Notes on the Greek New Testament Day 22 January 22 nd Matthew 14: Works frequently referenced in these notes on Matthew

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Notes on the Greek New Testament Day 22 January 22 nd Matthew 14: Works frequently referenced in these notes on Matthew"

Transcript

1 Notes on the Greek New Testament Day 22 January 22 nd Matthew 14:13-36 Works frequently referenced in these notes on Matthew Hagner, Donald A Word Biblical Commentary Vols.33a & 33b: Matthew 1-13 & Matthew 14-28, Word Books, Dallas, 1993 & 1995 Morris, Leon The Gospel According to Matthew, Eerdmans, Grand Rapids, 1992 Verse 13 Ἀκούσας δὲ ὁ Ἰησοῦς ἀνεχώρησεν ἐκεῖθεν ἐν πλοίῳ εἰς ἔρημον τόπον κατʼ ἰδίαν καὶ ἀκούσαντες οἱ ὄχλοι ἠκολούθησαν αὐτῷ πεζῇ ἀπὸ τῶν πόλεων. Ἀκούσας δὲ ὁ Ἰησοῦς "ties this passage to the end of the preceding one about the death of John the Baptist... The effect of this, however, is to ignore the fact that the story of John's death was a flashback and so to throw the entire sequence of narratives that follow back to that earlier time. Perhaps Matthew regarded John's death as having occurred only a few days earlier (thus McNeile). The suggestion that, given the parenthetical nature of vv 3-12, the object of ἀκουσας, 'having heard,' is Herod's evaluation of John in v 2 (Carson, Morris, Blomberg) ignores the placement of ἀκουσας immediately following the reference to the report of John's death to Jesus (v 22) [stet v.12?]. This verse is a counterpart to 4:12, which refers to Jesus' response to John's imprisonment using the same participle, ἀκουσας, 'having heard,' and main verb, ἀνεχωρησεν, 'he went away.' Presumably Jesus had gone εἰς ἔρημον τόπον κατʼ ἰδίαν, 'privately to a deserted place,' in order to pray, the death of John perhaps turning his mind to his own approaching passion." Hagner. ἀναχωρεω withdraw, go away ἐκειθεν from there πλοιον, ου n boat, ship ἐρημος, ου f deserted place, uninhabited region, desert; also ἐρνμος, ον adj lonely, deserted, uninhabited, desolate τοπος, ου m place, opportunity ἰδιος, α, ον one's own; κατ ἰδιαν privately ὀχλος, ου m see v.5 ἀκολουθεω follow πεζῃ on foot; by land πολις, εως f city, town Verse 14 καὶ ἐξελθὼν εἶδεν πολὺν ὄχλον, καὶ ἐσπλαγχνίσθη ἐπʼ αὐτοῖς καὶ ἐθεράπευσεν τοὺς ἀρρώστους αὐτῶν. ἐξελθων Verb, aor act ptc, nom m s ἐξερχομαι Morris thinks that the verb here means 'come ashore' εἶδεν Verb, aor act indic, 3 s ὁραω see ἐσπλαγχνίσθη Verb, aor pass dep indic, 3 s σπλαγχνιζομαι be moved with pity or compassion, have compassion Cf. 9:36; 15:32. θεραπευω heal, cure ἀρρωστος, ον sick, ill Verse 15 ὀψίας δὲ γενομένης προσῆλθον αὐτῷ οἱ μαθηταὶ λέγοντες Ἔρημός ἐστιν ὁ τόπος καὶ ἡ ὥρα ἤδη παρῆλθεν ἀπόλυσον τοὺς ὄχλους, ἵνα ἀπελθόντες εἰς τὰς κώμας ἀγοράσωσιν ἑαυτοῖς βρώματα. ὀψια, ας f evening προσῆλθον Verb, aor act indic, 1 s & 3 pl προσερχομαι come or go to, approach μαθητης, ου m see v.12 The disciples, like the crowds, must have walked to the spot. ὡρα, ας f hour, moment ἠδη adv now, already παρερχομαι pass, pass by, pass away ὡρα ἠδη παρηλθεν 'it is now late'. ἀπόλυσον Verb, aor act imperat, 2 s ἀπολυω release, send away, dismiss ἀπελθόντες Verb, aor act ptc, m nom pl ἀπερχομαι κωμη, ης f village, small town ἀγοράσωσιν Verb, aor act subj ἀγοραζω buy ἑαυτος, ἑαυτη, ἑαυτον him/her/itself βρωμα, τος n food, solid food

2 Verse 16 ὁ δὲ Ἰησοῦς εἶπεν αὐτοῖς Οὐ χρείαν ἔχουσιν ἀπελθεῖν δότε αὐτοῖς ὑμεῖς φαγεῖν. χρεια, ας f need, want δότε Verb, aor act imperat, 2 pl διδωμι ὑμεις is added for emphasis. φαγεῖν Verb, aor act infin ἐσθιω and ἐσθω eat, consume Verse 17 οἱ δὲ λέγουσιν αὐτῷ Οὐκ ἔχομεν ὧδε εἰ μὴ πέντε ἄρτους καὶ δύο ἰχθύας. ὡδε here, in this place πεντε (indeclinable) five ἀρτος, ου m bread, a loaf Small loaf a bun/roll. Five of them with the two small fish would have been a packed lunch for one boy (cf. Jn 6:9). δυο gen & acc δυο dat δυσιν two ἰχθυς, υος m fish "At this point the story bears some intentional similarity to the comment of Elisha in the miraculous provision of food from twenty loaves of barley and the response of the man from Baal-shalishah (2 Kings 4:42-44; cf. John 6:9, 'but what are those among so many?')." Hagner. Verse 18 ὁ δὲ εἶπεν Φέρετέ μοι ὧδε αὐτούς. φερω bring, carry, bear, lead Verse 19 καὶ κελεύσας τοὺς ὄχλους ἀνακλιθῆναι ἐπὶ τοῦ χόρτου, λαβὼν τοὺς πέντε ἄρτους καὶ τοὺς δύο ἰχθύας, ἀναβλέψας εἰς τὸν οὐρανὸν εὐλόγησεν καὶ κλάσας ἔδωκεν τοῖς μαθηταῖς τοὺς ἄρτους οἱ δὲ μαθηταὶ τοῖς ὄχλοις. κελευω order, command ἀνακλιθῆναι Verb, aor pass infin ἀνακλινω seat at table, recline χορτος, ου m grass, vegetation λαβων Verb, aor act ptc, m nom s λαμβανω ἀναβλεπω look up οὐρανος, ου m heaven εὐλογεω speak well of, bless Here used simply of a prayer of thanksgiving. Jesus did not bless the bread, he thanked God for his goodness, maybe in words similar to those found in the Mishnah, "Blessed art thou who bringest forth bread from the earth." κλαω break (only of bread) ἔδωκεν Verb, aor act indic, 3 s διδωμι "The sequence of verbs or participles, i.e., λαμβανειν, 'take,' εὐλογειν, 'bless,' κλαν, 'break,' διδοναι, 'give,' is the same as in the account of the Last Supper (26:26-27), suggesting an inevitable association of the two stories (but cf. the similarity with the description of the ordinary meal in Acts 27:35)." Hagner. Cf. Lk 24:30. Verse 20 καὶ ἔφαγον πάντες καὶ ἐχορτάσθησαν, καὶ ἦραν τὸ περισσεῦον τῶν κλασμάτων δώδεκα κοφίνους πλήρεις. ἔφαγον Verb, aor act indic, 1s & 3pl ἐσθιω πάντες Adjective, m nom pl πας χορταζω feed, satisfy This was not merely a 'token meal'; the crowd were fully satisfied with what they received. Hagner says that this verb, "has already been used with clearly eschatological associations in 5:6. The miracle in this sense anticipates the messianic age in which the hungry are to be fed (cf. Luke 1:53; 6:21). Messianic blessing also appears to be intended in the overabundance of food... This miracle recalls God's miraculous, abundant provision of manna, 'bread,' ἀρτος in the LXX, in the wilderness (cf. Exod 16:13-35; Num 11:7-9, 31-32). The eschatological connotation of the manna miracle is evident in 2 Apoc. Bar: 29:8 (cf. Rev 2:17)." Hagner. αἰρω take, take up, take away περισσευω be left over κλασμα, τος n fragment, piece δωδεκα twelve κοφινος, ου m basket πληρης, ες (sometimes not declined) full, complete "The miracle typifies the full and complete blessing of humanity in the meeting of human need and the experience of ultimate wellbeing, universal shalom. The feeding of the multitude is thus the harbinger of good news for Matthew's church and for Christians of every era. At another level and in specific contrast to the feeding of the four thousand (which, as will be seen, points to the Gentiles), the symbolism of the twelve baskets suggests the special significance of this miracle for Israel. Messianic fulfillment means (and especially for Matthew!) that Jesus will provide for Israel before considering the Gentiles. And the feeding of the five thousand is an indication to the Jews that the Messiah is in their midst, offering to them as in the miracle of manna in the wilderness the reality of salvation, the fulfilment of the promises." Hagner.

3 Verse 21 οἱ δὲ ἐσθίοντες ἦσαν ἄνδρες ὡσεὶ πεντακισχίλιοι χωρὶς γυναικῶν καὶ παιδίων. ἀνηρ, ἀνδρος m man, husband ὡσει as, about, approximately πεντακισχιλιοι, αι, α five thousand χωρις without, apart from, besides γυνη, αικος f woman, wife παιδιον, ου n child Verses Cf. Mark 6:45-52 also John 6: Verse 22 Καὶ εὐθέως ἠνάγκασεν τοὺς μαθητὰς ἐμβῆναι εἰς πλοῖον καὶ προάγειν αὐτὸν εἰς τὸ πέραν, ἕως οὗ ἀπολύσῃ τοὺς ὄχλους. εὐθεως is omitted from *א C* sy s,c. The UBS committee considered this an accidental omission. ἀναγκαζω force, compel, urge Some MSS read μαθητας αὐτου which the committee judged to have been introduced from the parallel in Mark 6:45. ἐμβαινω get into, embark πλοιον, ου n boat, ship προαγω go before or ahead of περαν beyond, across; το π. the other side οὗ adv where; ἑως οὑ until ἀπολυω see v.15 The reasons for this hasty dismissal can be found in John 6:15 which tells us that some of the 5000 wanted to make Jesus their king. Verse 23 καὶ ἀπολύσας τοὺς ὄχλους ἀνέβη εἰς τὸ ὄρος κατʼ ἰδίαν προσεύξασθαι. ὀψίας δὲ γενομένης μόνος ἦν ἐκεῖ. ἀπολύσας Verb, aor act ptc, m nom s ἀνέβη Verb, aor act indic, 3 s ἀναβαινω go up ὀρος, ους n mountain, hill ἰδιος, α, ον one's own; κατ ἰδιαν privately προσευχομαι pray "The right relation between prayer and conduct is not that conduct is supremely important and that prayer may help it, but that prayer is supremely important and conduct tests it." William Temple. ὀψια, ας f evening μονος, η, ον adj only, alone ἐκει there, in that place "The other references to Jesus praying (προσευχεσθαι) in Matthew are in 26:36, 39, 42, 44 (cf. Luke 9:28), all in connection with his own imminent suffering and death. In the present instance, the same thoughts may be presumed to be in Jesus' mind, prompted perhaps by the thought of John the Baptist's death (cf. the initial departure of Jesus into the wilderness privately in v 13 following the report referred to in v 12)." Hagner. Verse 24 τὸ δὲ πλοῖον ἤδη σταδίους πολλοὺς ἀπὸ τῆς γῆς ἀπεῖχεν, βασανιζόμενον ὑπὸ τῶν κυμάτων, ἦν γὰρ ἐναντίος ὁ ἄνεμος. ἠδη now, already σταδιοι, ων m (pl) stades, furlongs (about 200 metres) γη, γης f earth, land "John tells us that the disciples had gone 25 to 30 stadia. The greatest width of the lake is 61 stadia... they were well into their journey, though with quite a way to go." Leon Morris. ἀπεῖχεν Verb, imperf act indic, 3 s ἀπεχω be distant Many MSS read μεσον της θαλασσης ἠν rather than σταδίους πολλοὺς ἀπὸ τῆς γῆς ἀπεῖχεν. The committee judged this reading to be a harmonisation with Mark 6:47. βασανιζω torment, disturb κυμα, ατος n wave ἐναντιος, α, ον against, contrary to ἀνεμος, ου m wind Verse 25 τετάρτῃ δὲ φυλακῇ τῆς νυκτὸς ἦλθεν πρὸς αὐτοὺς περιπατῶν ἐπὶ τὴν θάλασσαν. τεταρτος, η, ον fourth φυλακη, ης f prison, watch (of the night) νυξ, νυκτος f night Between 3 and 6 in the morning. περιπατεω walk θαλασσα, ης f sea Verse 26 οἱ δὲ μαθηταὶ ἰδόντες αὐτὸν ἐπὶ τῆς θαλάσσης περιπατοῦντα ἐταράχθησαν λέγοντες ὅτι Φάντασμά ἐστιν, καὶ ἀπὸ τοῦ φόβου ἔκραξαν. ἰδόντες Verb, aor act ptc, m nom pl ὁραω see, observe ἐταράχθησαν Verb, aor pass indic, 3 pl ταρασσω trouble, frighten φαντασμα, τος n ghost, apparition φοβος, ου m fear κραζω cry out, call out

4 "OT symbolism concerning the mastery of God over the sea and specifically his walking upon it (e.g., Ps 77:16, 19; Job 9:8; 38:16; cf. wisdom in Sir 24:5), while significant in retrospect, could hardly have occurred to the disciples at the time, although for the evangelist and his readers it must have been suggestive." Hagner. Verse 27 εὐθὺς δὲ ἐλάλησεν αὐτοῖς ὁ Ἰησοῦς λέγων Θαρσεῖτε, ἐγώ εἰμι μὴ φοβεῖσθε. εὐθυς adv. straightway, immediately λαλεω speak, talk D 084 sy c sa bo omit ὁ Ἰησους, other *א witnesses (C L W Θ 0106 f 1,13 TR) place αὐτοις before ὁ Ἰησους. Although the shorter reading may be original, it is also possible that the name dropped out through homoioteleuton. Hence the committee placed the name in brackets. θαρσεω (only in imperat) Courage! Take courage! Cheer up! On the expression ἐγω εἰμι Filson remarks that it "implies that the speaker had authority and embodies God's power and claim. Jesus brings the answer to their need if only they perceive and believe that in him God is at work to save them. Hill says it is "not 'It is I', but 'I AM', the Living One, master of wind and wave." Morris says "the expression has overtones of deity, and who but God could walk on the stormy waters?" φοβεομαι fear, be afraid (of) Verse 28 Ἀποκριθεὶς δὲ αὐτῷ ὁ Πέτρος εἶπεν Κύριε, εἰ σὺ εἶ, κέλευσόν με ἐλθεῖν πρὸς σὲ ἐπὶ τὰ ὕδατα ἀποκριθεὶς Verb, aor pass dep ptc, m nom s ἀποκρινομαι answer, reply, say κελευω see v.19 ἐλθεῖν Verb, aor act infin ἐρχομαι ὑδωρ, ὑδατος n water It is difficult to know what lay behind Peter's request. It may have been that Peter wanted to participate with Jesus in this miracle as he had in the preceding one. Perhaps it was no more than impulsiveness or the desire to do something excitingly dangerous to have a once-in-a-lifetime experience which appealed to him. The impossible would be possible through the power of Jesus. Thus Peter's request is based upon faith in Jesus and not upon an uncertainty about whether the apparition really was Jesus (this really is assumed in the protasis of the condition)." Hagner. Verse 29 ὁ δὲ εἶπεν Ἐλθέ. καὶ καταβὰς ἀπὸ τοῦ πλοίου Πέτρος περιεπάτησεν ἐπὶ τὰ ὕδατα καὶ ἦλθεν πρὸς τὸν Ἰησοῦν. ἐλθέ Verb, aor act imperat, 2 s ἐρχομαι καταβαινω come or go down, descend πλοιον, ου n see v.22 περιπατεω see v.25 "We usually remember that Peter's faith failed and that Jesus drew attention to this. But we should bear in mind that it took courage for the apostle to venture on the water at all." Leon Morris. Verse 30 βλέπων δὲ τὸν ἄνεμον ἰσχυρὸν ἐφοβήθη, καὶ ἀρξάμενος καταποντίζεσθαι ἔκραξεν λέγων Κύριε, σῶσόν με. βλεπω see, look "The present participle βλεπων means something like 'as he saw'; the switch of attention from Jesus to the storm coincided with Peter's inability to stay on top of the water." Leon Morris. ἀνεμος, ου m see v.24 ἰσχυρος, α, ον strong, mighty, powerful Some important witnesses א) B* sa bo) omit ἰσχυρον, which may have been added to heighten the cause of Peter's fear (cf. the addition of σφοδρα in W). A majority of the committee, however, regarded the word as necessary to explain Peter's increased fear. Thus the word is enclosed in brackets. ἐφοβήθη Verb, aor pass dep indic, 3 s φοβεομαι see v.27 Phillips, "he panicked" ἀρξάμενος Verb, aor midd ptc, m nom s ἀρχω midd begin καταποντιζομαι sink, be drowned κραζω see v.26 σῶσόν Verb, aor act imperat, 2 s σωζω save, rescue Cf. 8:25. Verse 31 εὐθέως δὲ ὁ Ἰησοῦς ἐκτείνας τὴν χεῖρα ἐπελάβετο αὐτοῦ καὶ λέγει αὐτῷ Ὀλιγόπιστε, εἰς τί ἐδίστασας; ἐκτεινω stretch out, extend χειρ, χειρος f hand, power ἐπιλαμβανομαι take, take hold of, sieze ὀλιγοπιστος, ον of little faith δισταζω doubt, be doubtful

5 "The leading apostle might have been expected to trust more wholeheartedly, more especially since he had already taken some steps in his alien environment. He was learning that problems arise when doubt replaces trust." Leon Morris. "Here the object of the doubt is whether it was possible indeed to walk on the water and hence indirectly expresses a doubt concerning the power of Jesus. Peter was nevertheless saved. The underlying message here is as much for the disciples and for Matthew's church as it is for Peter himself." Hagner. Verse 32 καὶ ἀναβάντων αὐτῶν εἰς τὸ πλοῖον ἐκόπασεν ὁ ἄνεμος. ἀναβαινω go/come up, ascend, embark κοπαζω cease, stop "ἐκόπασεν ὁ ἄνεμος... not apparently in response to a command of Jesus (as in 8:26) but simply in response to his presence in the boat." Hagner. Verse 33 οἱ δὲ ἐν τῷ πλοίῳ προσεκύνησαν αὐτῷ λέγοντες Ἀληθῶς θεοῦ υἱὸς εἶ. προσκυνεω worship, fall down and worship, fall at another's feet ἀληθως adv truly, in truth Cf. the similar contrast with the ending of the similar story in 8: "... it is not easy to see precisely how they would have understood the expression at this time (after the resurrection it would have had fuller significance for all Christians). But at least they are saying more than that Jesus is one among many whose godliness entitles them to be addressed as 'sons of God.' They are saying that Jesus is uniquely related to the one God." Leon Morris. "Here 'Son of God' is probably understood by the disciples as the unique messenger of God, God's messianic agent, and not, as the later church will make explicit, the actual incarnation of God. This conclusion has an inevitability about it, given the preceding two narratives. It strangely anticipates the answer given to the direct question of Jesus in 16:16, which gives the impression of being the first time the question has received this answer. Yet Matthew's Christology builds throughout the narrative of the words and deeds of Jesus that begins in chap. 5. The present passage and verse are a climactic point in the narrative thus far (cf. Mark 15:39; Matt 27:54). 16:16 is yet a higher climax and a turning point of the whole Gospel." Hagner. Verses Cf. Mark 6:53-56; John 6: Verse 34 Καὶ διαπεράσαντες ἦλθον ἐπὶ τὴν γῆν εἰς Γεννησαρέτ. διαπεράσαντες Verb, aor act ptc, m nom pl διαπεραω cross over γη, γης f see v.24 "Gennesaret, or Gennesar, is either a village or a region (or both) that lies on the shore just a couple of miles southwest of Capernaum." Hagner. Verse 35 καὶ ἐπιγνόντες αὐτὸν οἱ ἄνδρες τοῦ τόπου ἐκείνου ἀπέστειλαν εἰς ὅλην τὴν περίχωρον ἐκείνην, καὶ προσήνεγκαν αὐτῷ πάντας τοὺς κακῶς ἔχοντας, ἐπιγινωσκω perceive, recognise ἀνηρ, ἀνδρος m man, husband τοπος, ου m place, opportunity ἐκεινος, η, ο demonstrative adj. that ἀποστελλω send, send out ὁλος, η, ον whole, all, complete, entire περιχωρος, ου f surrounding region, neighbourhood προσήνεγκαν Verb, aor act indic, 3 pl προσφερω bring, bring before κακως badly, severely; κακως ἐχω be sick Verse 36 καὶ παρεκάλουν αὐτὸν ἵνα μόνον ἅψωνται τοῦ κρασπέδου τοῦ ἱματίου αὐτοῦ καὶ ὅσοι ἥψαντο διεσώθησαν. παρακαλεω exhort, encourage, urge μονον adv only, alone ἅψωνται Verb, aor midd subj, 3 pl ἁπτω midd. take hold of, touch κρασπεδον, ου n fringe, edge, tassel ἱματιον, ου n garment, clothing, cloak Cf. 9:20. "Jesus probably healed in his normal way, i.e., directly. But there were apparently so many people in need of healing that they pressed around him and begged (παρεκαλουν; for the same use of the verb, cf. 8:5) to touch the hem of his garment (for this, see Comment on 9:20). Such is the power of Jesus that all who touched him on this occasion were instantly cured of their maladies." Hagner. ὁσος, η, ον correlative pronoun, as much as; pl. as many as, all ἥψαντο Verb, aor midd indic, 3 pl ἁπτω διεσωθησαν Verb, aor pass indic, 3 pl διασωζω bring safely through, cure

6 The compound verb is not to be distinguished in meaning from the simple σωζω, cf. 9:21-22.

Ἀκούσας δὲ ὁ Ἰησοῦς ἀνεχώρησεν ἐκεῖθεν ἐν πλοίῳ εἰς ἔρημον τόπον κατ ἰδίαν καὶ ἀκούσαντες οἱ ὄχλοι ἠκολούθησαν αὐτῷ πεζῇ ἀπὸ τῶν πόλεων.

Ἀκούσας δὲ ὁ Ἰησοῦς ἀνεχώρησεν ἐκεῖθεν ἐν πλοίῳ εἰς ἔρημον τόπον κατ ἰδίαν καὶ ἀκούσαντες οἱ ὄχλοι ἠκολούθησαν αὐτῷ πεζῇ ἀπὸ τῶν πόλεων. Matthew 14.13-21 13 Ἀκούσας δὲ ὁ Ἰησοῦς ἀνεχώρησεν ἐκεῖθεν ἐν πλοίῳ εἰς ἔρημον τόπον κατ ἰδίαν καὶ ἀκούσαντες οἱ ὄχλοι ἠκολούθησαν αὐτῷ πεζῇ ἀπὸ τῶν πόλεων. Now when Jesus heard about John, He withdrew

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

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

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

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

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

WEEK 21. The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1

WEEK 21. The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1 WEEK 21 The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1 I. The Feast of Firstfruits signifies the resurrected Christ as the firstfruits for our enjoyment as

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

Finite Field Problems: Solutions

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

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

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

Διαβάστε περισσότερα

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

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

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

Διαβάστε περισσότερα

CHAPTER 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

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

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

Croy Lessons Participles

Croy Lessons Participles A Croy Lessons 18-20 Participles Aorist (Act/Mid/Dep Dep) ) Participles Adjectival and Substantive Ω STEM + TENSE + THEME + PTCP CODE + ENDING PARTICIPLE CODES CASE ENDINGS ντ - masc and neut active (and

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Revelation 10. LGNT - September 7, 2019 Page 1. Book Chapter Verse. Word # Rev. Interlinear English. Numeric value. # of words. # of letters.

Revelation 10. LGNT - September 7, 2019 Page 1. Book Chapter Verse. Word # Rev. Interlinear English. Numeric value. # of words. # of letters. Book Chapter Verse Interlinear English Word # Rev Greek # of letters # of words Numeric value 271001 and 03876 ΚΑΙ 3 31 271001 I saw 03877 ΕΙΔΟΝ 5 139 271001 another 03878 ΑΛΛΟΝ 5 181 271001 [mighty] angel

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

The Accusative Case. A Target for the Action. A lesson for the Paideia web-app Ian W. Scott, 2015

The Accusative Case. A Target for the Action. A lesson for the Paideia web-app Ian W. Scott, 2015 The Accusative Case A Target for the Action A lesson for the Paideia web-app Ian W. Scott, 2015 The Accusative Case So far we've seen three noun cases Nominative Genitive Vocative We need one more case

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

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

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

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

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

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

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 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28. 2 December 2014

LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28. 2 December 2014 LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28 2 December 2014 Place/Seat Right (noun) I am right I am not right It matters It does not matter The same (singular) The same (Plural) Η θέση Το δίκιο Έχω

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

Notes on the Greek New Testament Day 54 February 23 rd Mark 6:30-56

Notes on the Greek New Testament Day 54 February 23 rd Mark 6:30-56 Notes on the Greek New Testament Day 54 February 23 rd Mark 6:30-56 Works frequently referenced in these notes on Mark Cranfield, CEB France, RT Guelich, Robert A The Gospel According to Mark (Cambridge

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

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

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

Διαβάστε περισσότερα

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

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 202/059/36-ADV. 4 March 2014

LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 202/059/36-ADV. 4 March 2014 LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 202/059/36-ADV 4 March 2014 Immediately/At once I arrive/reach αμέσως φτάνω I arrive I start/begin Present : φτάνω ξεκινάω (ξεκινώ) S.Past : έφτασα ξεκίνησα S.Future :

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

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

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

I haven t fully accepted the idea of growing older

I haven t fully accepted the idea of growing older I haven t fully accepted the idea of growing older 1 Peter Authorship Questions Πέτρος ἀπόστολος Ἰησοῦ Χριστοῦ ἐκλεκτοῖς παρεπιδήμοις διασπορᾶς Πόντου, Γαλατίας, Καππαδοκίας, Ἀσίας 1 Peter Authorship

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

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

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

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

Final Test Grammar. Term C'

Final Test Grammar. Term C' Final Test Grammar Term C' Book: Starting Steps 1 & Extra and Friends Vocabulary and Grammar Practice Class: Junior AB Name: /43 Date: E xercise 1 L ook at the example and do the same. ( Κξίηα ηξ παοάδειγμα

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

«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

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect)

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) 15 Ρηματική άποψη (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) imperfective perfective Verb forms in Modern Greek are based either on the imperfective or the perfective

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

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

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

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

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων Croy Lesson 18 First Declension SINGULAR PLURAL NOM -α / -η [-ης]* -αι GEN -ας / -ης [-ου]* -ων DAT -ᾳ / -ῃ -αις ACC -αν / -ην -ας VOC -α / -η -αι *Masculine Nouns of First Declension Second Declension

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

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

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

Διαβάστε περισσότερα

Notes on the Greek New Testament Week 145 Matthew 14:22-15:28

Notes on the Greek New Testament Week 145 Matthew 14:22-15:28 Notes on the Greek New Testament Week 145 Matthew 14:22-15:28 Day 721: Matthew 14:22-27 Verses 22-33 Cf. Mark 6:45-52 also John 6:16-21. Verse 22 Καὶ εὐθέως ἠνάγκασεν τοὺς µαθητὰς ἐµβῆναι εἰς τὸ πλοῖον

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

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds! MTH U341 urface Integrals, tokes theorem, the divergence theorem To be turned in Wed., Dec. 1. 1. Let be the sphere of radius a, x 2 + y 2 + z 2 a 2. a. Use spherical coordinates (with ρ a) to parametrize.

Διαβάστε περισσότερα

LESSON 15 (ΜΑΘΗΜΑ ΔΕΚΑΠΕΝΤΕ) REF : 202/058/35-ADV. 25 February 2014

LESSON 15 (ΜΑΘΗΜΑ ΔΕΚΑΠΕΝΤΕ) REF : 202/058/35-ADV. 25 February 2014 LESSON 15 (ΜΑΘΗΜΑ ΔΕΚΑΠΕΝΤΕ) REF : 202/058/35-ADV 25 February 2014 Often/frequently Συχνά (sihna) Seldom Σπάνια (spania) Early Νωρίς (noris) Late (adv)/slowly Αργά (arga) I am having a bath When/whenever

Διαβάστε περισσότερα

Αζεκίλα Α. Μπνπράγηεξ (Α.Μ. 261)

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

Διαβάστε περισσότερα

1999 MODERN GREEK 2 UNIT Z

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

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

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

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

LESSON 7 (ΜΑΘΗΜΑ ΕΦΤΑ) REF : 202/046/27-ADV. 17 December 2013

LESSON 7 (ΜΑΘΗΜΑ ΕΦΤΑ) REF : 202/046/27-ADV. 17 December 2013 LESSON 7 (ΜΑΘΗΜΑ ΕΦΤΑ) REF : 202/046/27-ADV 17 December 2013 Sometimes Other times I start/begin Never Always/every time Supper Μερικές φορές (merikes) Άλλες φορές Αρχίζω (arheezo) Ποτέ Πάντα (Panda) Ο

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

Modern Greek *P40074A0112* P40074A. Edexcel International GCSE. Thursday 31 May 2012 Morning Time: 3 hours. Instructions. Information.

Modern Greek *P40074A0112* P40074A. Edexcel International GCSE. Thursday 31 May 2012 Morning Time: 3 hours. Instructions. Information. Write your name here Surname Other names Edexcel International GCSE Centre Number Modern Greek Candidate Number Thursday 31 May 2012 Morning Time: 3 hours You do not need any other materials. Paper Reference

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

1 John 5. LGNT - September 6, 2019 Page 1. Book Chapter Verse. Word # 1 John Greek. # of words. Numeric value. Interlinear English.

1 John 5. LGNT - September 6, 2019 Page 1. Book Chapter Verse. Word # 1 John Greek. # of words. Numeric value. Interlinear English. Book Chapter Verse Interlinear English Word # 1 John Greek # of letters # of words Numeric value 230501 everyone 01709 ΠΑΣ 3 281 230501 01710 Ο 1 70 230501 believing 01711 ΠΙΣΤΕΥΩΝ 8 1845 230501 that 01712

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

ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ

ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ ΜΑΘΗΜΑΤΑ ΥΠΕΥΘΥΝΟΤΗΤΑΣ/ LESSONS ABOUT RESPONSIBILITY Μάθημα 1: Νιώθω υπερήφανος όταν.../ I feel proud when.

Διαβάστε περισσότερα

ΦωτίστεΤονΚόσμο. ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ Νοεμβρίου Δεκεμβρίου 2017

ΦωτίστεΤονΚόσμο. ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ Νοεμβρίου Δεκεμβρίου 2017 ΦωτίστεΤονΚόσμο ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ 2017 24 Νοεμβρίου -- 25 Δεκεμβρίου 2017 ΘΕΜΑ «Καθώς ακολουθούμε το παράδειγμα του Σωτήρος και ζούμε όπως ζούσε Εκείνος και όπως δίδασκε, αυτό το φως θα καίει μέσα

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

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

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS

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

Διαβάστε περισσότερα

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

Example of the Baum-Welch Algorithm

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

Διαβάστε περισσότερα

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

Conditional Sentences

Conditional Sentences Conditional Sentences It all depends! A lesson for the Paideia web-app Ian W. Scott, 2015 What is a conditional sentence? An If then sentence States that something will happen if some condition is fulfilled

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

TMA4115 Matematikk 3

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

Διαβάστε περισσότερα

Notes on the Greek New Testament Week 183 Mark 6:21-56

Notes on the Greek New Testament Week 183 Mark 6:21-56 Notes on the Greek New Testament Week 183 Mark 6:21-56 Day 911: Mark 6:21-29 Verse 21 Καὶ γενοµένης ἡµέρας εὐκαίρου ὅτε Ἡρῴδης τοῖς γενεσίοις αὐτοῦ δεῖπνον ἐποίησεν τοῖς µεγιστᾶσιν αὐτοῦ καὶ τοῖς χιλιάρχοις

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