 (1897) (diplomatic only and based on a copy of G. Colin); E. Bourguet, BCH 21 (1897) J. Pouilloux, REG 80 (1967) 380; J. Bousquet, Inscriptions de Delphes, BCH 88 (1964) , fig. 9 p Puech, Orateurs et sophistes 3, prints Τιτ. Φλά. 12 IG Bulg III ; I.Lindos II 465.c.4; G. Cousin and Ch. Diehl, BCH 14 (1890) no. 7; I.Ephesos , ; TAM II 459.7; I.Anazarbos 491.1; IG XIV Rare in the papyri as well: P.Berl.Leihg. I 1.r.4.13, 6.14; P.Col. II 1.r.8.17; P.Mich. XV (although here it must be said that Τί(του) could also be a plausible reading; see image linked from So also in Latin T(itus) is, again by overwhelming margin, the most common abbreviation, as searches for T(it, Ti(t, and Tit( in EDH show (

6 166 J. D. Sosin to such from the most common abbreviation smells of incompetence. Perhaps the intervention is related to the erasure of the same abbreviated praenomen in line 5. Whatever the cause, some confusion clearly arose over a common abbreviation. To surface the compositional peculiarities of this little text we might render: Ἀμφικτυόνων δόγματι Τίτ ͻ Φλάβιον Ἀλέ- 4 ξανδρον τὸν σοφιστὴν Φλά ͻ Φοῖνιξ καὶ Φύλαξ τὸν πατέρα καὶ διδάσκαλον, 8 σύνεδρον Θεσσαλῶν, Ὑπαταῖον. The disarray at lines 5 6 is considerable, the historical circumstances leading to which are agreeable only to speculation. The cause may have been no more sinister than a simple mason s omission (would that he had not abbreviated Φλά in 5; for then we should know). Or mere timing: Puech suggests that the sloppiness of the correction just might indicate that Phoinix s name was inserted after significant delay (i.e. not corrected immediately); that Phylax may have been the elder of the two and the only one of them, at the time of dedication, yet to have studied with their father. 13 To this we may add that Phoinix could, just as easily, have been of age but absent for some other reason. In any case, a later addition would have been an act of historical revision. This was not a private matter. The implied verb, ἐτίμησεν/-σαν is connected in both grammar and formal procedure to δόγματι. The Amphictyons granted the request of either one man or two. If Phoinix was present then both brothers honored their father with an embarrassingly sloppy text. If the Amphictyons approved a request from Phylax alone, as Puech well suggests, then the text as amended is not only sloppy and vain, but also and worse deceiving: it implies participation in a legal act of which Phoinix had no part. In the light of Puech s good and plausible speculation, we might add that in the history of brothers disagreements are known; and that the omission and insertion could be an artifact of rivalry. Phoinix himself was honored by his own students at Delphi, 14 but whether Phylax ever was, or even had students, we do not know; was the lesser brother a joke in Philostratos view especially drawn to the public gesture? In this period at Delphi, Hypataian elites were quite active 15 and honoring intellectuals was very much in fashion, 16 and this too may have affected Phylax s desire to shine the light of honor on father and, in so doing, self. But if Phylax moved first, Phoinix wanted in. The erasure between lines 5 and 6 must be part of the correction that added his name. It has drawn little attention but is interesting, for it suggests two stages of intervention: someone added something between the lines and then someone (else?) erased it. Could it be that Phoinix added (or had added) his name between the lines (there is room enough in the space covered by the erasure); that Phylax then erased it (or had it erased); and that Phoinix then added his name again, in the margin? If so, what he or anyone else meant to accomplish by erasing the praenomen in line 5 and converting a perfectly normal Τ ͻ to an unusual and awkward ΤΙΤ ͻ is anyone s guess. Whatever happened with the praenomina, the little text shows a complicated and multi-stepped mess, an awkwardness both social and epigraphic. 13 Puech, Orateus et sophistes 45 n. 5; see also 384 n Puech, Orateurs et sophistes 204: Τίτον Φλάβιο[ν] Φοί v νικα τὸν [σ]οφισ[τὴν] οἱ μ[α]θηταί. 15 J. Pouilloux, Delphes dans les Éthiopiques d Héliodore: La réalité dans la fiction, JSav (1983) , 273. And beyond Delphi: N. V. Sekunda, The Kylloi and Eubiotoi of Hypata during the Imperial Period, ZPE 118 (1997) ; J. A. O. Larsen, A Thessalian Family under the Principate, CP 48 (1953) C. van Liefferinge, Auditions et confé rences à Delphes, AC 69 (2000)

7 Notes on Inscriptions 167 Moreover, inasmuch as Philostratos notes that Phoinix was a student of Philagros, it is all the more interesting that he does not mention the brothers father at all. Did Philostratos not know him as a sophist? Or did he regard him as so unimportant as to be undeserving even of the scornful mention he offers the man s two sons? Was he so motivated to stress the brothers affiliation with competing minds that to have mentioned the father as their teacher would have run contrary to Philostratos purpose? 17 Philostratos silence invites speculation whether Flavius Alexander was a sophist and διδάσκαλος only inasmuch as his progeny honored him so; perhaps Phylax honored his father not as a sophist, but as his sophist, just as he was his father and teacher, a nod to the tradition by which one s teacher was διδάσκαλος καὶ πατήρ, 18 and a playful boast that his natural father was his true doctor-father. If so, then as slippery as the word sophist was, 19 T. Flavius Alexander may have been such in his son s estimation but not in a more conventional sense. 20 In the epigraphic universe omissions and corrections are not rare and this one might not demand our attention, except that something similar seems to have happened on the statue base honoring the same Phylax at Olympia (IvO 464 = Puech, Orateurs et sophistes 205): ἀγαθῆι τύχ[ηι]. ἔδοξε τῇ βουλῇ τῇ Ὀλυμπικῆι. 4 Φλάβιος Φύλαξ Ἀλεξάνδρου Θεσσαλὸς σοφιστής, Θεσσαλῶν 8 σύνεδρος, Ἀθηναίων Ἀρεοπαγείτης. The text itself appears never to have been edited from autopsy; Dittenberger apparently only had access to a copy and description of Purgold. 21 But autopsy or not, the Greek is disturbing. 22 This is the only inscribed utterance to indicate resolution of the council with the phrase ἔδοξε τῇ βουλῇ τῇ Ὀλυμπικῇ. Now, one could note that the similar δόγματι τῆς Ὀλυμπικῆς βουλῆς is attested but once, as are the comparable ψ(ηφίσματι) Ὀλ(υμπικῆς) β(ουλῆς) and ψηφίσματι τῆς Ὀλυμπικῆς βουλῆς. 23 But the attributive with article repeated, ἡ βουλὴ ἡ Ὀλυμπική, appears to be an epigraphic hapax. 24 A red flag. 17 A good point that I owe to W. Johnson. See K. Eshleman, Defining the Circle of Sophists: Philostratus and the Construction of the Second Sophistic, CP 103 (2008) , C. P. Jones, BCH 96 (1972) 265 n S. Swain, The Reliability of Philostratus s Lives of the Sophists, ClAnt 10 (1991) , On understandings of the term see K. Eshleman, Neither Inside nor Outside: Becoming Heretical in Second-Century Christianity (Diss. U. Michigan 2004) 85 88; ead., CP 103 (2008) W. Dittenberger, Inschriften aus Olympia, AZ 38 (1880) 52 62, no IvO 464 p. 554, already, citing Philostratos uncharitable remarks on Phylax: Beachtenswert ist auch hier die nachlässige und allem Gebrauch widersprechende Fassung der Inschrift. 23 IvO (III AD), (III AD), (II AD). That the Olympian βουλή was an institution of post-classical origin: T. H. Nielsen, Olympia and the Classical Hellenic City-State Culture (Copenhagen 2007) 50 52; M. H. Hansen and T. Fischer-Hansen, Monumental Political Architecture in Archaic and Classical Greek Poleis, in D. M. Whitehead (ed.), From Political Architecture to Stephanus Byzantius: Sources for the Ancient Greek Poleis [= Historia Einz. 87] (Stuttgart 1994) 88 89; S. G. Miller, Old Metroon and Old Bouleuterion in the Classical Agora of Athens, in M. H. Hansen and K. Raaflaub (eds.), Studies in the Ancient Greek Polis [= Historia Einz. 95] (Stuttgart 1995) 144 with n. 31. On its possible size: SEG LI Beyond Olympia too. Querying the more than 200,000 inscriptions in the PHI Epigraphy database for εδοξε τη βουλη τη (and the same with all possible combinations of iota adscript and with Doric τα/ται) returns this text alone: packhum.org/inscriptions. Search of the same in TLG returns no results. In the nominative the phrase is limited to references to the council of the Areopagos: ἡ βουλὴ ἡ ἐξ Ἀρείου πάγου. In the Hellenistic period ἔδοξε τῆι πόλει τῆι + genitive is attested in Thessaly, whence Phylax and family came, and especially at Gonnoi: IG IX, ; AE (1910) 344, , (1916) 18, 272.1, (1917) 10, ; I.Gonnoi 41.9, , , 81.9, , , 106.9, 109.1, ; Nouveau Choix

8 168 J. D. Sosin The syntax is worse. The text purports to advertise the council s decision to honor Phylax with a statue. He, the honorand, ought to be in the accusative, as countless parallels from across the time and space of epigraphic Greek tell, and not in the nominative. 25 Not, By consent of the council (sc. I am/this is) Flavius Phylax, a meaningless assertion and an impossible decree, but By consent of the council (some subject) (sc. dedicated a statue of) Flavius Phylax. The elliptical utterance was normative. In the formal sense of grammar, logic, and the mechanics of honor, Phylax s monument is nonsense. Thus, Puech suggested that the council must not have awarded the statue, for it would have gotten the Greek right; instead, it must have authorized Phylax to pay for and erect a statue of himself as he liked. 26 If so, then the orator s own monument was a second-class honor, clumsily implemented. On the other hand, if the council did award the statue and inscription then it was shockingly incapable of producing the most standard of sentences, and so was Phylax, who accepted and erected the thing. And if the council did not decree anything of the sort that is, if it neither voted the honors nor approved Phylax s self-congratulatory gesture then the inscription simply lies. Whatever the case, for an ancient reader of a statue base whose text begins ἀγαθῆι τύχηι. ἔδοξε τῆι βουλῆι, the expectation will almost invariably have been state award. This inscription too, then, depicts a professional speaker who was either inept, deceitful, or both. A photograph taken by a tourist on 30 June 2011 and posted to Flickr intensifies that impression. 27 It shows quite clearly that lines 7 10 were added after the fact, in a hastier, less adept hand. The upper text, which covers roughly the top half of the inscribable surface, features four-bar sigma, whereas the lower has squared lunate sigma. This, at least, has always been inferable from the drawing published at IvO 464 (see drawing below), but the lower section is also, in places, undular, awkward, and poorly kerned, which the drawing does not reveal (see Θεσσαλῶν in photo below). Thus, what has been universally received as a single utterance is in fact two. Again, the epigraphic fact only hints at historical circumstances that are beyond recovery. Perhaps at the time of the dedication Phylax was not yet σύνεδρος or Areopagite; and so on a later visit to Olympia he, as it were, updated his 25 A few from Olympia: IvO 355 (III AD): ἀγαθῇ τύχῃ. τὸν λαμπρό τατον ὑπατι κὸν Ἄππιον Σαβεῖνον ἡ Ὀ λυμπικὴ βουλὴ ἀρετῆς ἕνεκα. ψ(ηφίσματι) Ὀλ(υμπικῆς) β(ουλῆς); 356 (III AD): ἀγαθῇ τύχῃ. ἡ Ὀλυμπικὴ βουλὴ καὶ ὁ δῆμος ὁ Ἠλείων Γ. Ἀσίνιον Κουαδρᾶτον ἀνθύπατον, ὕπατον ἀποδεδειγμένον, τειμήσαντα τὴν Ὀλυμπί αν καὶ λόγῳ καὶ ἔργῳ; 439 (II AD): [Κ(λαύδιον)] Λουκηνὸν [Σ]αίκλαρον [Βετ]ληνὴ Κασ [σί]α Χρυσαρέτα [τ]ὸν ἑαυτῆς ἄν δρα, ψηφίσματι τῆς Ὀλυμπικῆς βουλῆς καὶ τοῦ δήμου καὶ τῶν συνέδρων; 455 (149 AD): ἡ Ὀλυμπικὴ βουλὴ Γ(άϊον) Ἰούλιο[ν] Φίλιππον Τραλ λιανόν, τὸν ἀσι άρχην, ἠθῶν ἕνε κα, Ὀλυμπιάδι σλβ; 461 (II AD): Γ(άϊον) Φουφεί κιον Σειλέαν Μ(ᾶρκος) Οὐιψάνιος Σειλέας τὸν πάπ πον ψηφισαμένης τῆς Ὀλυμπικῆς βουλῆς; 466 (II AD?): ἡ Ὀλυμπικὴ βουλὴ καὶ ὁ δῆμος Ἠλείων Τίτον Φλάουιον Ἡράκλειτον, τὸν ἀπὸ Φειδίου, φαιδυντὴν τοῦ ιὸς τοῦ Ὀλυμπίου, τῆς εἰς τὸν θεὸν εὐσε βείας καὶ τῆς εἰς ἑαυτοὺς εὐνοίας ἕνεκεν; 476 (III AD): ἀγαθῇ τύχῃ. δόγματι τῆς Ὀλυμπι κῆς βουλῆς Φλ(άβιον) Φιλόστρατον Ἀθη ναῖον, τὸν σοφιστήν, ἡ λαμπροτάτη πατρίς; 479 (III AD): Κλαύδιον Ζηνόφι λον τὸν κράτιστον ἀλυτάρχην καὶ πά τρωνα τῆς πόλε ως ἡ Ὀλυμπικὴ βουλὴ εὐνοίας ἕνεκα καὶ τῆς εἰς αὑτὴν δα ψιλοῦς φιλο τειμίας. 26 Puech, Orateurs et sophistes 386: Le décret du Conseil Olympique n avait probablement pas décerné la statue: un hommage public aurait été présenté de manière moins désinvolte. Il a dû accorder l autorisation de l élever, l initiative en incombant à particulier. Des lors, puisque personne d autre n est mentionné, le dédicant était sans doute Phylax lui-même. Il avait dû choisir d assurer sa publicité par un monument plus durable que le souvenir de sa prestation: cette initiative, qui expliquerait le caractère insolite du texte, pourrait ne pas avoir été exceptionnelle. So, faced with Greek dedicatory convention that could not tolerate ἑαυτὸν Φλάβιος Φύλαξ Ἀλεξάνδρου Θεσσαλὸς σοφιστής or some other such embarrassment, Phylax had only the subject inscribed, the object being visible in the form of the statue? Paying for one s own honors was surely unexceptional, but doing such while implying state sponsorship was not. Compare SEG XXV 211, in which the honorand s home city paid for a monument honoring him at Athens, for his services to Athens: τὸ κοινὸν τῶν Θεσσα λῶν Τίτον Φλάουιον Κύλλον ἄρξαντα Πα νελλήνων καὶ ἀγω νοθετήσαντα τῶν μεγάλων Πανελλη νίων, ἀρετῆς ἕνεκεν καὶ εὐνοίας τῆς τε εἰς τὸ Πανελλήνι ον καὶ τὴν Ἀθηναί ων πόλιν. On Kyllos, a fellow Hypataian and rough contemporary of Flavius and Phylax, see N. V. Sekunda, ZPE 118 (1997) James Irish Photography, Greek Inscription, Olympia, Greece, , accessed 2 January Another photograph taken by a tourist and posted to Picassa shows the top half more clearly: accessed 2 January The inscription does not appear in the lavish X. Arapogianne, Olympia: The Cradle of the Olympic Games (Athens 2004).

9 Notes on Inscriptions 169 IvO 464 (p. 553) James Irish Photography curriculum vitae, on a text that masqueraded as civic honor but was in fact self-indulgence. 28 Or perhaps Olympia did grant the honors, but with less grandeur, Phylax may have learned on delivery, than he had wished; and so he offered a private amendment to the public document, adding accomplishments to his name. Now, sophists, with whom Phylax self-identified, often considered their unadorned name sufficient for recognition. Thus Antonius Polemo is merely Polemo when honoring Demosthenes at Pergamon, and Aelius Aristides is always Aristides in the various dedications that he makes at home or on his travels. 29 This laconism was a boast, a claim that in a world in which multiple names were required to identify all but the most exalted individuals as such, one was enough a claim to be a Homer or a Plato, a Mommsen or a Robert, and not Fred son of George, city councillor and Esteemed Loyal Knight of the Elks Lodge, from Dubuque. Phylax s inclusion of the patronym and after the fact, no less extra-professional political 28 The Areopagos honored plenty of men of learning and culture, e.g.: TAM II 910 (Herakleitos of Rhodiapolis), SEG XIX 208 (Theodoros of Gadara), XLIII 864 (Polybios of Sardis; see C. P. Jones, Polybius of Sardis, CP 91 [1996] ), Claudius Anteros (I.Labraunda 66); M. Ulpius Eurykles (OGIS 505); IG II (Euphrates of Tyre; see C. P. Jones, Epigraphica VI VII, ZPE 144 [2003] , ); IG II = Puech, Orateurs et Sophistes 25 (Apollonios). But I know no other example of Areopagite status listed as an honorand s accomplishment; the appearance of such as a textual addition after the fact could be cause for worry, but neither do I know grounds for doubting Phylax s claim. Precisely how the Areopagos was populated in this era remains a thorny question; see J. M. Rainer, Bü rgerrechtsprobleme im 2. Jahrhundert n. Chr.: Flavius Phylax, in G. Wesener (ed.), Festschrift für Arnold Kränzlein: Beiträge zur antiken Rechtsgeschichte (Graz 1986) 83 93, On multiple citizenship, see Rainer; also now C. P. Jones, Joys and Sorrows of Multiple Citizenship: The Case of Dio Chrysostom, in A. Heller and A.-V. Pont (eds.), Patrie d origine et patries é lectives: les citoyenneté s multiples dans le monde grec d é poque romaine (Bordeaux 2012) C. P. Jones, Epigraphica, ZPE 139 (2002) , 113, with references. See e.g. CID IV 157: ἀγαθῆι τύχηι. τὸν σοφιστὴν Σώτηρον ἡ λαμ προτάτη Ἔφε [σ]ος κατὰ δό γμα τῶν Ἀμφι κτυόνων. I.Ephesos : Σώτηρο[ν] τὸν σοφιστ[ὴν] κατὰ ψήφισμα τῆ[ς] βουλῆς, κ[ατ ἐπίδοσιν] τῶν μαθ[ητῶν ].

10 170 J. D. Sosin and honorary attainments rings of the small time, underscores the need for such precision and qualification. Even in a culture that did not value humility quite so much as some others, this updating is not only a sad bid for recognition, but it is also reminiscent of the clumsy corrections made to Phylax s Delphic dedication. The importance antiquity placed on honor is such that the coincidence of two epigraphic insertions of the same sort, on the same kind of text, from similar sites, in texts concerning sibling honorands, might be explained away as honest and appropriate attempts to set the record straight: Phoinix wanted all to know that he too honored his father and Phylax had to insist that, whether at the time of dedication or later, he was more than a sophist. But this seems too much for coincidence and it is hard not to interpret the inscriptions and Philostratos comments in the light of each other. Philostratos was not impartial or immune to faction; who in his intellectual milieu was? And so it is certainly tempting to think that his apparent contempt for these Flavii arose from conflicting professional, intellectual, and social allegiances, or from authorial design. 30 But among Second Sophistic intellectuals vying for prominence, not everyone was the best, 31 a fact which underscores the intellectual ferment of the age, much as the abundance of bad Greek in the documentary papyri can be an indication of quickening literacy rather than the opposite. In all domains of elite competition, second place often seems to be a mile away from first. But Phylax does not appear even to have made the team. The inattention to proper form at Olympia and the clumsy vanity of the insertions there and at Delphi too do not urge us to think Philostratos who may even have seen the Olympian inscription 32 unjustified, unfair, or biased. He may have been, but on the other hand these brothers may simply have been the also-rans that he made them out to be. Joshua D. Sosin, Duke University joshua.sosin@duke.edu 30 As K. Eshleman, CP 103 (2008) , well suggests. S. Swain, ClAnt 10 (1991) 158, 162, suggests that Philostratos roster of laughing-stock sophists may have come from his source, but that his contempt for Phylax was his own. 31 It is tempting to see errors in two well known Pompeiian graffiti: C(aium) Cuspium Pansam aed(ilem) d(ignum) r(ei) p(ublicae) o(ro) v(os) f(aciatis) Saturninus / cum discentes(!) rog(at) (CIL IV 275); Sabinum et Rufum aed(iles) d(ignos) r(ei) p(ublicae) Valentinus cum discentes(!) suos rog(at) (CIL IV 698). Of course, other examples of cum + accusative are known; see e.g. CIL IV 221: M(arcum) Cerrinium Vatiam aed(ilem) dignum rei p(ublicae) Tyrannus cupiens fecit cum sodales. Prepositions came increasingly and overwhelmingly to govern the accusative: see e.g. J. Herman [R. Wright transl.], Vulgar Latin (University Park 2000) But in the street Latin of the Pompeiian graffiti, cum almost always takes the ablative: e.g. CIL IV 103: M(arcum) Holconium Priscum / C(aium) Gavium Rufum IIvir(os) Phoebus cum emptoribus suis rogat; 175: Fuscus cum Vaccula facit; 235: Faventinus cum suis rog(at); 581: scr(ipsit) Florus cum Fructo; 668: Sema cum pueris rog(at); 7665: Infanticulus cum sodalibus rog(at). 32 He too was honored there. IvO 476: ἀγαθῇ τύχῃ. δόγματι τῆς Ὀλυμπι κῆς βουλῆς Φλ(άβιον) Φιλόστρατον Ἀθη ναῖον, τὸν σοφιστήν, ἡ λαμπροτάτη πατρίς.

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

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

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

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

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας»

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας» ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙ ΕΥΤΙΚΟΥ ΣΧΕ ΙΑΣΜΟΥ «ΠΑΙ ΙΚΟ ΒΙΒΛΙΟ ΚΑΙ ΠΑΙ ΑΓΩΓΙΚΟ ΥΛΙΚΟ» ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που εκπονήθηκε για τη

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

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

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

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

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

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

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

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

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

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

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

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

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ»

«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ» I ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΝΟΜΙΚΩΝ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΠΟΛΙΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ «ΔΙΟΙΚΗΣΗ ΚΑΙ ΟΙΚΟΝΟΜΙΑ» ΚΑΤΕΥΘΥΝΣΗ: ΟΙΚΟΝΟΜΙΚΗ

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

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

FACE VALUE: THE POWER OF IMAGES AT APHRODISIAS

FACE VALUE: THE POWER OF IMAGES AT APHRODISIAS FACE VALUE: THE POWER OF IMAGES AT APHRODISIAS H O W D I G I T A L R E S O U R C E S C A N T R A N S F O R M O U R U N D E R S T A N D I N G O F P A L A E O G R A P H Y KEY QUESTIONS: What elements of

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

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS ΟΜΗΡΟΥ ΙΛΙΑΔΑ ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS www.scooltime.gr [- 2 -] The Project Gutenberg EBook of Iliad, by Homer This ebook is for the use of anyone anywhere at no cost and with almost no restrictions

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

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

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

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

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

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

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΣΥΓΚΡΙΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΓΚΡΑΤΗΤΙΚΗΣ ΙΚΑΝΟΤΗΤΑΣ ΟΡΙΣΜΕΝΩΝ ΠΡΟΚΑΤΑΣΚΕΥΑΣΜΕΝΩΝ ΣΥΝΔΕΣΜΩΝ ΑΚΡΙΒΕΙΑΣ

Διαβάστε περισσότερα

Στο εστιατόριο «ToDokimasesPrinToBgaleisStonKosmo?» έξω από τους δακτυλίους του Κρόνου, οι παραγγελίες γίνονται ηλεκτρονικά.

Στο εστιατόριο «ToDokimasesPrinToBgaleisStonKosmo?» έξω από τους δακτυλίους του Κρόνου, οι παραγγελίες γίνονται ηλεκτρονικά. Διαστημικό εστιατόριο του (Μ)ΑστροΈκτορα Στο εστιατόριο «ToDokimasesPrinToBgaleisStonKosmo?» έξω από τους δακτυλίους του Κρόνου, οι παραγγελίες γίνονται ηλεκτρονικά. Μόλις μια παρέα πελατών κάτσει σε ένα

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

ΙΩΑΝΝΗΣ ΛΑΣΚΑΡΗΣ, ΠΗΓΩΝΙΤΗΣ Ή ΣΥΡΠΑΓΑΝΟΣ, Ο ΚΑΛΟΜΙΣΙΔΗΣ

ΙΩΑΝΝΗΣ ΛΑΣΚΑΡΗΣ, ΠΗΓΩΝΙΤΗΣ Ή ΣΥΡΠΑΓΑΝΟΣ, Ο ΚΑΛΟΜΙΣΙΔΗΣ ΙΩΑΝΝΗΣ ΛΑΣΚΑΡΗΣ, ΠΗΓΩΝΙΤΗΣ Ή ΣΥΡΠΑΓΑΝΟΣ, Ο ΚΑΛΟΜΙΣΙΔΗΣ Ἀναπάντεχες λεπτομέρειες γιὰ τὸν βίο καὶ τὴν πολιτεία τοῦ Ἰωάννη Λάσκαρη μᾶς εἶναι γνωστὲς ἀπὸ μιὰ σειρὰ ἐγγράφων (ποὺ ἀνακάλυψε στὰ κρατικὰ ἀρχεῖα

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

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης

ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΒΑΛΕΝΤΙΝΑ ΠΑΠΑΔΟΠΟΥΛΟΥ Α.Μ.: 09/061. Υπεύθυνος Καθηγητής: Σάββας Μακρίδης Α.Τ.Ε.Ι. ΙΟΝΙΩΝ ΝΗΣΩΝ ΠΑΡΑΡΤΗΜΑ ΑΡΓΟΣΤΟΛΙΟΥ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ «Η διαμόρφωση επικοινωνιακής στρατηγικής (και των τακτικών ενεργειών) για την ενδυνάμωση της εταιρικής

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

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

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

Physical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible.

Physical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible. B-Trees Index files can become quite large for large main files Indices on index files are possible 3 rd -level index 2 nd -level index 1 st -level index Main file 1 The 1 st -level index consists of pairs

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

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

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 1: Elements of Syntactic Structure Το περιεχόμενο του μαθήματος διατίθεται με άδεια

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

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

F-TF Sum and Difference angle

F-TF Sum and Difference angle F-TF Sum and Difference angle formulas Alignments to Content Standards: F-TF.C.9 Task In this task, you will show how all of the sum and difference angle formulas can be derived from a single formula when

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

Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς

Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς We review side by side a model of stems ending in ι: πόλις, πόλεως, ἡ = city-state and a masculine model of stems ending in υ: πρέσβυς,

Διαβάστε περισσότερα

Μηχανική Μάθηση Hypothesis Testing

Μηχανική Μάθηση Hypothesis Testing ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Μηχανική Μάθηση Hypothesis Testing Γιώργος Μπορμπουδάκης Τμήμα Επιστήμης Υπολογιστών Procedure 1. Form the null (H 0 ) and alternative (H 1 ) hypothesis 2. Consider

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

Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your

Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your Πώς μπορεί κανείς να έχει έναν διερμηνέα κατά την επίσκεψή του στον Οικογενειακό του Γιατρό στο Ίσλινγκτον Getting an interpreter when you visit your GP practice in Islington Σε όλα τα Ιατρεία Οικογενειακού

Διαβάστε περισσότερα

Πανεπιστήμιο Κρήτης, Τμήμα Επιστήμης Υπολογιστών Άνοιξη 2009. HΥ463 - Συστήματα Ανάκτησης Πληροφοριών Information Retrieval (IR) Systems

Πανεπιστήμιο Κρήτης, Τμήμα Επιστήμης Υπολογιστών Άνοιξη 2009. HΥ463 - Συστήματα Ανάκτησης Πληροφοριών Information Retrieval (IR) Systems Πανεπιστήμιο Κρήτης, Τμήμα Επιστήμης Υπολογιστών Άνοιξη 2009 HΥ463 - Συστήματα Ανάκτησης Πληροφοριών Information Retrieval (IR) Systems Στατιστικά Κειμένου Text Statistics Γιάννης Τζίτζικας άλ ιάλεξη :

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

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΗΡΑΚΛΕΙΟ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ Π Τ Υ Χ Ι Α Κ Η Ε Ρ Γ Α Σ Ι Α: Ο ΡΟΛΟΣ ΤΗΣ ΣΥΝΑΙΣΘΗΜΑΤΙΚΗΣ ΝΟΗΜΟΣΥΝΗΣ ΣΤΗΝ ΑΠΟΤΕΛΕΣΜΑΤΙΚΗ ΗΓΕΣΙΑ ΕΠΙΜΕΛΕΙΑ

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

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

ST5224: Advanced Statistical Theory II

ST5224: Advanced Statistical Theory II ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known

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

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

Lecture 2. Soundness and completeness of propositional logic

Lecture 2. Soundness and completeness of propositional logic Lecture 2 Soundness and completeness of propositional logic February 9, 2004 1 Overview Review of natural deduction. Soundness and completeness. Semantics of propositional formulas. Soundness proof. Completeness

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

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

1 ΚΩΝΣΤΑΝΤΙΝΟΣ Δ. ΤΡΙΤΑΡΗΣ

1 ΚΩΝΣΤΑΝΤΙΝΟΣ Δ. ΤΡΙΤΑΡΗΣ 69 Φεβρουάριος 2011 Περιεχόμενα Η συμβολή του Ιωάννη Καποδίστρια στην εδραίωση της ανεξαρτησίας και της ουδετερότητας της Ελβετίας σ. 1 Οι νέες ισορροπίες στην Ασία και Μ. Ανατολή Η ινδοϊστραηλινή συνεργασία

Διαβάστε περισσότερα

"ΦΟΡΟΛΟΓΙΑ ΕΙΣΟΔΗΜΑΤΟΣ ΕΤΑΙΡΕΙΩΝ ΣΥΓΚΡΙΤΙΚΑ ΓΙΑ ΤΑ ΟΙΚΟΝΟΜΙΚΑ ΕΤΗ 2011-2013"

ΦΟΡΟΛΟΓΙΑ ΕΙΣΟΔΗΜΑΤΟΣ ΕΤΑΙΡΕΙΩΝ ΣΥΓΚΡΙΤΙΚΑ ΓΙΑ ΤΑ ΟΙΚΟΝΟΜΙΚΑ ΕΤΗ 2011-2013 ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΚΑΙ ΧΡΗΜΑΤΟΟΙΚΟΝΟΜΙΚΗΣ Επιμέλεια Κρανιωτάκη Δήμητρα Α.Μ. 8252 Κωστορρίζου Δήμητρα Α.Μ. 8206 Μελετίου Χαράλαμπος Α.Μ.

Διαβάστε περισσότερα

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ

Επιβλέπουσα Καθηγήτρια: ΣΟΦΙΑ ΑΡΑΒΟΥ ΠΑΠΑΔΑΤΟΥ EΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΕΚΠΑΙΔΕΥΤΙΚΟ ΤΕΧΝΟΛΟΓΙΚΟ ΙΔΡΥΜΑ ΤΕΙ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : Λεωφ. Αντ.Τρίτση, Αργοστόλι Κεφαλληνίας Τ.Κ. 28 100 τηλ. : 26710-27311 fax : 26710-27312

Διαβάστε περισσότερα

Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας

Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας ΤΕΙ ΚΑΒΑΛΑΣ ΠΑΡΑΡΤΗΜΑ ΔΡΑΜΑΣ ΤΜΗΜΑ ΑΡΧΙΤΕΚΤΟΝΙΚΗΤΟΠΙΟΥ Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας

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 7: More about gerunds Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

Διαβάστε περισσότερα

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE «ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE We would like to invite you to participate in GAMIAN- Europe research project. You should only participate if you want to and choosing

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

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

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

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

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

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics Fourier Series MATH 211, Calculus II J. Robert Buchanan Department of Mathematics Spring 2018 Introduction Not all functions can be represented by Taylor series. f (k) (c) A Taylor series f (x) = (x c)

Διαβάστε περισσότερα

BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN. Fairly true If I decide to learn something hard, I can.

BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN. Fairly true If I decide to learn something hard, I can. BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN Name GRADE Science Teacher A. What do I think about School? bit I try hard to do well in school. I look forward to coming to school.

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

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

Θέμα διπλωματικής εργασίας: «Από το «φρενοκομείο» στη Λέρο και την Ψυχιατρική Μεταρρύθμιση: νομικό πλαίσιο και ηθικοκοινωνικές διαστάσεις»

Θέμα διπλωματικής εργασίας: «Από το «φρενοκομείο» στη Λέρο και την Ψυχιατρική Μεταρρύθμιση: νομικό πλαίσιο και ηθικοκοινωνικές διαστάσεις» ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΕΣ ΙΑΤΡΙΚΗΣ & ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΤΜΗΜΑΤΑ ΝΟΜΙΚΗΣ & ΘΕΟΛΟΓΙΑΣ ΔΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ «ΣΥΓΧΡΟΝΕΣ ΙΑΤΡΙΚΕΣ ΠΡΑΞΕΙΣ: ΔΙΚΑΙΙΚΗ ΡΥΘΜΙΣΗ ΚΑΙ ΒΙΟΗΘΙΚΗ

Διαβάστε περισσότερα

ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ

ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΑΓΡΟΝΟΜΩΝ & ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΓΕΩΓΡΑΦΙΑΣ ΚΑΙ ΠΕΡΙΦΕΡΕΙΑΚΟΥ ΣΧΕΔΙΑΣΜΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «Η ΕΞΕΛΙΞΗ ΤΗΣ ΠΟΛΗΣ ΤΗΣ ΚΑΛΑΜΑΤΑΣ ΜΕ ΕΠΙΚΕΝΤΡΟ ΤΟ ΙΣΤΟΡΙΚΟ ΤΗΣ ΚΕΝΤΡΟ»

Διαβάστε περισσότερα

Galatia SIL Keyboard Information

Galatia SIL Keyboard Information Galatia SIL Keyboard Information Keyboard ssignments The main purpose of the keyboards is to provide a wide range of keying options, so many characters can be entered in multiple ways. If you are typing

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

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

Statistical Inference I Locally most powerful tests

Statistical Inference I Locally most powerful tests Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided

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

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

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

ΠΑΡΑΜΕΤΡΟΙ ΕΠΗΡΕΑΣΜΟΥ ΤΗΣ ΑΝΑΓΝΩΣΗΣ- ΑΠΟΚΩΔΙΚΟΠΟΙΗΣΗΣ ΤΗΣ BRAILLE ΑΠΟ ΑΤΟΜΑ ΜΕ ΤΥΦΛΩΣΗ

ΠΑΡΑΜΕΤΡΟΙ ΕΠΗΡΕΑΣΜΟΥ ΤΗΣ ΑΝΑΓΝΩΣΗΣ- ΑΠΟΚΩΔΙΚΟΠΟΙΗΣΗΣ ΤΗΣ BRAILLE ΑΠΟ ΑΤΟΜΑ ΜΕ ΤΥΦΛΩΣΗ ΠΑΝΕΠΙΣΤΗΜΙΟ ΜΑΚΕΔΟΝΙΑΣ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΚΠΑΙΔΕΥΤΙΚΗΣ ΚΑΙ ΚΟΙΝΩΝΙΚΗΣ ΠΟΛΙΤΙΚΗΣ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΑΡΑΜΕΤΡΟΙ ΕΠΗΡΕΑΣΜΟΥ ΤΗΣ ΑΝΑΓΝΩΣΗΣ- ΑΠΟΚΩΔΙΚΟΠΟΙΗΣΗΣ ΤΗΣ BRAILLE

Διαβάστε περισσότερα

ΔΙΕΡΕΥΝΗΣΗ ΤΗΣ ΣΕΞΟΥΑΛΙΚΗΣ ΔΡΑΣΤΗΡΙΟΤΗΤΑΣ ΤΩΝ ΓΥΝΑΙΚΩΝ ΚΑΤΑ ΤΗ ΔΙΑΡΚΕΙΑ ΤΗΣ ΕΓΚΥΜΟΣΥΝΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ

ΔΙΕΡΕΥΝΗΣΗ ΤΗΣ ΣΕΞΟΥΑΛΙΚΗΣ ΔΡΑΣΤΗΡΙΟΤΗΤΑΣ ΤΩΝ ΓΥΝΑΙΚΩΝ ΚΑΤΑ ΤΗ ΔΙΑΡΚΕΙΑ ΤΗΣ ΕΓΚΥΜΟΣΥΝΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία ΔΙΕΡΕΥΝΗΣΗ ΤΗΣ ΣΕΞΟΥΑΛΙΚΗΣ ΔΡΑΣΤΗΡΙΟΤΗΤΑΣ ΤΩΝ ΓΥΝΑΙΚΩΝ ΚΑΤΑ ΤΗ ΔΙΑΡΚΕΙΑ ΤΗΣ ΕΓΚΥΜΟΣΥΝΗΣ ΑΝΔΡΕΟΥ ΣΤΕΦΑΝΙΑ Λεμεσός 2012 i ii ΤΕΧΝΟΛΟΓΙΚΟ

Διαβάστε περισσότερα

Η ΠΡΟΣΩΠΙΚΗ ΟΡΙΟΘΕΤΗΣΗ ΤΟΥ ΧΩΡΟΥ Η ΠΕΡΙΠΤΩΣΗ ΤΩΝ CHAT ROOMS

Η ΠΡΟΣΩΠΙΚΗ ΟΡΙΟΘΕΤΗΣΗ ΤΟΥ ΧΩΡΟΥ Η ΠΕΡΙΠΤΩΣΗ ΤΩΝ CHAT ROOMS ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ Ι Ο Ν Ι Ω Ν Ν Η Σ Ω Ν ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : ΑΤΕΙ Ιονίων Νήσων- Λεωφόρος Αντώνη Τρίτση Αργοστόλι Κεφαλληνίας, Ελλάδα 28100,+30

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

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

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

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

«Έντυπο και ψηφιακό βιβλίο στη σύγχρονη εποχή: τάσεις στην παγκόσμια βιομηχανία».

«Έντυπο και ψηφιακό βιβλίο στη σύγχρονη εποχή: τάσεις στην παγκόσμια βιομηχανία». ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : ΑΤΕΙ Ιονίων Νήσων- Λεωφόρος Αντώνη Τρίτση Αργοστόλι- Κεφαλληνίας, Ελλάδα 28100, +30

Διαβάστε περισσότερα

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- ----------------- Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin

Διαβάστε περισσότερα

Αζεκίλα Α. Μπνπράγηεξ (Α.Μ. 261)

Αζεκίλα Α. Μπνπράγηεξ (Α.Μ. 261) ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΧΝ ΥΟΛΖ ΑΝΘΡΧΠΗΣΗΚΧΝ ΚΑΗ ΚΟΗΝΧΝΗΚΧΝ ΠΟΤΓΧΝ ΠΑΗΓΑΓΧΓΗΚΟ ΣΜΖΜΑ ΓΖΜΟΣΗΚΖ ΔΚΠΑΗΓΔΤΖ ΜΔΣΑΠΣΤΥΗΑΚΟ ΠΡΟΓΡΑΜΜΑ ΠΟΤΓΧΝ ΘΔΜΑ ΓΗΠΛΧΜΑΣΗΚΖ ΔΡΓΑΗΑ: Ζ ΑΝΣΗΛΖΦΖ ΣΧΝ ΔΚΠΑΗΓΔΤΣΗΚΧΝ ΓΗΑ ΣΖ ΖΜΑΗΑ ΣΖ ΑΤΣΟΔΚΣΗΜΖΖ

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

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται

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