It is common in Koiné Greek for subject-topics that are identified with a noun phrase to be placed

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "It is common in Koiné Greek for subject-topics that are identified with a noun phrase to be placed"

Transcript

1 Τις Noun Order as an Anchoring Device in Luke-Acts Stephen H. Levinsohn and Anthony G. Pope SIL International Abstract Clausal and phrasal constituents in Koiné Greek are placed before the verb for two distinct reasons: 1. to emphasise a focal constituent 2. to provide a cohesive anchor to something which is already in the context (i.e., to something accessible in the hearer s mental representation). 1 This paper argues that the second of these reasons explains every instance in Luke-Acts in which the indefinite adjective τις precedes a head noun in the same case (N). Such preposing of τις cohesively anchors the referent of the phrase to the preceding context (e.g., to signal, in Ac 16.14, that Lydia is a member of the group of women mentioned in the previous line ). 2 When τις follows N, in contrast, the referent is unmarked for anchoring. Since N τις order is default, a positive claim that the referent is unanchored is not possible. Nevertheless, referents of N τις are typically not tied to anything in the preceding context (e.g., because they occur at the beginning of a parable or episode). 1. Preliminaries It is common in Koiné Greek for subject-topics that are identified with a noun phrase to be placed after the verb in narratives. For example, in Acts 16.36a (ἀπήγγειλεν δὲ ὁ δεσµοφύλαξ τοὺς λόγους [τούτους] πρὸς τὸν Παῦλον), the subject as topic is the noun phrase ὁ δεσµοφύλαξ, and the subject follows the verb ἀπήγγειλεν. 3 Typologically, Koiné Greek shares a number of features with other languages that often locate the verb before subject-topics that are noun phrases in stories. 4 One such feature is the potential to place clausal and phrasal constituents before the verb for two distinct reasons: 1. to emphasise a focal constituent 5 2. to provide a cohesive anchor to something which is already in the context (i.e., to something accessible in the hearer s mental representation). 6 We first illustrate a focal constituent placed before the verb to emphasise it. The topic of Lk 22.44b (ἐκτενέστερον προσηύχετο) is he and the proposition has predicate focus, 7 which in this 1 Dooley, Robert A., and Stephen H. Levinsohn, Analyzing Discourse: A Manual of Basic Concepts. (Dallas: SIL International, 2001), p Read-Heimerdinger, Jenny, The Bezan Text of Acts: A Contribution to Textual Criticism. Journal of the Study of the New Testament, Supplement Series 236 (London/New York: Sheffield Academic Press, 2002), p A referent is interpreted as the topic of a proposition if in a given situation the proposition is construed as being about this referent, i.e. as expressing information which is relevant to and which increases the addressee s knowledge of this referent Lambrecht, Knud, Information Structure and Sentence Form: Topic, Focus, and the Mental Representation of Discourse Referents (New York: Cambridge University Press, 1994), p See Levinsohn, Stephen H., Language Types, Discourse Studies and Translation. Paper presented at a public meeting at Handong Global University, Pohang, South Korea, in April 2008, sec. 1.1 (electronic copy available on request). As well as Ancient Hebrew, many N.W. Austronesian languages of the Philippines and Oto-Manguean languages of Mexico commonly place subject-topics that are noun phrases after the verb in narratives (ibid.). 5 The focus of a proposition is what is relatively the most important information in the given setting Dik, Simon, Functional grammar (Amsterdam: North-Holland, 1978), p Dooley and Levinsohn, Analysing Discourse, p Lambrecht, Information Structure, p. 222.

2 Τις Noun Order as an Anchoring Device in Luke-Acts p.2 instance, means that ἐκτενέστερον προσηύχετο is focal. However, one of these focal constituents, ἐκτενέστερον, is placed before the verb to emphasise it. Now consider Ac 21.6c (ἐκεῖνοι δὲ ὑπέστρεψαν εἰς τὰ ἴδια). The topic is they and the pronoun ἐκεῖνοι is placed before the verb to signal the switch of attention from we in 6b (καὶ ἀνέβηµεν εἰς τὸ πλοῖον). In other words, notwithstanding the change of topic from we to they, the pre-verbal subject ἐκεῖνοι anchors the new proposition to something which is already in the context, which in this case is the previous subject. Linguists view the verb as the HEAD of its clause, with other constituents in a dependent relation to it. 8 So, to generalise the principle that Ac 21.6c has just illustrated, one of the reasons for placing a dependent constituent before its HEAD is to provide a cohesive anchor to something which is already in the context. We will now argue that this same principle explains nearly every instance in Luke- Acts in which the indefinite adjective τις 9 precedes a HEAD noun in the same case (N). 10 In other words, the dependent constituent τις is placed before its HEAD noun to provide a cohesive anchor to something in the preceding context. When τις follows N, in contrast, the referent is unmarked for anchoring. The rest of the paper concentrates on N τις versus τις N orders in references to animate participants in Luke-Acts (sec. 2). This is followed by short sections on N τις versus τις N ordering with references to times (sec. 3) and places (sec. 4). 2. N τις and τις N orders in references to animate participants We start, then, with the assumption that the N τις order is default. Robertson states that τις naturally follows the substantive or adjective. 11 Read-Heimerdinger writes, Adjectival τις is more often than not placed after the noun and describes this as the usual order. 12 Statistics confirm these claims; N τις order is found about 28 times in Luke and 39 times in Acts, whereas τις N order occurs 10 times in Luke and 28 times in Acts, sometimes with an intervening constituent (see discussion below). 13 Since N τις order is default, it would be inappropriate to make a positive claim that the referent of such a noun phrase is unanchored. Nevertheless, it is true that referents of N τις are typically not tied to anything in the preceding context. This is particularly evident when the reference occurs at the beginning of a parable (10 times in Luke) 14 or episode (at least 9 times in Luke and 14 times in 8 See, for example, Van Valin Jr., Robert D., Exploring the Syntax-Semantics Interface (Cambridge: Cambridge University Press, 2005), p Winer calls τις an indefinite pronoun Winer, G. B., A Treatise on the Grammar of New Testament Greek. (Edinburgh: T. and T. Clark, 1882), p This paper does not discuss the placement of τις before a genitive expression as in τις τῶν µαθητῶν αὐτοῦ. Nor does it address what Winer (Treatise, p. 212) calls the use of τις with rhetorical emphasis, as he cites no examples from Luke-Acts. The same is true of Turner s discussion of τις meaning quidam = so to speak Turner, N., Syntax. Vol. 3, A Grammar of New Testament Greek, by J. H. Moulton (Edinburgh: T. and T. Clark, 1963), p Τις relatively rarely modifies a noun in the same case in the other Gospels. N τις ordering is found in Mk 14.47, 14.51, 15.21, 16.18, Jn 12.20, and as a variant in Mk 5.25 (D Θ Byz). Τις N ordering occurs in Mt and Jn 1.46, 4.46, 5.5, Robertson, A. T., A Grammar of the Greek New Testament in the Light of Historical Research. (New York, London: Harper, n.d. [copyrighted 1934]), p Read-Heimerdinger, Bezan Text of Acts, p. 99. See also Turner s observation: tis and ti occasionally, when used adjectivally, stand before their noun Turner, Grammar, p The text followed is Nestle-Aland 27 th edition revised (Aland, Barbara, Kurt Aland, Johannes Karavidopoulos, Carlo M. Martini, and Bruce M. Metzger (eds.), Novum Testamentum Graece [Stuttgart: Deutsche Bibelgesellschaft, 1994]). 14 Lk 7.41, 10.30, 12.16, 14.16, 15.11, 16.1, & 20, 18.2a,

3 Τις Noun Order as an Anchoring Device in Luke-Acts p.3 Acts). 15 See, for example, the parable that begins in Lk (Ἄνθρωπός τις κατέβαινεν ἀπὸ Ἰερουσαλὴµ εἰς Ἰεριχὼ) and the episode that begins in Lk 1.5 (Ἐγένετο ἐν ταῖς ἡµέραις Ἡρῴδου βασιλέως τῆς Ἰουδαίας ἱερεύς τις ὀνόµατι Ζαχαρίας). In contrast, placing τις before its HEAD noun is a marked order that cohesively anchors the referent of the noun phrase to the preceding context. In Ac 16.14, for instance, it anchors Lydia (καί τις γυνὴ ὀνόµατι Λυδία) to the group of women mentioned at the end of v. 13 (ἐλαλοῦµεν ταῖς συνελθούσαις γυναιξίν). As Read-Heimerdinger observes, Tις precedes γυνὴ in the introduction of Lydia when she is singled out from the group of women mentioned in the previous line. 16 In Ac 20.9, τις N order anchors Eutychus (τις νεανίας ὀνόµατι Εὔτυχος ἐπὶ τῆς θυρίδος) to the group in Troas that Paul was teaching (ὁ Παῦλος διελέγετο αὐτοῖς v. 7) and who had assembled in an upstairs room (ἐν τῷ ὑπερῴῳ οὗ ἦµεν συνηγµένοι v. 8). In Ac 9.43, τις N order anchors Simon the tanner (Ἐγένετο δὲ ἡµέρας ἱκανὰς µεῖναι ἐν Ἰόππῃ παρά τινι Σίµωνι βυρσεῖ) to the believers in Joppa (καὶ ἐπίστευσαν πολλοὶ ἐπὶ τὸν κύριον). 17 In Ac (below), the angel makes reference to two Simons. The first (Σίµωνά τινα ὃς ἐπικαλεῖται Πέτρος) employs default N τις order, as no attempt is made to anchor Simon Peter to anything in the context. 18 In contrast, the reference to the second Simon (παρά τινι Σίµωνι βυρσεῖ) employs τις N order, thus anchoring the reference to something in the earlier part of the speech, such as the town in which he lived. 19 (1) καὶ νῦν πέµψον ἄνδρας εἰς Ἰόππην καὶ µετάπεµψαι Σίµωνά τινα ὃς ἐπικαλεῖται Πέτρος οὗτος ξενίζεται παρά τινι Σίµωνι βυρσεῖ, ᾧ ἐστιν οἰκία παρὰ θάλασσαν. (Ac ) 15 Lk 1.5, 7.2, 8.2, 8.27, 10.25, 10.38b, 14.2, 18.35, 23.26; Ac 5.1, 8.9, 9.33, 10.1, 13.6, 16.1, 16.9 (beginning the report of a vision), 16.16, 18.24, 19.24, 22.12, 24.1a & 1b, See also Lk (A C W Θ Ψ Byz and early versions; also D but reversing the order) and 20.9 (A W Θ al syr). An episode is a group of events that belong together and are described in one or more paragraphs Levinsohn, Stephen H., Discourse Features of New Testament Greek: A Coursebook on the Information Structure of New Testament Greek, 2 nd. edition. (Dallas: SIL International, 2000), p The Nestle-Aland text often marks the beginning of a new episode with paragraph indentation. In each instance cited here, the expression with τις occurs in the first or second sentence after the indentation. 16 Read-Heimerdinger, Bezan Text of Acts, p However, she describes the placement of τις before the noun more in terms of focussing attention on the person it refers to (p. 99) than on its anchoring effect. In many languages, an adjective translated one, a certain is used to indicate that the referent is salient (Hopper, Paul J., and Sandra A. Thompson, The discourse basis for lexical categories in universal grammar. Language , 1984), p In other words, when a referent is introduced with an adjective like τις (either before or after the head noun), he or she continues to be topical in the following material, particularly if the referent becomes uniquely identifiable Wallace, Daniel B., Greek Grammar Beyond the Basics: An Exegetical Syntax of the New Testament (Grand Rapids MI: Zondervan, 1995), p In Ac (κατῆλθέν τις ἀπὸ τῆς Ἰουδαίας προφήτης ὀνόµατι Ἅγαβος), Read-Heimerdinger (Bezan Text of Acts, p. 100) relates Agabus to the Judean prophets mentioned in We think it more likely that the position of τις in anchors him to v. 9, where Philip s daughters are described as having the gift of prophecy. 17 When he says that Peter stayed with a tanner, it can be deduced from this the kind of people of which the church at Joppa consisted Calvin, John, The Acts of the Apostles, volume I, translated by W.J.G. McDonald (Grand Rapids MI: Eerdmans, 1965), p That Simon the tanner was a member of the church is also recognized by Zahn Zahn, Theodor, Die Apostelgeschichte des Lucas (Leipzig: Deichert, 1919), p א E Ψ omit τινα corr from respect to the Apostle Alford, Henry, The Greek Testament, 5 th edition (London: Rivingtons, 1863), Vol. II, p Ac 18.2 (καὶ εὑρών τινα Ἰουδαῖον ὀνόµατι Ἀκύλαν) is similar. Placing τινα before Ἰουδαῖον probably anchors Aquila to the city of Corinth in which he is now resident, this being the location that has just been introduced.

4 Τις Noun Order as an Anchoring Device in Luke-Acts p.4 In Lk 21.2 (below), τις N order is used to refer to the poor widow (τινα χήραν πενιχρὰν), 20 thus anchoring her to the scene in which the wealthy are putting their gifts into the treasury. 21 (2) Ἀναβλέψας δὲ εἶδεν τοὺς βάλλοντας εἰς τὸ γαζοφυλάκιον τὰ δῶρα αὐτῶν πλουσίους. εἶδεν δέ τινα χήραν πενιχρὰν βάλλουσαν ἐκεῖ λεπτὰ δύο, (Lk ) In Ac 5.34 (ἀναστὰς δέ τις ἐν τῷ συνεδρίῳ Φαρισαῖος ὀνόµατι Γαµαλιήλ), τις is separated from its HEAD noun Φαρισαῖος by the locative ἐν τῷ συνεδρίῳ. 22 However, the τις N order still anchors the referent to the scene in which the council was deliberating over the case of the apostles. 23 Τις N ordering is particularly noteworthy when it is found at the beginning of what the Nestle-Aland text judges to be a new paragraph, as such an ordering anchors the referent to the previous episode. For example, the Nestle-Aland text begins a new paragraph at Ac 14.8 (below), but it is clear from v. 9 that the lame man in Lystra (τις ἀνὴρ ἀδύνατος ἐν Λύστροις τοῖς ποσὶν) was one of the people to whom Paul and Barnabas were preaching the good news. (3) συνιδόντες κατέφυγον εἰς τὰς πόλεις τῆς Λυκαονίας Λύστραν καὶ έρβην καὶ τὴν περίχωρον, κἀκεῖ εὐαγγελιζόµενοι ἦσαν. Καί τις ἀνὴρ ἀδύνατος ἐν Λύστροις τοῖς ποσὶν ἐκάθητο, χωλὸς ἐκ κοιλίας µητρὸς αὐτοῦ ὃς οὐδέποτε περιεπάτησεν. οὗτος ἤκουσεν τοῦ Παύλου λαλοῦντος (Ac ) The Nestle-Aland text also begins a new paragraph at Ac 9.10 (below). By referring to Ananias with τις N order, he is anchored to the context of the previous episode. The anchoring is in the first instance to the reference to Damascus in v. 8, but also links him to Saul s planned persecution of the believers in Damascus (v. 2) something he himself alludes to later (v. 13). (4) χειραγωγοῦντες δὲ αὐτὸν εἰσήγαγον εἰς αµασκόν. καὶ ἦν ἡµέρας τρεῖς µὴ βλέπων καὶ οὐκ ἔφαγεν οὐδὲ ἔπιεν. Ἦν δέ τις µαθητὴς ἐν αµασκῷ ὀνόµατι Ἁνανίας, (Ac 9.8b-10a) Ac 19.1 (below) is another instance of τις N ordering at the beginning of an episode. Such ordering anchors the disciples Paul found (τινας µαθητὰς) to Apollos ( ). 24 (5) Ἰουδαῖος δέ τις Ἀπολλῶς ὀνόµατι, Ἀλεξανδρεὺς τῷ γένει, ἀνὴρ λόγιος, κατήντησεν εἰς Ἔφεσον, δυνατὸς ὢν ἐν ταῖς γραφαῖς. οὗτος ἦν κατηχηµένος τὴν ὁδὸν τοῦ κυρίου καὶ ζέων τῷ πνεύµατι ἐλάλει καὶ ἐδίδασκεν ἀκριβῶς τὰ περὶ τοῦ Ἰησοῦ, ἐπιστάµενος µόνον τὸ βάπτισµα Ἰωάννου Ἐγένετο δὲ ἐν τῷ τὸν Ἀπολλῶ εἶναι ἐν Κορίνθῳ Παῦλον διελθόντα τὰ ἀνωτερικὰ µέρη [κατ]ελθεῖν εἰς Ἔφεσον καὶ εὑρεῖν τινας µαθητὰς εἶπέν τε πρὸς αὐτούς, Εἰ πνεῦµα ἅγιον ἐλάβετε πιστεύσαντες; οἱ δὲ πρὸς αὐτόν, Ἀλλ οὐδ εἰ πνεῦµα ἅγιον ἔστιν ἠκούσαµεν. (Ac , ) In a number of passages, an episode with τις N ordering at the beginning follows one with a related theme, so the τις N ordering provides an anchor to that episode. For example, consider the τις N 20 A variant reading is τινα καὶ χήραν πενιχρὰν (A W Θ Byz), in which case χήραν πενιχρὰν would be in apposition to τινα. 21 In contrast to the many rich is one poor widow Bock, Darrell L., Luke Volume 2: 9:51-24:53 (Grand Rapids MI: Baker Books, 1996), p Alternatively, ἐν τῷ συνεδρίῳ Φαρισαῖος ὀνόµατι Γαµαλιήλ may be judged to be in apposition to τις. 23 Ac (τι περὶ σοῦ πονηρόν) is similar. The τι N ordering anchors the referent to the context, in particular, Paul s claim (v. 17), οὐδὲν ἐναντίον ποιήσας τῷ λαῷ ἢ τοῖς ἔθεσι τοῖς πατρῴοις. 24 These seem to have been in the same situation as Apollos, knowing only John s baptism Alford, Greek Testament, Vol. II, p. 210.

5 Τις Noun Order as an Anchoring Device in Luke-Acts p.5 ordering in Lk 18.9 (Εἶπεν δὲ καὶ πρός τινας τοὺς πεποιθότας ἐφ ἑαυτοῖς ὅτι εἰσὶν δίκαιοι καὶ ἐξουθενοῦντας τοὺς λοιποὺς τὴν παραβολὴν ταύτην). Such ordering anchors those who trusted in themselves that they were righteous and regarded others with contempt to the parable of the unjust judge (18.1-8), both of which ostensibly have to do with prayer ostensibly since, in each case, much more is at stake than prayer when defined modestly as a practice. 25 In fact, the anchoring of the self-righteous to the context is confirmed by other surface features: the initial event-type verb (Εἶπεν), which suggests continuity with the context; 26 the particle δέ, which indicates that the new episode builds on and develops from the previous one; 27 and the additive καί, which draws a parallel between the parable told in this episode and the one told before. 28 A similar argument may be applied to Lk 13.31, in which the τις N ordering of reference to some Pharisees (τινες Φαρισαῖοι) anchors the new episode to the previous one, in particular, the theme of progress towards Jerusalem in v. 22, which is the point of vv In Ac 3.2 (below), τις N ordering anchors the lame man (τις ἀνὴρ χωλὸς ἐκ κοιλίας µητρὸς αὐτοῦ ὑπάρχων) to the context. The immediately preceding verse describes Peter and John going up to the temple at the hour of prayer, accompanied, no doubt, by thousands of other people (2.46a reads, καθ ἡµέραν τε προσκαρτεροῦντες ὁµοθυµαδὸν ἐν τῷ ἱερῷ). Is the reference to the lame man, then, to be anchored to the implied crowds who were going up to the temple, or is he cited as an example of the signs and wonders that were being done by the apostles (2.43)? 30 (6) Πέτρος δὲ καὶ Ἰωάννης ἀνέβαινον εἰς τὸ ἱερὸν ἐπὶ τὴν ὥραν τῆς προσευχῆς τὴν ἐνάτην. καί τις ἀνὴρ χωλὸς ἐκ κοιλίας µητρὸς αὐτοῦ ὑπάρχων ἐβαστάζετο, (Ac 3.1-2) Before leaving this section, we need to point out three examples which are residual, because it is not clear why τις and its HEAD noun have been separated by another constituent. They are Lk (ἐπάρασά τις φωνὴν γυνὴ ἐκ τοῦ ὄχλου), 31 Lk (Καὶ ἐπηρώτησέν τις αὐτὸν ἄρχων) 32 and Ac 9.36 (Ἐν Ἰόππῃ δέ τις ἦν µαθήτρια ὀνόµατι Ταβιθά). 25 Green, Joel B., The Gospel of Luke. The New International Commentary on the New Testament (Grand Rapids MI: Eerdmans, 1997), p Green also thinks that the hearers of the two parables may have been the same, since the designation of the audience of Jesus parable seems to assume an expanded audience (ibid.). Michael Wilcock (The Saviour of the World: The Message of Luke's Gospel, Leicester: IVP, 1979) notes (p. 164) that the link is more profound than merely two parables about prayer; it is the spiritual reality on which true prayer must be based, namely the personal relationship which enables man to get in touch with God. 26 v 9 contains nothing to suggest a change of scene Green, Luke), ibid. See also Levinsohn, Discourse Features, p Levinsohn, Discourse Features, p Levinsohn, Discourse Features, p. 99. However, A W Byz omit the καί. 29 The theme of Jesus' journey to Jerusalem, announced in v. 22, comes into sharper focus Marshall, I. Howard, The Gospel of Luke: A Commentary on the Greek Text (Exeter: The Paternoster Press, 1978), pp. 568f. Luke ties this conversation into its local co-text by employing a temporal reference, at that very hour, that urges his readers to see an interpretive link between vv and the present pericope (Green, Luke, pp. 534f). 30 He [Luke] has referred to the many wonders and signs which were performed through the apostles (2.43); now he proceeds to record one instance of these Bruce, F.F., The Acts of the Apostles: Greek text with Introduction and Commentary, 3 rd revised and enlarged edition (Grand Rapids MI: Eerdmans, 1990), p Zahn thinks the lame man would not only have been recognized by the apostles but would also have recognized them, given that they were regular templegoers and the believers were known for their generosity to the needy ( ) Zahn, Apostelgeschichte, p The pre-verbal reference to Peter and John in Ac 3.1 anchors the new episode to the transitional material by signalling a switch of attention to them from the subjects of the previous verses, while the particle δέ indicates that the new episode builds on and develops from what has already been stated. 31 In Lk 11.27, however, the split phrase is found only in אp75 B L. The rest of the Greek manuscript tradition has ἐπάρασά τις γυνὴ and then proceeds with one of two further word order variations.

6 Τις Noun Order as an Anchoring Device in Luke-Acts p.6 In the case of Lk 11.27, not only is there a thematic link between the teaching of the two pericopes, 33 but the rest of the phrase itself (γυνὴ ἐκ τοῦ ὄχλου) anchors the woman to those who heard the teaching of the previous pericope. In the case of Lk 18.18, the link with the previous episode (vv ) is thematic; both concern entry into the Kingdom of God. In particular, the reference to the ruler, who is rich (v. 23), may have been anchored to the children, who have nothing, to bring out the contrast between them. 34 As for Ac 9.36, the preposing of Ἐν Ἰόππῃ already anchors the episode to the previous one on the basis of a switch of place. 35 So it is entirely appropriate that the reference to the disciple called Tabitha should be anchored to the previous episode, which also concerns a healing involving the apostle Peter. 36 We conclude that it seems safe to assert that τις N order in Luke-Acts always has the effect of anchoring the referent to the context, whether within an episode or across episode boundaries. 3. N τις and τις N orders in references to times References to some days with a plural form of τις are found six times in Acts (none occur in Luke). Default order is used on three occasions when a comment about a topic includes ἡµέρας τινὰς (e.g., Ἐγένετο δὲ µετὰ τῶν ἐν αµασκῷ µαθητῶν ἡµέρας τινὰς Ac 9.19; see also and 16.12). Ac is similar, except that the temporal expression is χρόνον τινὰ. Ac begins Ἡµερῶν δὲ διαγενοµένων τινῶν, which again has default order, but this time the phrase is split. When this happens, the author usually wishes to emphasise one part of the phrase. 37 In this instance, however, it is by no means certain that such is the case. 38 The other two references to times that include τις are both pre-verbal and anchor the new proposition to something which is already in the context (sec. 1); viz., the time of the previous episode. We discuss them in turn. In Ac (below), τινας is placed before ἡµέρας. This has the effect of further anchoring the time to the period that Paul and Barnabas were staying in Antioch (v. 35). (7) Παῦλος δὲ καὶ Βαρναβᾶς διέτριβον ἐν Ἀντιοχείᾳ διδάσκοντες καὶ εὐαγγελιζόµενοι µετὰ καὶ ἑτέρων πολλῶν τὸν λόγον τοῦ κυρίου. Μετὰ δέ τινας ἡµέρας εἶπεν πρὸς Βαρναβᾶν Παῦλος, (Ac a) 32 Blass, Debrunner and Funk cite Lk as a New Testament example of the old rule that unemphatic (enclitic) pronouns and the like are placed as near the beginning of the sentence as possible Blass, F., A. Debrunner, and R. W. Funk, A Greek Grammar of the New Testament (Chicago: Chicago University Press, 1961), [True blessedness] belongs to those into whose hearts he has come with his message of salvation, so that there is no longer any place there for the ousted spirit of evil Wilcock, Saviour of the World, p The children, like the publican, are nearer the Kingdom than they could suppose themselves to be; the rich young man, like the Pharisee, is farther from it than he supposed himself to be Plummer, Alfred, A Critical and Exegetical Commentary on the Gospel according to St. Luke (Edinburgh: T. and T. Clark. 1896), p See also Zahn, Theodor, Das Evangelium des Lucas, (Leipzig: Deichert, 1913) p The same sequence of episodes occurs in Matthew and Mark. 35 Levinsohn, Discourse Features, p See Marshall, I. Howard, The Book of Acts: An Introduction and Commentary. The Tyndale New Testament Commentaries (Grand Rapids MI: Eerdmans, 1980), p See Levinsohn, Discourse Features, p All one can say of the period is that it seemed more natural to measure it in days than in years Barrett, C.K., Acts Volume II: XV-XXVIII. The International Critical Commentary (Edinburgh: T. & T. Clark, 1998), p

7 Τις Noun Order as an Anchoring Device in Luke-Acts p.7 The Nestle-Aland text of Ac (below) places ἡµέρας before τινὰς, which is the default order and does not specifically anchor some days to the time of vv (8) Ἀνεβάλετο δὲ αὐτοὺς ὁ Φῆλιξ, ἀκριβέστερον εἰδὼς τὰ περὶ τῆς ὁδοῦ εἴπας, Ὅταν Λυσίας ὁ χιλίαρχος καταβῇ, διαγνώσοµαι τὰ καθ ὑµᾶς διαταξάµενος τῷ ἑκατοντάρχῃ τηρεῖσθαι αὐτὸν ἔχειν τε ἄνεσιν καὶ µηδένα κωλύειν τῶν ἰδίων αὐτοῦ ὑπηρετεῖν αὐτῷ. Μετὰ δὲ ἡµέρας τινὰς παραγενόµενος ὁ Φῆλιξ σὺν ρουσίλλῃ τῇ ἰδίᾳ γυναικὶ (Ac a) 4. N τις and τις N orders in references to places Most references to places that include τις have default order. 40 The examples with marked order are discussed below. The first example of marked order is in Lk 17.12, which may be contrasted with Lk 10.38a, as both refer to a certain village. The Nestle-Aland text begins a new paragraph at (Ἐν δὲ τῷ πορεύεσθαι αὐτοὺς αὐτὸς εἰσῆλθεν εἰς κώµην τινά) and the context makes no reference to a location, so default order is to be expected. In contrast, Lk (below) follows a reference to the region between Samaria and Galilee (v. 11), so placing τινα before κώµην has the effect of anchoring the village to these places. (9) καὶ αὐτὸς διήρχετο διὰ µέσον Σαµαρείας καὶ Γαλιλαίας. καὶ εἰσερχοµένου αὐτοῦ εἴς τινα κώµην (Lk a) In Lk 18.2 (Κριτής τις ἦν ἔν τινι πόλει), placing τινι before πόλει has the effect of anchoring the place to the judge, as he was judge in that city. 41 In Ac 8.36 (ὡς δὲ ἐπορεύοντο κατὰ τὴν ὁδόν, ἦλθον ἐπί τι ὕδωρ), placing τι before ὕδωρ has the effect of anchoring the water to the road along which the travellers were going. 42 Ac (below) also places τινὰ before its head noun (χώραν), which suggests that the reference to the land is anchored to the place mentioned in the preceding clause (ἐν τῷ Ἀδρίᾳ). (The phrase is split by αὐτοῖς see the comment about split phrases at the end of sec. 2.) (10) Ὡς δὲ τεσσαρεσκαιδεκάτη νὺξ ἐγένετο διαφεροµένων ἡµῶν ἐν τῷ Ἀδρίᾳ, κατὰ µέσον τῆς νυκτὸς ὑπενόουν οἱ ναῦται προσάγειν τινὰ αὐτοῖς χώραν. (Ac 27.27) 5. Conclusion We have shown that, when the indefinite adjective τις precedes a head noun in the same case in Luke-Acts, such preposing of τις cohesively anchors the referent of the phrase to the context. Such an order is particularly significant when it occurs at the beginning of a new episode, as it indicates that the referent is to be anchored to something in the context of the previous episode. We began this paper by pointing out that clausal and phrasal constituents in Koiné Greek are placed before the verb for two distinct reasons: to provide a cohesive anchor to something which is already in the context, or to emphasise a focal constituent. Preliminary studies of the order of constituents in 39 The variant ordering Μετὰ δέ τινας ἡµέρας (A E Ψ pc) would have the effect of anchoring the some days of v. 24 to the implied period of v. 23 during which Paul was in the custody of the centurion (p74 reads ὀλίγας ἡµέρας). 40 Lk 10.38a, 11.1; Ac 27.8, 16, 26, Jesus links this judge with a city probably because that is where the audience expected a judge to function Hendriksen, William, The Gospel of Luke (Edinburgh: The Banner of Truth Trust, 1978), p when the travellers reached a stream Marshall, Acts, p. 165.

8 Τις Noun Order as an Anchoring Device in Luke-Acts p.8 noun phrases indicate that one or both of these factors explain not only the marked positioning of τις, but also the preposing of adjectives, numerals and other modifiers before their HEAD noun.

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

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

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

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

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

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

Section 8.3 Trigonometric Equations

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

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

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

Διαβάστε περισσότερα

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

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

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

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

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

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

Modern Greek Extension

Modern Greek Extension Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

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

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

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 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

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

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

Διαβάστε περισσότερα

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

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

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

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

Herodian and the Greek language: rules of thumb for accenting Greek enclitics. Stephanie Roussou (a joint project with Philomen Probert)

Herodian and the Greek language: rules of thumb for accenting Greek enclitics. Stephanie Roussou (a joint project with Philomen Probert) Herodian and the Greek language: rules of thumb for accenting Greek enclitics Stephanie Roussou (a joint project with Philomen Probert) What are enclitics? Enclitics are small words forming close-knit

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

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

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

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

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

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

Subject - Students love Greek.

Subject - Students love Greek. A Summer Greek 2009 Ω Parts of Speech NOUN - person, place, thing, quality, idea, or action ARTICLE Indefinite = a / an ; Definite = the ADJECTIVE - describes a noun (includes in/definite articles) VERB

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

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 9: Inversion Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons εκτός

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

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

Λέξεις, φράσεις και προτάσεις

Λέξεις, φράσεις και προτάσεις 1 Λέξεις, φράσεις και προτάσεις (Words, phrases and clauses) The Greek language, like all human languages, has a Lexicon and a Grammar that are used to create sentences. The Lexicon consists of the words

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

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

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

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

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

Present Participles. Verbal Adjectives with Present Aspect. A lesson for the Paideia web-app Ian W. Scott, 2015

Present Participles. Verbal Adjectives with Present Aspect. A lesson for the Paideia web-app Ian W. Scott, 2015 Present Participles Verbal Adjectives with Present Aspect A lesson for the Paideia web-app Ian W. Scott, 2015 Participles with Present Aspect Participle = a verbal adjective Allows a whole clause to tell

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

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

LESSON TEN: THE ADJECTIVE. Memorization of vocabulary ten

LESSON TEN: THE ADJECTIVE. Memorization of vocabulary ten LESSON TEN: THE ADJECTIVE Memorization of vocabulary ten ἀγαθος good ἁγιος holy, set apart ἀλλα but (the regular contrasting particle, with δε used at times) ἀληθεια truth ἀληθινος true/genuine αὐτος he

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ - ΤΜΗΜΑ ΠΛΗΡΟΦΟΡΙΚΗΣ ΕΠΛ 133: ΑΝΤΙΚΕΙΜΕΝΟΣΤΡΕΦΗΣ ΠΡΟΓΡΑΜΜΑΤΙΣΜΟΣ ΕΡΓΑΣΤΗΡΙΟ 3 Javadoc Tutorial

ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ - ΤΜΗΜΑ ΠΛΗΡΟΦΟΡΙΚΗΣ ΕΠΛ 133: ΑΝΤΙΚΕΙΜΕΝΟΣΤΡΕΦΗΣ ΠΡΟΓΡΑΜΜΑΤΙΣΜΟΣ ΕΡΓΑΣΤΗΡΙΟ 3 Javadoc Tutorial ΕΡΓΑΣΤΗΡΙΟ 3 Javadoc Tutorial Introduction Το Javadoc είναι ένα εργαλείο που παράγει αρχεία html (παρόμοιο με τις σελίδες στη διεύθυνση http://docs.oracle.com/javase/8/docs/api/index.html) από τα σχόλια

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

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

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

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

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

[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

«Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων. Η μεταξύ τους σχέση και εξέλιξη.»

«Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων. Η μεταξύ τους σχέση και εξέλιξη.» ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΑΓΡΟΝΟΜΩΝ ΚΑΙ ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΓΕΩΓΡΑΦΙΑΣ ΚΑΙ ΠΕΡΙΦΕΡΕΙΑΚΟΥ ΣΧΕΔΙΑΣΜΟΥ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ: «Χρήσεις γης, αξίες γης και κυκλοφοριακές ρυθμίσεις στο Δήμο Χαλκιδέων.

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

Summer Greek Lesson 3 - Vocabulary

Summer Greek Lesson 3 - Vocabulary A Summer Greek 2006 Ω ἀδελφή, ἡ ἀλήθεια, ἡ βασιλεία, ἡ δόξα, ἡ ἐκκλησία, ἡ ἔχω ζωή, ἡ ἡμέρα, ἡ θάλασσα, ἡ καρδία, ἡ φωνή, ἡ ὥρα, ἡ Parts of Speech NOUN - person, place, thing, quality, idea, or action

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 ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία "Η ΣΗΜΑΝΤΙΚΟΤΗΤΑ ΤΟΥ ΜΗΤΡΙΚΟΥ ΘΗΛΑΣΜΟΥ ΣΤΗ ΠΡΟΛΗΨΗ ΤΗΣ ΠΑΙΔΙΚΗΣ ΠΑΧΥΣΑΡΚΙΑΣ" Ειρήνη Σωτηρίου Λεμεσός 2014 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ

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

Summer Greek. Lesson 3. NOUNS GENDER (does not refer to fe/male) masculine feminine neuter NUMBER singular plural. NOUNS -Case.

Summer Greek. Lesson 3. NOUNS GENDER (does not refer to fe/male) masculine feminine neuter NUMBER singular plural. NOUNS -Case. A Summer Greek Lesson 3 Ω Parts of Speech NOUN- person, place, thing, quality, idea, or action ARTICLE Indefinite = a / an ; Definite = the ADJECTIVE- describes a noun (includes in/definite articles) PRONOUN-word

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

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

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

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

LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS

LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS 1. Developing a grammar fragment...1 2. A formalism that is too strong and too weak at the same time...3 3. References...4 1. Developing a grammar fragment The

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

ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «ΘΕΜΑ»

ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «ΘΕΜΑ» ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙΔΕΥΤΙΚΟΥ ΣΧΕΔΙΑΣΜΟΥ Π.Μ.Σ. «ΠΕΡΙΒΑΛΛΟΝΤΙΚΗ ΕΚΠΑΙΔΕΥΣΗ» ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «ΘΕΜΑ» «Εφαρμογή

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

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

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

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

εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016

εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016 εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016 Conditional Relative Clauses relative clauses referring to an indefinite person or thing (whoever, whatever, anyone,

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

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

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

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

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

Saint Thomas the Apostle Catholic Academy September 20, 2017

Saint Thomas the Apostle Catholic Academy September 20, 2017 Saint Thomas the Apostle Catholic Academy September 20, 2017 WHAT IS TERRA NOVA? Terra Nova is a norm-reference nationally standardized achievement test. Nationally standardized means that the test was

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

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

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

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

5.4 The Poisson Distribution.

5.4 The Poisson Distribution. The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable

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

ΔΗΜΟΚΡΙΤΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΡΑΚΗΣ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΑΓΩΓΗΣ

ΔΗΜΟΚΡΙΤΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΡΑΚΗΣ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΑΓΩΓΗΣ ΔΗΜΟΚΡΙΤΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΡΑΚΗΣ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΑΓΩΓΗΣ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΕΚΠΑΙΔΕΥΣΗΣ ΣΤΗΝ ΠΡΟΣΧΟΛΙΚΗ ΗΛΙΚΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Διαπολιτισμική Εκπαίδευση και Θρησκευτική Ετερότητα: εθνικές και θρησκευτικές

Διαβάστε περισσότερα

Modbus basic setup notes for IO-Link AL1xxx Master Block

Modbus basic setup notes for IO-Link AL1xxx Master Block n Modbus has four tables/registers where data is stored along with their associated addresses. We will be using the holding registers from address 40001 to 49999 that are R/W 16 bit/word. Two tables that

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

Uniform Convergence of Fourier Series Michael Taylor

Uniform Convergence of Fourier Series Michael Taylor Uniform Convergence of Fourier Series Michael Taylor Given f L 1 T 1 ), we consider the partial sums of the Fourier series of f: N 1) S N fθ) = ˆfk)e ikθ. k= N A calculation gives the Dirichlet formula

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

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

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

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

Διαβάστε περισσότερα

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

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

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ Π.Μ.Σ: «Σύγχρονες Προσεγγίσεις στη γλώσσα και στα κείμενα» ΚΑΤΕΥΘΥΝΣΗ ΓΛΩΣΣΟΛΟΓΙΑΣ ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΑΤΡΙΒΗ Το φωνηεντικό

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

105 Verses in the Critical Greek Text of the New Testament Without Any Manuscript Support

105 Verses in the Critical Greek Text of the New Testament Without Any Manuscript Support 105 Verses in the Critical Greek Text of the New Testament Without Any Manuscript Support These notes were sent to me by Dr. Maurice Robinson and detail 105 places in the Critical Greek Text of the New

Διαβάστε περισσότερα