On Greek Dedicatory Practices: The Problem of hyper

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "On Greek Dedicatory Practices: The Problem of hyper"

Transcript

1 On Greek Dedicatory Practices: The Problem of hyper Theodora Suk Fong Jim IN COMMUNICATING with the gods, whether by means of prayers, sacrifice, or dedications, one of the most common Greek formulae involved the preposition ὑπέρ. Individuals might present gifts to the gods hyper themselves and their family, their crops and livestock, their group and community, etc. Innumerable Greek decrees carry the formula ὑπερ ὑγιείας καὶ σωτηρίας (or similar). But perhaps because it is seemingly so familiar, little attention has been paid to its applications and meanings, 1 and mistakes in this field can lead to grave misinterpretations of Greek religious practices. 2 This article aims to clarify the various religious uses of hyper, and to draw attention to ambiguities associated with the formulae, with a view to 1 M. L. Lazzarini, Iscrizioni votive greche, ScAnt 3 4 ( ) , at , discusses hyper formulae briefly, focusing on hyper soterias and hyper animals and crops (and their variants). R. Parker, Polytheism and Society at Athens (Oxford 2005) 66 67, 95 97, and F. S. Naiden, Smoke Signals for the Gods: Ancient Greek Sacrifice from the Archaic through Roman Periods (Oxford 2013) , discuss sacrifices hyper tinos. 2 According to schol. vet. Ar. Ach. 747b, every initiate at the Eleusinian Mysteries had to sacrifice a piglet ὑπερ ἑαυτοῦ. This is rendered by W. Burkert, Greek Religion: Archaic and Classical (Oxford 1985) 286, as in his stead (revised ed. Griechische Religion der archaischen und klassischen Epoche. [Stuttgart 2011] 426: an seiner Statt ). This mistranslation introduces the suspect idea of substitution sacrifice, that is, the idea that an animal was sacrificed in place of the person who brought it. On the problem of substitution sacrifice see R. Parker, Substitution in Greek Sacrifice, in R. Gagné and P. Bonnechere (eds.), Sacrifices humains: Perspectives croisées et représentations (Liège 2013) Theodora Suk Fong Jim

2 618 THE PROBLEM OF HYPER shedding light on wider issues related to Greek dedicatory practices. The focus will be on dedicatory inscriptions, though sacrificial uses and literary attestations will also be mentioned where hyper had similar meanings and uses. 1. hyper a beneficiary When the Greeks made offerings to secure the favour of the gods, hyper s major function was to identify the recipients of the benefits associated with the offerings, the most common ones being the dedicators themselves and their family members. Such formulae were rare in the Archaic and early Classical periods, but became much more common from the fourth century B.C. An early example (probably incomplete) from Erythrae reads Ἀπόλλωνι Δ ελφινίωι Φανόδικος ὁ Φιλήτεω ἀ[ν]έθηκεν εὐχω[λὴν ὑ]πὲρ ἑαυτο, To Apollo Delphinios, Phanodikos son of Philetes dedicated (this) votive offering on behalf of himself. 3 Another dedication, from Athens, bears this verse: [Μ]ικύθη µ ἀνέ[θηκεν] [Ἀθ]ηναίηι τό[δ ἄγαλµα] / [εὐξ]αµένη δ [εκάτην] [καὶ] ὑ πὲρ πα[ίδων] [κ]αὶ ἑαυτῆ [ς], Mikythe dedicated this statue to Athena, having vowed a tithe on behalf of her children and herself. 4 In the vast majority of such uses, hyper can be rendered on behalf of, in the interest of, or for the sake of the persons named in the genitive. Its primary function was to specify the direction in which the charis associated with the offering should flow, as if to make sure that the gods would dispense their favours to the right persons. The need to indicate this to the Greek gods seems markedly different from early Christian dedications, many of which left both the dedicators and the beneficiaries anonymous. 5 3 I.Erythrai 209 = M. L. Lazzarini, Le formule delle dediche votive nella Grecia arcaica (Rome 1976) no. 741 = LSAG 2 344, no. 50, pl. 65 (ca ?). The statue base is broken at the bottom, so the text may not be complete and hyper probably does not identify only the dedicator. Lazzarini restores [ὑ]πὲρ ἑαυτο [καὶ γενεῆς?]; cf. no. 784 = DAA no. 282 [Ὀ]νέτορ [τόδ hυπὲρ] h αυτο καὶ γ [ενεᾶς] (ca. 500). 4 IG I (ca ?) = CEG An example from Eleusis, recently published by E. Sironen, Two Early

3 THEODORA SUK FONG JIM 619 In many Greek dedicatory inscriptions hyper was followed only by the dedicator s family members without mention of himself/herself. 6 Indeed it is far less common to find ὑπὲρ ἑαυτοῦ/ἑαυτῆς standing alone, indicating the dedicator himself/herself as the sole beneficiary. 7 In healing contexts hyper may be followed by a body part, which might be depicted in an accompanying relief. 8 Close relatives aside, individuals might dedicate on behalf of the group to which they belonged with such expressions as ὑπὲρ τῆς φυλῆς, ὑπὲρ τῶν συνεφήβων, ὑπὲρ τῆς κώµης, and ὑπὲρ τῆς πόλεως. 9 All these were prayers on Christian Inscriptions from Eleusis, in G. Reger et al. (eds.), Studies in Greek Epigraphy and History in Honor of Stephenn V. Tracy (Pessac 2010) 84: καλλιεργία ὑπὲρ εὐχῆς κ<αὶ> σωτηρίας ὧν οἶδεν ὁ Θ(εὸ)ς τὰ ὀνώ µα<τ>α, This beautiful work (is dedicated) for the vow and safety of those whose names God knows. See similar Christian formulae in e.g. Bull.épigr. 1970, 383; IG X ; SEG XXXVII 737. But L. Robert, Dans une maison d Ephèse, un serpent et un chiffre, CRAI (1982) , at 132 (repr. Opera minora selecta V , at 776), and Documents d Asie Mineure, BCH 107 (1983) , at 572 (repr. Documents d Asie Mineure (Athens/Paris 1987) , at 416), suggested that a similar idea the gods know probably underlies Greek dedications that lack inscriptions. 6 E.g. IG II ὑπὲρ τῆς γυναικός, 4400 ὑπὲρ τῶν παίδων, 4412 ὑπὲρ τῆς θυγατρός, 4588 ὑπὲρ τοῦ παιδίου, XI ὑπὲρ τῶν παιδίων; SEG XLI 1218 ὑπὲρ τέκνων [κ]ὲ τῆς οἰκείας κὲ Ἀλυµας οἱ ἀδεφοί, 1221 ὑπὲρ ἀ[ν]εψιῶν, 1224 [ὑ]πὲρ τῶν τέκνων, 1232 [ὑπὲρ τῆ]ς οἰκίας; TAM V ὑπὲρ ἀδελφῶν, 462 ὑπὲρ γυνεκός. 7 Standing alone: e.g. I.Kanais 37 38; I.Délos 2225, 2328; IGBulg II 487, 677; IG II E.g. TAM V ὑπὲρ τῶν µ αστῶν εὐχήν (relief depicting a pair of breasts), 461b ὑπὲρ παρωτίδων εὔξατο εὐχήν (no iconography; παρωτίς a tumour of the parotid gland, LSJ), 533 ὑπὲρ το[ῦ] ποδὸς εὐχαριστοῦσ[α] [ε]ὐ χὴν (a leg is depicted between two standing figures), 534 ὑπὲρ τοῦ ποδὸς εὐχήν (foot or lower part of leg); T. Drew-Bear, C. M. Thomas, and M. Yildizturan, Phrygian Votive Steles (Ankara 1999) nos. 340 ὑπὲρ τοῦ ἰδίου σώµατος εὐχήν (no iconography), 526 ὑπὲρ ἰδίου σώµα[το]ς εὐχήν (relief of an arm). 9 ὑπὲρ τῆς φυλῆς: e.g. Agora XVIII C109 (by supplement). ὑπὲρ τῶν συνεφήβων: e.g. Agora XVII C132. ὑπὲρ τῆς κώµης: e.g. SEG LVIII 1424; T. Drew-Bear, Nouvelles inscriptions de Phrygie (Zutphen 1978) 34 no. 1.3;

4 620 THE PROBLEM OF HYPER behalf of or for the welfare/benefit of the persons or groups concerned: all those named would supposedly benefit from the offering even though they had not made it themselves. That beneficiaries could be absent and far away is shown by sacrifices performed by Athenian magistrates on behalf of various groups of Athenians, their friends, and allies. 10 From the Hellenistic period onwards we find individuals and cities making sacrifices or dedications to the gods on behalf of their king and queen (ὑπὲρ τοῦ βασιλέως καὶ τῆς βασιλίσσης) and sometimes other members of the royal family. 11 By channelling the charis to the hegemones, these offerings were expressions of goodwill towards the monarchs, and not prayers for monarchs who were in illness or trouble. A related use of hyper can be found in inscriptions concerning religious subscriptions. Individuals could make donations for religious purposes such as the construction or adornment of sanctuaries hyper themselves and/or members of their family. Many entries in subscription texts from Hellenistic Delos re- I.Prusa 23. ὑπὲρ τῆς πόλεως: IGBulg II 665, IG VII 3418, I.Olbia 83. C. Schuler, Inscriptions and Identities of Rural Population Groups in Roman Asia Minor, in J. Davies and J. Wilkes (eds.), Epigraphy and the Historical Sciences (Oxford 2012) , at 80, notes that the formula ὑπὲρ τῆς κώµης was confined to rural Asia Minor, though the concern for a community s well-being was not. 10 E.g. Agora XV 293 ὑπέρ τε τῶν π ρυτάνεων καὶ τῆς βουλῆς καὶ τοῦ δήµου καὶ παίδων [καὶ] γυναικῶν καὶ τῶν φίλων καὶ συµµάχων; IG II ὑπέρ τε τ[ῆς βουλῆς καὶ τοῦ δήµου καὶ παίδω]ν καὶ γυναικῶν καὶ [τῶν φίλων καὶ συµµάχων], 1224 [ὑπὲρ τῆς τοῦ δή]µου τοῦ Ἀθηναίων εὐδ[ο]ξίας τε καὶ σ[ω]τηρίας καὶ τῆς τῶν φίλ[ων καὶ συµµάχων] [τῶ]ν αὐτοῦ. That dedications could be set up by one individual hyper another is illustrated in e.g. an Epidaurian cure inscription IG IV (iama 7): Echedoros was given money from Pandaros (whose tattoos had been removed by Asclepius) to dedicate to the god at Epidaurus on his behalf (ὑπὲρ αὐ[του]). Having failed to dedicate as entrusted, he was punished by acquiring Pandaros tattoos. 11 E.g. IG XII B.22 23; SEG XLIX ; OGIS ; IG XII.3 468; I.Délos 1561, Sacrifices hyper emperors are discussed in S. R. F. Price, Rituals and Power (Cambridge 1984)

5 THEODORA SUK FONG JIM 621 cord contributions made by a donor for himself and his wife and his children, ὑπὲρ ἑαυτοῦ καὶ τῆς γυναικὸς καὶ τῶν τέκνων (or similar). 12 The individuals named alongside the donor probably did not give the sums themselves; the donations were made in their name. This use of hyper overlaps with, and yet does not fall neatly into, what we have considered so far: in this context the sense is in the name of rather than for the benefit of, but even in religious subscriptions there was probably still some vague hope of benefit for the individuals named. Hyper could also introduce worshippers livestock, crops, and possessions. Roman Asia Minor, particularly Phrygia and to a lesser extent Lydia, provide an abundance of votive dedications made for the well-being of animals. Many of these were for oxen (ὑπὲρ τοῦ βοός, ὑπὲρ βοῶν), 13 some for mules (ὑπὲρ τοῦ ἡµιόνου), 14 and some for herds of goats (ὑπὲρ αἰπολίου) 15 or for herds in general (ὑπὲρ τῶν θρεµµάτων, ὑπὲρ τῶν ζῴων, ὑπὲρ τῶν τετραπόδων, and ὑπὲρ τῶν κτηνῶν). 16 In some contexts θρέµµατα could apply to human beings, but its juxtaposition with children (τέκνα) in ὑπὲρ τέκνων καὶ θρεµµάτων and 12 E.g. I.Délos 2619.a.6ff., The same practice of donating hyper someone is seen in secular subscriptions (such as for fortifications), on which see L. Migeotte, Les souscriptions publiques dans les cités grecques (Quebec/ Geneva 1992), and recently A. Ellis-Evans, The Ideology of Public Subscriptions, in P. Martzavou and N. Papazarkadas (eds.), Epigraphical Approaches to the Post-Classical Polis: Fourth Century BC to Second Century AD (Oxford 2013) Singular: TAM V.1 509; plural: SEG XXXII 1273, LVI 1517, 1520, 1524; MAMA V 120, , 212, VII 303. See also RECAM II 61 ὑπὲρ βοιδίων. 14 TAM V Drew-Bear et al., Phrygian Votive Steles 305. The editors think that the fragmentary relief depicts a cow and a calf, but a goat and a kid are more probable according to the inscription. 16 E.g. L. Robert, Hellenica X (1955) 34 Δ ιὶ Ἐναυλίῳ Ἧρις Μελιφθόνγου εὐξάµενος ὑπὲρ τῶν θρεµµάτων (I.Byzantion 20, with SEG L 664 on the epithet Ἐναύλιος); TAM IV.1 74 ὑπὲρ τῶν ζῴων; Drew-Bear et al., Phrygian Votive Steles 609 ὑπὲρ κτήνους; SEG XXXIV 1214, ὑπὲρ τῶν κτηνῶν.

6 622 THE PROBLEM OF HYPER similar formulae suggests that young animals are meant: 17 the well-being of both was a main concern for agrarian families. 18 Just as pastoralists could pray for their livestock, farmers and vine-growers could pray for their crops with such formulae as ὑπὲρ (τῶν) καρπῶν, 19 ὑπὲρ σίτων, 20 ὑπὲρ ἀνπέλων. 21 The allinclusive formula ὑπὲρ τῶν ἰδίων or ὑπὲρ τῶν ἰδίων πάντων may refer to all family members and/or all personal matters (including possessions, and possibly livestock and crops). 22 The range of possible beneficiaries reflects the fundamental feature of Greek religion that benefits associated with offerings could flow to a third party in absence, and this need not be a human being. It illustrates the spheres of life in which Greeks depended on divine favours, and bears out Socrates advice that men should propitiate the gods in matters of agriculture no less than in war, and that sensible men would cultivate the gods for the good of their fruits, crops, cattle, horses, sheep, and indeed for all their possessions, οἱ σώφρονες καὶ ὑπὲρ ὑγρῶν καὶ ξηρῶν καρπῶν καὶ βοῶν καὶ ἵππων καὶ προβάτων καὶ ὑπὲρ πάντων γε δὴ τῶν κτηµάτων τοὺς θεοὺς θεραπεύουσιν (Xen. Oec. 5.20). In ancient societies where farming and animal husbandry constituted the main sources of livelihood, prayers for the healthy growth of crops and livestock were essentially 17 TAM V.1 322, with G. Petzl, Ländliche Religiosität in Lydien, in P. Herrmann (ed.), Forschungen in Lydien (Bonn 1995) 37 48, at 42 43, pl. 6.1 (the relief represents a leg, a pair of eyes, and breasts). For the combination of human beings and animals see also e.g. IG VII 50 ὑπὲρ ἑαυτῆς καὶ τῶν τέκνων καὶ τοῦ ἀνδρὸς καὶ τῶν θρεµµάτων; CIG 4120 ὑπὲρ ἑαυτῶν κὲ τῶν ἰδίων τ[ε]τραπόδων; L. D. Loukopoulou, Epigraphes tes Thrakes tou Aigaiou (Athens 2005) 389 ὑπὲρ ἑαυτοῦ καὶ θρεµµάτων καὶ τῶν ἰδίων εὐχαριστήριον; SEG LVII 1330 ὑπὲρ ἀνθρώπων καὶ τετραπόδων. 18 Discussed in Robert, Hellenica X E.g. MAMA V ; I.Iznik 1083, 1153, Th. Wiegand, AthMitt 29 (1904) 301 ὑπὲρ τῶν [καρπῶν καὶ] σίτων. 21 Drew-Bear et al., Phrygian Votive Steles 425 ὑπὲρ ἀνπ[έλων ]. 22 E.g. I.Délos 2413; TAM IV.1 89; Drew-Bear, Nouvelles inscriptions 42 no. 10, 47 no. 23; Drew-Bear et al., Phrygian Votive Steles 134, 498, 522; SEG XLI 1214, 1216, 1219, 1226.

7 THEODORA SUK FONG JIM 623 prayers for wealth and prosperity, and we would expect many more farmers, goatherds, shepherds, and cowherds all over the Greek world to have beseeched the gods for the well-being of their crops and animals. It is surprising, then, that, despite the great importance of these activities in most Greek societies, dedications for crops and animals come predominantly from Asia Minor. Farmers feature often in dedicatory epigrams and oracular consultations, 23 but are much harder to identify in the epigraphic record of mainland Greece. A rare instance from Attica is a third-century B.C. inscription mentioning sacrifice to Dionysus for the health and safety of the Council, the people of the Athenians, and the crops in the countryside, ἐφ ὑγιείαι καὶ σωτη[ρίαι τῆς βο]υλῆς καὶ τοῦ δήµου τοῦ Ἀθηναίων κα[ὶ τῶν κ]αρπῶν τῶν ἐν τεῖ χώραι. Oliver links this prayer for crops to the importance of the food supply to Athens survival during the Chremonidean War; yet this still does explain the absence of this formula in other periods of Athenian history when the food supply was equally critical. 24 Recently Schuler has explained the geographical imbalance of such epigraphic mater- 23 Epigrams: e.g. Anth.Gr , 31, 36, 40 42, 44 45, 53, 56, 79, 95, 98, 102, 104, 169, 225, 238, 258, 297. Oracular consultations concerning (περί) crops were quite common: e.g. E. Lhôte, Les lamelles oraculaires de Dodone (Geneva 2006) nos. 2, 76 79a. 24 IG II (266/5 B.C.), with discussion in G. J. Oliver, War, Food, and Politics in Early Hellenistic Athens (Oxford 2007) 131, 212. Other rites for agricultural prosperity were not absent in Attica and elsewhere. E.g. according to the lexicographers, the proerosia were pre-ploughing sacrifices performed by the Athenians on behalf of all the Greeks for the maturity of future crops (Suda π 2420 s.v. Προηροσίαι: αἱ πρὸ τοῦ ἀρότρου γινόµεναι θυσίαι περὶ τῶν µελλόντων ἔσεσθαι καρπῶν, ὥστε τελεσφορεῖσθαι ἐγίνετο δὲ ὑπὸ Ἀθηναίων ὑπὲρ πάντων Ἑλλήνων. A third-century B.C. calendar from Mykonos (LSCG 96) mentions a song for the crops, ᾠδὴ ὑπέρ καρποῦ, and sacrifices to Zeus Chthonios and Ge Chthonia ὑπὲρ κα[ρ]πῶν (16, 24 25). Several dedications for animals are attested in Hellenistic Crete: these were addressed to the Kouretes for larger cattle, πρὸ καρταιπόδων, and inscribed with similar formulae: I.Cret. I XXV 3, XXXI 7 8, Bull.épigr. 2012, 343 (second to first centuries B.C.).

8 624 THE PROBLEM OF HYPER ials in terms of what he calls regional epigraphic habit : prayers hyper crops and livestock must have been widespread, but only certain regions had the practice of inscribing them permanently on stone Hyper benefits While hyper in the above uses identifies the beneficiary without specifying the divine favour hoped for and/or attained (the safety or general well-being of the beneficiary is implied), the second kind of hyper explicitly names the benefit received and/ or sought from the gods. These two types of hyper are closely associated insofar as the benefit (in the genitive) was often attached to its recipient (in the genitive). The most common benefits prayed for were ὑγίεια ( health ) and σωτηρία ( safety, deliverance, salvation ). 26 One individual, for example, dedicated to Apollo ὑπὲρ τῆς ἑαυτοῦ σωτηρίας καὶ τῶν ἰδίων ἀµπέλων ἐπὶ ἄκραν, for his well-being and that of his vines at Akra (or on hilltop ). 27 It can be hard to distinguish ὑγίεια from σωτηρία when they appear alongside each other, but sometimes they could betray rather different concerns. In northwestern Lydia in 276/5 one Argeios set up a stele to Apollo Pityaenos for the health of himself and his wife and for the deliverance of his son Phanokritos, who was saved after being captured by the Galatians, ὑπέρ τε τῆς αὐτοῦ καὶ τῆς γυναικὸς ὑγιείας καὶ τῆς τοῦ υἱοῦ Φανοκρίτου σωτηρίας, ὃς ἁλοὺς ὑπὸ τῶν Γαλατῶν ἐσώθη (TAM V.2 881). This thankoffering combines different types of experiences and benefits: it was brought to the god for the well-being (ὑγίεια) of the couple 25 Schuler, in Epigraphy E.g. IG II ὑπὲρ ὑγιε[ίας καὶ σωτηρία]ς τῶν δηµοτῶν, ὑπὲρ ὑγιείας αὐτῶ[ν καὶ τῆς τοῦ δήµου] σωτηρ[ίας; Alt.Perg. VIII.3 81 ὑπὲρ σωτηρίας εὐχαριστήριν; SEG XXXIII 1153 ὑπὲρ τῆς κώµης σωτηρίας; IG XII.4 541, 543 ὑπὲρ σωτηρίας τῆς πόλεως; Drew-Bear et al., Phrygian Votive Steles 336 ὑπὲρ προβάτων σωτηρίας; MAMA V 212 ὑπὲρ βοῶν σωτηρ ίας κὲ [τ]ῶν ἰδί[ων π]άντων; VII 303 ὑπέρ βοῶν σωτηρίας; I.Iznik 1506 [ὑπὲρ] σωτηρίας καρ πῶ [ν]. 27 IGBulg I² 374. The marble relief depicts someone offering a sacrifice.

9 THEODORA SUK FONG JIM 625 (who were not captured) and the deliverance (σωτηρία) of their son Phanokritos, taken prisoner but now released, and demonstrates the capacity of Greek offerings to look simultaneously backward and forward. Instead of erecting two dedications, for his son and for his wife and himself, Argeios economically combined his attempts to return and secure divine favours in a single stele. As Argeios example shows, nothing prevented individuals from praying for different benefits for different beneficiaries in the same offering. Thus at Mons Claudianus in Egypt, an architect Apollonios dedicated an altar to Zeus Helios great Sarapis for the genius of the sovereign Caesar Trajan (ὑπερ τῆς τοῦ κυρίου Καίσαρος Τραιανου τύχης) and for the protection of all his (Apollonios ) works (ὑπὲρ τῆς σωτηρίας αὑτοῦ πάντων ἔργων). 28 While setting up an altar for the emperor s benefit, Apollonios did not forget to secure divine protection for his own (architectural) works. In the later period ὑγίεια and σωτηρία were occasionally replaced with ὀλοκληρία ( good health ) and διαµονή ( continuance, permanence ). 29 The use of διαµονή in prayers for ordinary individuals may have been due to imperial influence: dedicatory formulae for Roman emperors often used ὑπὲρ τῆς (αἰωνίου/ἀθανάτου) διαµονῆς, sometimes in conjunction with νίκη and σωτηρία A. Bernand, Pan du Désert 38, with SEG XLII 1577: Δ ιὶ Ἡλίῳ µεγάλῳ Σαράπιδι ὑπὲρ τῆς τοῦ κυρίου Καίσαρος Τραιανοῦ τύχης, ἐπὶ Ἐνκολπίῳ ἐπιτρόπῳ καὶ Κουίντῳ Ἀκκίῳ Ὀπτάτῳ (ἑκατοντά)ρχ(ῳ), Ἀπολλώνιος Ἀµµωνίου Ἀλεξανδρεὺς ἀρχιτέκτων ἀνέθηκεν ὑπὲρ τῆς σωτηρίας αὑτοῦ πάντων ἔργων. 29 E.g. TAM V [ὑ]πὲρ τῆς ὁλοκληρίας [τῶν] ποδῶν εὐχήν (relief of a pair of legs); I.Iznik 1131 ὑπὲρ τῆς ἑαυτοῦ καὶ τῶν ἰδίων πάντων καὶ Π. Πουστουµίου Σεουηρεανοῦ Ἀπολλόθεµι τοῦ ἰδίου πάτρωνος ὁλοκληρίας καὶ διαµονῆς Δ ιὶ Σωτῆρι. Robert, Hellenica X , discussed the rare and late formula ὑπὲρ τῆς ὁλοκληρίας καὶ διαµονῆς substituting for the usual ὑπὲρ ὑγιείας καὶ σωτηρίας; at he discussed imperial influence on the use of διαµονή. 30 E.g. IG II ὑπὲρ ὑγε[ίας] καὶ νείκης κα[ὶ διαµονῆς] τῶν Αὐτοκρα[τόρων] Μ. Αὐρηλίου Ἀντ[ωνείνου] καὶ Λουκίου Β[ήρου Σεβα]στῶν,

10 626 THE PROBLEM OF HYPER We find, used in relation to crops, ὑπὲρ εὐκαρπίας ( for good fruits ), ὑπὲρ ἀβλαβίας ( for freedom from harm ), and ὑπὲρ τελεσφορίας τῶν καρπῶν ( for the fulfilment of the crops ). 31 In the village of Nisyra in northeastern Lydia in the third century A.D., a dedication to Zeus Seleukios and the Nymphs Karpodoteirai ( Givers of Fruit ) was set up according to divine command for freedom from harm and the fulfilment of the crops (ὑπ ὲρ τῆς ἀβλαβείας καὶ τελεσφορίας τῶν καρπῶν ). 32 In Mysia, the villagers of the Thracian village (Θρακιοκωµῆται) prayed to Zeus Chalazios Sozon ( Protector from Hail ) for the fruitfulness and freedom from harm of their crops, and for the health and safety of their farmers and those assembling for the god and residents in the Thracian village, ὑπὲρ εὐκαρπίας καὶ ἀβλαβίας τῶν καρπῶν καὶ ὑπὲρ ὑγιείας καὶ σωτηρίας τῶν γεοκτειτῶν καὶ τῶν συνερχοµένων ἐπὶ τὸν θεὸν καὶ κατοικούντων Θρακίαν κώµην. 33 As these two texts show, in addition (and sometimes as an alternative) to using hyper, worshippers could express the benefits hoped and/or thanked for with the gods epithets, as if to reinforce the desired result. There were other ways of expressing benefits in dedicatory inscriptions. To mention only one related formula, clauses like 5205 [ὑ]πὲρ νίκης καὶ σωτηρίας καὶ ἀθανάτου δια[µο]νῆς τῶν δεσποτῶν τῆς οἰκουµέ[νης] Φλ. Ἀρκαδίου καὶ Φλ. Ὁνωρίου τῶν ἀηττήτω[ν Αὐγούσ]- των. 31 SEG XXXVI 1155 ὑπὲρ εὐκαρπίας, and nn below. See similarly with the preposition περί: Bull.épigr. 1956, 294 = SEG XIV 787 περὶ καρπῶν τηλεσφορίας; Drew-Bear, Nouvelles inscriptions 38 no. 3 περὶ τῶν ἰδίων πάντων σωτηρίας καρπῶν θελεσπορίας, for the safety of all private affairs (and) fulfilment of crops. 32 TAM V The phrase κατ ἐπιταγήν is also used in relation to crops in e.g. I.Iznik 1153, F. W. Hasluck, Unpublished Inscriptions from the Cyzicus Neighbourhood, JHS 24 (1904) 20 40, at 21 23, no. 4, with fig. 1. On Zeus as a weather god who could send and stop hail see A. B. Cook, Zeus III (Cambridge 1940) (this inscription), 944, and H. Schwabl, Zeus I. Epiklesien, RE 10A (1972) This is apparently the only epigraphic attestation of Zeus Chalazios; Apollo Chalazios is reported in Thebes.

11 THEODORA SUK FONG JIM 627 σωθεὶς ἐκ πολλῶν καὶ µεγάλων κινδύνων (or similar) were often used in conjunction with a hyper formula, though the two could also be used independently. A Coan (merchant?) who was saved from many great dangers set up a thank-offering on Delos to Sarapis, Isis, Anubis, Apollo, and gods in the same temple for (the deliverance of) himself and his two children: Πρῶτος Πυθίωνος Κῶιος, σωθεὶς ἐκ πολλῶν καὶ µεγάλων κινδύνων Σεράπει, Ἴσει, Ἀνούβει, Ἀπόλλωνι, θεοῖς συννάοις, ὑπὲρ αὑτοῦ καὶ τῶν παιδίων Φιλουµένης καὶ Πυθίωνος. 34 This is an expanded version of the more concise hyper soterias tinos. 3. hyper the deceased The third kind of hyper identifies a deceased person in whose name an offering was made. A rectangular base from Larissa from perhaps the fifth century B.C. bears this verse: Ἀργεία : µ ἀνέθεκε ὑπὲρ πα[ι]δὸς τόδ ἄγαλµα / εὔξατ ο : δ Ἁγέ[τ]ορ ϝαστικᾶι : Ἐνοδίαι, Argeia dedicated me, this statue, on behalf of her son, but Hagetor vowed it to Enodia of the city. 35 If it is correct to understand Argeia as Hagetor s mother, the implication seems to be that her son had died before dis- 34 I.Délos 2119 (undated). See also I.Alex.Imp. 6 ὑπὲρ Θεανοῦς τῆς θυγατρὸς σωθείσ[ης] ἐ γ µεγάλων κ<ι>ν δ ύ ν ω ν. Thank-offerings for rescue are discussed in C. Habicht, Danksagungen Geretteter an die Götter, Hyperboreus 7 (2001) , and Weitere Weihungen Geretteter, Hyperboreus 8 (2002) IG IX.2 575; Lazzarini, Le formule no. 725; CEG 342; SEG XXXV 590 (dated ca ); C. Löhr, Griechische Familienweihungen (Rahden 2000) no. 63; LGPN III.b s.v. Ἀργεία (3). But surrogate dedications in fulfilment of another s vow could be expressed by formulae other than hyper: e.g. IG I [τ]ο π[α]τρὸς εὐχσ[αµένο], 705 [εὐχσα(?)]µένον προγό[νον], 735 το τέκνο εὐχ[σαµένο], 773 µετρ<ὸ>ς ἐπ[ευχσαµένες]; IG IX [µ]ατέρος εὐχολάν; Drew-Bear et al., Phrygian Votive Steles 465 Ἐπίτησσις διὰ πα[ιδ]ί ων εὐχήν. See also Diog. Laert : Aristotle had made a vow for Nikanor s safety but died before being able to discharge it; in his will, therefore, he asked Nikanor to dedicate, upon his safe return, four-cubit stone statues to Zeus Soter and Athena Soteira in Stagira, in fulfilment of the vow made on his behalf, ἀναθεῖναι δὲ καὶ Νικάνορα σωθέντα, ἣν εὐχὴν ὑπὲρ αὐτοῦ ηὐξάµην.

12 628 THE PROBLEM OF HYPER charging his vow to Enodia; consequently it became necessary for the mother to perform this on his behalf. The mother made the dedication in place of or in the name of her deceased son. This is different from the above instances where ὑπὲρ παιδός (or similar, cf. n.6) refers to the act of dedicating in the interest of or for the well-being of the child named. The repayment of a vow was normally the obligation of the person who made it, but in cases such as death it might be undertaken by someone else. Underlying surrogate dedications is the Greeks concept that debts owed to the gods must be settled: not even death could erase them. The fear of owing the gods their due is alluded to in Plato s Republic: Cephalus tells Socrates that the greatest use of money is in settling a debt, so that one need not fear going to the other world while owing any sacrifice to a god or money to a person (331B C). Some dedications were made ὑπὲρ τοῦ πατρός and/or µητρός; 36 but the lack of contextual information makes it difficult to know whether these were erected in the name of deceased parents (who could not fulfill their vow), for the health of aging parents (as in category (1) above), or for some other purpose. Some dedications mention that the father or mother had held certain public offices, with hyper taking on the sense of in honour of. In Hellenistic Lindos, for example, honorific dedications were set up hyper the dedicator s father who had served as the priest of Athena Lindia and Zeus Polieus, ὑπὲρ τοῦ πατρὸς ἰερατεύ σαντος Ἀθαναίας Λινδίας καὶ Δ ιὸς Πολιέως, sometimes with the addition of other gods E.g. Lindos II 132 ὑπὲρ τᾶς µατρός; 133 ὑπὲρ τοῦ πατρός; 145 ὑπὲρ τοῦ πατρὸς κ<α>ὶ τᾶς µατρός; Löhr, Griechische Familienweihungen no. 119 ὑπὲρ τῆς µητρός. Little is known about the individuals in these inscriptions, but all the statue bases appear to have supported the portrait statue of the parent(s) named, suggesting that these families must have been well-off. 37 E.g. IG XII.1 813, 820; Lindos II 157, 168. Cf. other priesthoods or offices commemorated: e.g. CIRB 6 = Löhr, Griechische Familienweihungen no. 97 ὑπὲρ πατρὸς τοῦ ἑαυτοῦ Δ εινοστράτο ἱερησαµένου Ἀπόλλωνι Ἰητρῶι; Clara Rhodes 2 (1932) 196 no. 24 ὑπὲρ τοῦ πατρὸς φυλαρχήσαντος καὶ νικάσαντος Δ ιοσκούρια καὶ γραµµατεύσαντος βουλᾶι; IGBulg I² 21 ὑπὲρ τῆς

13 THEODORA SUK FONG JIM 629 Nevertheless, without knowing the parents life dates and the precise time of the dedications, it is difficult to tell whether these monuments were set up posthumously or during the parents life-time. As we have seen, 38 however, death need not be the only reason why an individual fulfilled a religious obligation hyper another. A late inscription from Gerasa in Syria illustrates another context in which an offering might be brought hyper another (I.Gerasa 53, A.D. 119/120): ἀγαθῇ τύχῃ. ἔτους βπρʹ. ὑ[πὲρ] τῆς τῶν Σεβαστῶν σωτηρίας Δ ιογένης Ἐµµεγάνου ἱερασάµενος 4 τῶν τεσσάρων ἐπαρχειῶν ἐν Ἀντιοχείᾳ τῇ µητροπόλι ἄγαλµα Δ ικαιοσύνης ὑπὲρ Εὐµένους τοῦ υἱοῦ τῇ πατρίδι ἀνέθηκεν, ὃ ἐπηνγείλατο ὑπὲρ τοῦ 8 Εὐµένους ἀγορανοµοῦντος. With good fortune. In the 182th year. For the well-being of the Emperors, Diogenes, son of Emmeganos, priest of the four eparchies in Antioch the mother-city, dedicated a statue of Justice on behalf of his son Eumenes to the fatherland, which he promised for Eumenes office of agoranomos. This text is interesting for its successive uses of hyper. The formula ὑ[πὲρ] τῆς τῶν Σεβαστῶν σωτηρίας (1 2) was extremely common in the imperial period as a prayer for the general wellbeing of the Roman emperors and an expression of the dedi- µητρὸς Γ<λ>υκέρας ζακορευούσης Δ ήµητρος. See recently J. Ma, Statues and Cities: Honorific Portraits and Civic Identity in the Hellenistic World (Oxford 2013) (on statues commemorating the tenure of a priesthood or other offices by family members, attested on Rhodes and elsewhere), (statues set up as memorials of the deceased, sometimes upon their wish or instruction). Contrast Jewish dedications for the memory of the deceased: e.g. IGLS IV 1370 ὑπερ µνίας προγόνων. The phrase ὑπερ µνίας occurs also in IGLS IV 1636, but it is uncertain whether this was a dedication or a tombstone. 38 E.g. IG IV (n.10 above).

14 630 THE PROBLEM OF HYPER cator s goodwill and loyalty to them. The second hyper clause (6), though also identifying a third party (the dedicator s son) for whom the dedication was set up, is rather different in meaning and function: Diogenes was setting up a statue on behalf of or in the name of his son, who was appointed agoranomos. What is alluded to is the imperial practice of summa honoraria: magistrates would erect a monument, undertake public work, or pay a sum for holding a particular office, ὑπερ τῆς ἀρχῆς or ἀντὶ τῆς ἀρχῆς, 39 here for Eumenes office of agoranomos, ὑπὲρ τοῦ Εὐµένους ἀγορανοµοῦντος. It is unclear whether Eumenes had promised the monument but could not fulfill it, or whether his father had promised to do so on his behalf should he become agoranomos (as the third hyper clause seems to suggest, that is, if it is correct to understand ἐπηνγείλατο as referring to Diogenes announcement). 40 Both cases are possible: such an obligation was normally announced and discharged by the office-holder, but it could also be performed by a family member on his behalf. A comparable text from Laodicea in Syria shows a woman undertaking various constructions on behalf of her husband in return for his appointment as a council member, ὑπὲρ Νεικάτορος ἀντὶ τῆς βολῆς, and for (the general well-being of ) her children, ὑπ[ὲρ τέ]κνων <α>ὐτῆς, with the two hyper clauses conveying rather different concerns. 41 In Laodicea, as in the Gerasa text, the dedicator was fulfilling a religious obligation on behalf of or in the name of a family member, a duty in- 39 On summa honoraria see L. Robert, Etudes épigraphiques, BCH 60 (1936) , at (with further examples); Etudes anatoliennes (Paris 1937) Robert (1936) 196: au titre de telle magistrature (ὑπερ τῆς ἀρχῆς) or en échange de telle magistrature (ἀντὶ τῆς ἀρχῆς). 40 Cf. the formula ἐξ ἐπαγγελίας ἀνέθηκεν in I.Gerasa 10, 15, , where the office-holder appears to be the one who both promised the dedication and fulfilled it. 41 IGLS IV 1259, discussed in Robert, BCH 60 (1936) : Ἀπολλωνία Ζη[ ] ὑπὲρ Νεικάτορος Τερτύλλου τοῦ αὑτῆ[ς ἀνδρός], ἀντὶ τῆς βολῆς τὰς ἓ[ξ/ἔ[ξω] θυρίδας ἐθύρωσε καὶ ε[ἰς] εἴκοσι µεσόστυλ<α> ὑπ[ὲρ τέ]κνων <α>ὐτῆς τὰς βαθ[µίδας] ταῖς <λ>ιθοστρώτο<ι>ς ἐ[πέθηκε(?)].

15 THEODORA SUK FONG JIM 631 curred by the tenure of an office. The final hyper in the Gerasa inscription has a vaguely causal sense, and may be translated as on account of, for the tenure of or for the appointment of (not for the benefit of or in honour of ) Eumenes as agoranomos, though there is probably a vague sense of benefit for the individual named and a desire to commemorate his tenure of the office. Used in a myriad of formulae, hyper requires a slightly varying translation if we are to spell out its precise meaning in a given context, but we can also pass over the differences by rendering it vaguely as for. In fact the Greek hyper functioned like English for : one can expand or abbreviate its meaning as one wants. Its pervasive and wide-ranging applications probably lie in part in its flexibility and imprecision. Despite the frequent use of hyper, other prepositions might also be used in the same sense, the most common being περί with genitive. 42 Perhaps because of the confusion and/or the combination of the two, we sometimes find the form ὑπερί. 43 Other prepositions include ἀντί (with genitive, for the sake of ), ἕνεκα/ ἕνεκεν (with genitive, on account of, for the sake of ), ἐπί 42 E.g. Drew-Bear, Nouvelles inscriptions 29 no.1 περὶ τῶν ἰδίων σωτηρίας, 35 no. 2 πε[ρ]ὶ τῆς κ[ώ]µ[ης] σ[ω]τ [ηρίας], 38 no. 3 περὶ τῶν ἰδίων πάντων σωτηρίας κ(αὶ) καρπῶν θελεσπορίας; Drew-Bear et al., Phrygian Votive Steles 601 περὶ ὤµου; SEG LVI 1523 περὶ ἑαυτοῦ κὲ τῶν ἰδίων, 1608 περὶ τέκνων [κὲ τῶν?] εἰδίων [πάντων], 1613 [π]ε ρ ὶ β ο ῶ ν σ ωτηρίας. 43 Drew-Bear et al., Phrygian Votive Steles 588 ὑπερὶ ὑπ[αρ]χόντων; SEG LVI 1518 ὑπερ ὶ β [οῶν]. The formula ὑπερὶ εὐχῆς (καὶ σωτηρίας) appears in e.g. IG XII.1 911, TAM IV.1 370, MAMA IV 120B, 120(a). Further examples are cited in Bull.épigr. 1968, 541, and S. Şahin, ZPE 38 (1980) 184. The form is hardly ever explained, except in E. Nachmanson, Syntaktische Inschriftenstudien, Eranos 9 (1909) 30 81, at 74: ὑπερί aus ὑπέρ und περί kontaminiert, and the commentary of H. Grégoire, Recueil des inscriptions grecques chrétiennes d Asie Mineure (Paris 1922) no. 2 (ὑπερὶ εὐχῆς τῶν χωρίων καὶ ): l existence de cette préposition, née de la contamination de περί et de ὑπέρ, est certaine. Grégoire, Recueil no. 40, reads ὑπερεὶ εὐχ[ῆς ], and he wondered la graphie ὑπερεὶ est-elle due à l analogie de ὡσεί, ὡσανεί, ὡσπερεί?

16 632 THE PROBLEM OF HYPER (with genitive, with reference to, or with dative, for the purpose of ), and χάριν (with genitive, for the sake of ). 44 Whether to use hyper or other formulae was a matter of personal choice, exercised perhaps completely randomly and without conscious thought. If the various uses and meanings of hyper seem more or less clear, it is less easy to uncover the precise circumstances in which the prayers and/or offerings were made. Broadly speaking, we may distinguish between two main kinds of offerings associated with hyper: precautionary ones made to maintain the beneficiary s present well-being (or low-intensity offerings), and those induced by crises when someone was sick or in trouble ( high-intensity offerings). 45 Where hyper is followed by a plural noun (ὑπὲρ τῶν παιδίων/τέκνων, ὑπὲρ βοῶν), a generic noun (ὑπὲρ τῶν κτηνῶν/τετραπόδων/ἰδίων) or family members combined with livestock (ὑπὲρ ἑαυτοῦ καὶ θρεµµάτων καὶ τῶν ἰδίων), the original prayers were probably precautionary, made for the health and safety of the whole group, and not when any single one was at risk. Yet this cannot be taken as a general rule, as we cannot exclude the possibilities that some calamity might have affected all of them or that different needs and experiences might have been combined in a single formula. 46 The interpretative problems presented by these formulae can be illustrated with a few examples. In the fourth century B.C., at Hermonassa on the north coast of the Black Sea, someone brought a dedication on behalf of his wife to Apollo the Healer, 44 E.g. Gonnoi II 173 ἀντὶ τέκνων; Anth.Gr νίκης ἀντὶ τῆς ἰδίης; TAM V σωτηρίας ἕνεκεν; IG II 2 223, 354, 410 ἐφ ὑγιείαι καὶ σωτηρίαι; F. T. van Straten, Gifts for the Gods, in H. S. Versnel (ed.), Faith, Hope and Worship (Leiden 1981) , at 136 no ἐπὶ τοῦ ἰδίου σώµατος; Strab and , τῆς τῶν πλοϊζοµένων σωτηρίας χάριν. Note also πρό with genitive in the Cretan dedications mentioned in n.24, πρὸ καρταιπόδῶν. 45 This distinction between low intensity and high intensity rituals was used originally by J. Van Baal, Offering, Sacrifice and Gift, Numen 23 (1976) As in TAM V (quoted 624 above).

17 THEODORA SUK FONG JIM 633 Δ ηµοφῶν Ἐργίνο ἀνέθηκεν ὑπὲρ τῆς γυναικὸς Ἄκιος Ἀπόλλωνι Ἰητρῶι. Was this an acknowledgement of his wife s recovery from some affliction, or was it a low intensity offering intended to build up favour with Apollo in his role as healer? 47 Equally ambiguous are such texts as Ἀσκλαπιῶι Ἀρχίδαµος Κνίδιος ὑπὲρ τοῦ ὑοῦ Συµµάχου and Κράτης ὑπὲρ Εὐφράνορος Σαράπι, Ἴσι when we are given no further contextual information. 48 Another interesting instance comes from fourthcentury Athens: a couple dedicated in fulfilment of a vow to Asclepius on behalf of their children, on behalf of Hediste, Sosikles, and Olympiodoros, Μει δ ίας καὶ Δ αναὶς εὐξάµενοι Ἀσκληπιῶι ὑπὲρ τῶν παιδίων ὑπὲρ Ἡδίστης καὶ Σωσικλέους καὶ Ὀλυνπιοδώρου. 49 Given that Asclepius had already granted a favour (presumably concerning the children s health), why should the couple be so specific as to name each of their children with a second hyper formula, as if ὑπὲρ τῶν παιδίων were not sufficient? Doubtless they wanted to thank Asclepius for the favour received and at the same time bring each of their children to the god s attention again, so as to place them under his continued protection. If the original prayer was precautionary, as Parker suggests, made for the health of the whole group and not for healing when one was sick, we have yet to consider how and when the parents decided on the right moment to discharge the vow. Might they have waited until their children reached a certain age (say, their tenth birthday), or until they could afford the expenses? Or might their original vow have 47 CIRB 1037 = Löhr, Griechische Familienweihungen no. 92 (a base for a bronze statue); Löhr entertains the possibility that this was associated with healing. 48 IG XII (fourth century, Cos), cf. 548 (third century, Cos). Similar interpretative problems arise from IG II Ἀσσκληπιῶι ἀ[νέθηκε] ὑπὲρ τῆς θυγα[τρὸς] Θεαν[οῦς] (a small marble base). 49 IG II = R. Parker, Dedications. Greek Dedications, ThesCRA I (2004) , at , no. 54 = Löhr, Griechische Familienweihungen no On dedications hyper children (plural) in fulfilment of a vow see also IG II , 4481; I.Kourion 61; SEG XXXIII 1003.

18 634 THE PROBLEM OF HYPER been time-restricted ( if our children are well for the next two years, then )? As the last Athenian example shows, many dedicatory formulae with hyper were associated with vows. This was indicated usually by εὐξάµενος/εὐξαµένη and occasionally εὐχωλή in the early period, and by the noun εὐχή from the fourth century on. 50 Some late inscriptions have εὐχῆς ἕνεκεν, 51 κατὰ εὐχήν, 52 and sometimes ὑπὲρ ὧν εὐξάµην ( for what I vowed ). 53 A similar idea seems to have been expressed by the related formula ὑπὲρ εὐχῆς, common in Christian dedicatory inscriptions. 54 It is fair to assume that, where the aorist participle εὐξάµενος (and/or χαριστήριον/α) is used, the offering was a response to some divine favour already attained. The plain εὐχή, however, allows some room for alternative interpretations, as strictly speaking εὐχή can mean a prayer, a vow, or a votive offering. 55 One Menandros dedicated on behalf of his oxen to Zeus Limenos (in fulfilment of?) a vow, ὑπὲρ βοῶν Δ ι ὶ Λιµνην [ῷ ε]ὐ χήν. Another individual dedicated on behalf of all his private matters to Zeus Alsenos (in fulfilment of?) a vow, ὑπὲρ τῶν ἰδίων πάντων Δ ιὶ Ἀλσηνῷ εὐχήν. 56 Could any of these have been presented to the gods 50 Dedicatory formulae related to vow fulfilment are studied in Lazzarini, Le formule On vows and votive religion see e.g. Burkert, Greek Religion (Griechische Religion ); J. Rudhardt, Notions fondamentales de la pensée religieuse et actes constitutifs du culte dans la Grèce classique 2 (Paris 1992) ; S. Pulleyn, Prayer in Greek Religion (Oxford 1997) E.g. IGBulg. III , III ; I.Iznik E.g. TAM IV.1 59, V ; SEG XLIV 637; IG VII 225; I.Délos 2127, E.g. SEG XLI 1012; see also P. Herrmann and H. Malay, New Documents from Lydia (Vienna 2007) 98 περὶ ὧν εὐξάµην. 54 E.g. IG V.1 974; SEG XV 141, XXX , XXXI 587, XXXIV 584, XXXV 643, XXXVII 464, 502, LVI 1678 ὑπὲ[ρ] εὐχῆς κὲ σωτ ηρίας. 55 LSJ Suppl. s.v. εὐχή I.b understands the noun without a verb in dedicatory contexts as votive offering. 56 SEG LVI 1520 = Drew-Bear et al., Phrygian Votive Steles 498.

19 THEODORA SUK FONG JIM 635 prospectively instead of retrospectively, with εὐχή referring to the prayer made at the time of bringing the object? As Pulleyn points out, the Greeks did not normally pray empty-handed, but would accompany their prayers with a cultic action or an offering, usually a libation or a sacrifice. 57 Yet nothing prevented worshippers from bringing a durable gift when making a request, while promising another one should it be granted, as long as they could afford to do so. In healing contexts, it has been suggested, anatomical dedications could have been offerings preliminary to treatment instead of thank-offerings for cures already effected. 58 Nevertheless, attestations of the phrase ἀποδιδόναι εὐχήν, to discharge a vow (which one had made), in some late inscriptions make it more likely that the plain εὐχή was an abbreviated way of saying (in fulfilment of) a vow. 59 The processes of making a vow, attaining the prayer, and fulfilling the promise, normally left implicit in most offerings, are in some inscriptions spelt out by the formula εὐξάµενος καὶ ἐπιτυχών. A late dedication from Thrace was set up for the safety of Roimetalkos and Pythodoris from the danger in the war against the Koilaletai, having made a vow and obtained it, as a thank-offering, θεῶι ἁγίωι ὑψίστωι ὑπὲρ τῆς Ῥοιµητάλκου καὶ Πυθοδωρίδος ἐκ τοῦ κατὰ τὸν Κοιλα[λ]ητικὸν πόλεµον κινδύνου σωτηρίας εὐξάµενος καὶ ἐπιτυχὼν Γάϊος Ἰούλιος Πρόκ<λ>ος χαριστ[ήρι]ον. 60 More ambiguous in fact 57 Pulleyn, Prayer, esp W. H. D. Rouse, Greek Votive Offerings (Cambridge 1902) 191; van Straten, in Faith , , with doubts in Parker, ThesCRA I (2004) E.g. G. E. Bean and T. B. Mitford, Journeys in Rough Cilicia (Vienna 1970) 249 εὐξάµενος ἀπέδωκεν τὴν εὐχήν; SEG XXIII 763 εὐξαµένη τὴν εὐχὴν ἀπέδωκεν; I.Iznik εὐχὴν ἀπέδωκεν; TAM V εὐχὴν ἀπέδωκα, 319 ἀπέδω[καν] τὴν εὐχήν (a confession stele); L. Robert, Hellenica VI (1948) no. 42 [ἀπέδ]ωκα τὴν εὐχήν. 60 IGR I 777. The formula εὐξάµενος καὶ ἐπιτυχών is attested in dedications mostly in Thrace and Moesia Inferior, and some in Asia Minor: e.g. IGBulg III , 1888, IV 2134; TAM V.1 455; SEG XXXIV 1214; W. Ameling, Inscriptiones Judaicae Orientis II (Tübingen 2004) 149.

20 636 THE PROBLEM OF HYPER are dedications without εὐξάµενος/εὐξαµένη or εὐχή (or similar), 61 and those which depict a body part without any accompanying inscription. 62 The brevity, ambiguity, and sometimes absence of these dedicatory formulae leave the precise details difficult to reconstruct. Prospective and retrospective offerings are also often confused and muddled because of the continuous nature of giftexchange: gifts and counter-gifts between men and gods could, and ideally would, form a constant cycle, so that it is not always clear which party first initiated the process. However interesting it may be for historians to uncover the precise context of dedication, in fact the distinction between prospective and retrospective offerings ceases to be meaningful when a gift is considered, not as an isolated act, but as part of a continuous series of interactions between the Greeks and their gods. 63 The distinction drawn above between low-intensity (precautionary) and high-intensity (crisis-induced) offerings is in fact not always clear-cut. It can be blurred and fluid since the moment a divine favour was granted was also very likely the moment of transition from a high- to a low-intensity situation. 61 Consider e.g. Lindos II 153: in the second century B.C. a general named Kleisimbrotidas, son of Antigonos, together with Timokrates, son of Aretakritos, set up a dedication to the gods for the safety of Kleisimbrotidas (i.e. himself) who was general over the territory, ὑπὲρ Κλεισιµβροτίδα στραταγήσαντος ἐπὶ τᾶς χώρας. Was this dedication set up before the general went to battle or after his safe return, and/or is it a commemoration of his generalship? 62 Anatomical dedications without inscriptions: e.g. Drew-Bear et al., Phrygian Votive Steles 27, 30, 34, 35, 40, 42 43, 46, (with illustrations). The examples cited here have survived more or less intact, but of course there remains the possibility that some inscriptions were obliterated and that some stelai were not completed for dedication. 63 On reciprocity between men and gods see A. J. Festugière, Ἀνθ Ὧν, RSPh 60 (1976) ; J. M. Bremer, Reciprocity of Giving and Thanksgiving in Greek Worship, in C. Gill et al. (eds.), Reciprocity in Ancient Greece (Oxford 1998) ; R. Parker, Pleasing Thighs: Reciprocity in Greek Religion, in Reciprocity

21 THEODORA SUK FONG JIM 637 A confession stele from the area of Ibrahim in Lydia tells how one Diogenes had made a vow on behalf of his ox but failed to discharge it. Consequently his daughter was punished with respect to her eyes, and he set up the stele to appease the god: Δ ιεὶ Πειζηνῷ Δ ιογένη[ς] εὐξάµενος ὑπὲρ τοῦ βοὸς κὲ µὴ ἀποδοὺς ἐκολάσθη αὐτοῦ ἡ θυγάτηρ Τατιανὴ ἰς τοὺς ὀφθαλµούς νῦν οὖν εἱλασάµενοι ἀνέθηκαν. 64 His ox must have been cured of some illness by the god, who then withdrew his favour by making Diogenes daughter sick instead. Whether Diogenes simply forgot or intentionally evaded his debt, his neglect of the promise shows that once his prayer was granted, it became less important to him to fulfil the vow. What was originally a highintensity offering had become, after his ox was saved, in some sense a low-intensity one. Worshippers who duly discharged their vow after a crisis might often have both the past and the future in mind: their thank-offering could acknowledge a past favour and, at the same time, the hope that their present fortune might last, so that it was crisis-related and precautionary at once. This dual nature of offerings can be illustrated with Herodas Fourth Mime: two women bring a cock and a pinax to Asclepius in gratitude for being cured, and pray that they may come again with their husbands and children in full health bringing larger offerings. 65 Whether an offering was high- or low-intensity or both, therefore, can be a matter of perspective: it depends on where we focus our attention (the original prayer, its answer, vow fulfilment, a new request) and which direction we look (backward and/or forward) in a continuum of humandivine interactions. Seemingly simple to translate, hyper formulae often leave their 64 G. Petzl, Die Beichtinschriften Westkleinasiens, Epigr.Anat. 22 (1994) no. 45 = TAM V = L. Robert, Nouvelles inscriptions de Sardes I (Paris 1964) Herod , 86 88; parallels cited in W. Headlam, Herodas: The Mimes and Fragments (Cambridge 1922). See also Aristid Keil: the hymn to Sarapis is described explicitly as a thank-offering for past favours and a supplication for the future.

22 638 THE PROBLEM OF HYPER readers baffled on closer scrutiny, given their frustratingly vague, uninformative, and ambiguous nature. So much is left implicit that it can be difficult for historians to pin down the nature of the original prayer (precautionary or crisis-induced), the context of offering (prospective or retrospective or both), and, if precautionary, how individuals decided when to discharge their vow (if one was involved). We therefore have to concede the impossibility of discovering fully the precise details behind these formulae. They assume a degree of knowledge that was not felt to require further specification or explanation: what is unclear to us must have been clear to their divine recipients. Seen thus, Greek dedications are perhaps not so markedly different from the anonymous Christian texts after all: the gods knew. 66 June, 2014 Lancaster University t.jim@lancaster.ac.uk 66 I am most grateful to Professor Robert Parker and GRBS s anonymous referees for helpful comments and suggestions on earlier versions of this article.

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

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

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

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

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

«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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 1 State vector space and the dual space Space of wavefunctions The space of wavefunctions is the set of all

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

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

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ

ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΛΛΗΝΙΔΕΣ ΕΛΛΗΝΙΔΕΣ ΣΟΡΟΠΤΙΜΙΣΤΡΙΕΣ ΕΚΔΟΣΗ ΤΗΣ ΣΟΡΟΠΤΙΜΙΣΤΙΚΗΣ ΕΝΩΣΗΣ ΕΛΛΑΔΟΣ - ΤΕΥΧΟΣ Νο 110 - Δ ΤΡΙΜΗΝΟ 2014 Το πρώτο βραβείο κέρδισε η Ελλάδα για την φωτογραφία Blue + Yellow = Green στον διαγωνισμό 2014 του

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

«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

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

PARTIAL NOTES for 6.1 Trigonometric Identities

PARTIAL NOTES for 6.1 Trigonometric Identities PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot

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

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

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

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

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

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

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

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

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

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1

Econ 2110: Fall 2008 Suggested Solutions to Problem Set 8  questions or comments to Dan Fetter 1 Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test

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

3.4 Αζηίεξ ημζκςκζηήξ ακζζυηδηαξ ζημ ζπμθείμ... 64 3.4.1 Πανάβμκηεξ πνμέθεοζδξ ηδξ ημζκςκζηήξ ακζζυηδηαξ... 64 3.5 οιαμθή ηςκ εηπαζδεοηζηχκ ζηδκ

3.4 Αζηίεξ ημζκςκζηήξ ακζζυηδηαξ ζημ ζπμθείμ... 64 3.4.1 Πανάβμκηεξ πνμέθεοζδξ ηδξ ημζκςκζηήξ ακζζυηδηαξ... 64 3.5 οιαμθή ηςκ εηπαζδεοηζηχκ ζηδκ 2 Πεξηερόκελα Δονεηήνζμ πζκάηςκ... 4 Δονεηήνζμ δζαβναιιάηςκ... 5 Abstract... 6 Πενίθδρδ... 7 Δζζαβςβή... 8 ΘΔΩΡΗΣΙΚΟ ΜΔΡΟ... 12 Κεθάθαζμ 1: Θεςνδηζηέξ πνμζεββίζεζξ βζα ηδκ ακζζυηδηα ζηδκ εηπαίδεοζδ...

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ. Πτυχιακή Εργασία

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ. Πτυχιακή Εργασία ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία ΣΤΑΣΕΙΣ ΚΑΙ ΓΝΩΣΕΙΣ ΤΩΝ ΝΟΣΗΛΕΥΤΩΝ ΓΙΑ ΤΟΝ ΕΓΚΕΦΑΛΙΚΟ ΘΑΝΑΤΟ ΚΑΙ ΤΗ ΔΩΡΕΑ ΟΡΓΑΝΩΝ Μαρία Χάννα Λεμεσός 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ

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

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

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

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

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

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

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

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

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

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

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

Η ΨΥΧΙΑΤΡΙΚΗ - ΨΥΧΟΛΟΓΙΚΗ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΗ ΣΤΗΝ ΠΟΙΝΙΚΗ ΔΙΚΗ

Η ΨΥΧΙΑΤΡΙΚΗ - ΨΥΧΟΛΟΓΙΚΗ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΗ ΣΤΗΝ ΠΟΙΝΙΚΗ ΔΙΚΗ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΝΟΜΙΚΗ ΣΧΟΛΗ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΤΟΜΕΑΣ ΙΣΤΟΡΙΑΣ ΦΙΛΟΣΟΦΙΑΣ ΚΑΙ ΚΟΙΝΩΝΙΟΛΟΓΙΑΣ ΤΟΥ ΔΙΚΑΙΟΥ Διπλωματική εργασία στο μάθημα «ΚΟΙΝΩΝΙΟΛΟΓΙΑ ΤΟΥ ΔΙΚΑΙΟΥ»

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

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

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

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

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

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Οικονομία Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών Τέλος Ενότητας Χρηματοδότηση Το παρόν εκπαιδευτικό υλικό έχει αναπτυχθεί

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

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

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

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

Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους

Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους ΑΛΕΞΑΝΔΡΕΙΟ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΣΧΟΛΗ ΤΕΧΝΟΛΟΓΙΑΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΜΗΜΑ ΔΙΑΤΡΟΦΗΣ ΚΑΙ ΔΙΑΙΤΟΛΟΓΙΑΣ Πτυχιακή Εργασία Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους Εκπόνηση:

Διαβάστε περισσότερα

Η αλληλεπίδραση ανάμεσα στην καθημερινή γλώσσα και την επιστημονική ορολογία: παράδειγμα από το πεδίο της Κοσμολογίας

Η αλληλεπίδραση ανάμεσα στην καθημερινή γλώσσα και την επιστημονική ορολογία: παράδειγμα από το πεδίο της Κοσμολογίας Η αλληλεπίδραση ανάμεσα στην καθημερινή γλώσσα και την επιστημονική ορολογία: παράδειγμα από το πεδίο της Κοσμολογίας ΠΕΡΙΛΗΨΗ Αριστείδης Κοσιονίδης Η κατανόηση των εννοιών ενός επιστημονικού πεδίου απαιτεί

Διαβάστε περισσότερα

HIV HIV HIV HIV AIDS 3 :.1 /-,**1 +332

HIV HIV HIV HIV AIDS 3 :.1 /-,**1 +332 ,**1 The Japanese Society for AIDS Research The Journal of AIDS Research +,, +,, +,, + -. / 0 1 +, -. / 0 1 : :,**- +,**. 1..+ - : +** 22 HIV AIDS HIV HIV AIDS : HIV AIDS HIV :HIV AIDS 3 :.1 /-,**1 HIV

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

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

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

Capacitors - Capacitance, Charge and Potential Difference

Capacitors - Capacitance, Charge and Potential Difference Capacitors - Capacitance, Charge and Potential Difference Capacitors store electric charge. This ability to store electric charge is known as capacitance. A simple capacitor consists of 2 parallel metal

Διαβάστε περισσότερα

Terabyte Technology Ltd

Terabyte Technology Ltd Terabyte Technology Ltd is a Web and Graphic design company in Limassol with dedicated staff who will endeavour to deliver the highest quality of work in our field. We offer a range of services such as

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΠΕΛΟΠΟΝΝΗΣΟΥ

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΠΕΛΟΠΟΝΝΗΣΟΥ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΠΕΛΟΠΟΝΝΗΣΟΥ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΔΙΟΙΚΗΣΗΣ ΕΠΙΧΕΙΡΗΣΕΩΝ ΚΑΙ ΟΡΓΑΝΙΣΜΩΝ Κατ/νση Τοπικής Αυτοδιοίκησης ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ «Μοντέλα στρατηγικής διοίκησης και

Διαβάστε περισσότερα

Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1

Main source: Discrete-time systems and computer control by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 A Brief History of Sampling Research 1915 - Edmund Taylor Whittaker (1873-1956) devised a

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

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 3: Phrases to use in business letters and e-mails Το περιεχόμενο του μαθήματος διατίθεται

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

ω ω ω ω ω ω+2 ω ω+2 + ω ω ω ω+2 + ω ω+1 ω ω+2 2 ω ω ω ω ω ω ω ω+1 ω ω2 ω ω2 + ω ω ω2 + ω ω ω ω2 + ω ω+1 ω ω2 + ω ω+1 + ω ω ω ω2 + ω

ω ω ω ω ω ω+2 ω ω+2 + ω ω ω ω+2 + ω ω+1 ω ω+2 2 ω ω ω ω ω ω ω ω+1 ω ω2 ω ω2 + ω ω ω2 + ω ω ω ω2 + ω ω+1 ω ω2 + ω ω+1 + ω ω ω ω2 + ω 0 1 2 3 4 5 6 ω ω + 1 ω + 2 ω + 3 ω + 4 ω2 ω2 + 1 ω2 + 2 ω2 + 3 ω3 ω3 + 1 ω3 + 2 ω4 ω4 + 1 ω5 ω 2 ω 2 + 1 ω 2 + 2 ω 2 + ω ω 2 + ω + 1 ω 2 + ω2 ω 2 2 ω 2 2 + 1 ω 2 2 + ω ω 2 3 ω 3 ω 3 + 1 ω 3 + ω ω 3 +

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

Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ

Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Τ.Ε.Ι. ΔΥΤΙΚΗΣ ΜΑΚΕΔΟΝΙΑΣ ΠΑΡΑΡΤΗΜΑ ΚΑΣΤΟΡΙΑΣ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Η προβολή επιστημονικών θεμάτων από τα ελληνικά ΜΜΕ : Η κάλυψή τους στον ελληνικό ημερήσιο τύπο Σαραλιώτου

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

ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΟΥ ΑΝΘΡΩΠΟΥ

ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΟΥ ΑΝΘΡΩΠΟΥ ΓΕΩΠΟΝΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΗΣ ΤΡΟΦΙΜΩΝ ΚΑΙ ΔΙΑΤΡΟΦΗΣ ΤΟΥ ΑΝΘΡΩΠΟΥ Πρόγραμμα Μεταπτυχιακών Σπουδών «Επιστήμη και Τεχνολογία Τροφίμων και Διατροφή του Ανθρώπου» Κατεύθυνση: «Διατροφή, Δημόσια

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