Notes on the Greek New Testament Day 285 October 12 th 1 Thessalonians 5:1-28. Works frequently referenced in these notes on Thessalonians

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Notes on the Greek New Testament Day 285 October 12 th 1 Thessalonians 5:1-28. Works frequently referenced in these notes on Thessalonians"

Transcript

1 Notes on the Greek New Testament Day 285 October 12 th 1 Thessalonians 5:1-28 Works frequently referenced in these notes on Thessalonians John Drane John Eadie Leon Morris Paul, Lion Publishing, Berkhamstead,1976 A Commentary on the Greek Text of the Epistles of Paul to the Thessalonians, MacMillan, London, 1877 The First and Second Epistles to the Thessalonians, The New International Commentary on the New Testament, Eerdmans, Grand Rapids, 1991 Verse 1 Περὶ δὲ τῶν χρόνων καὶ τῶν καιρῶν, ἀδελφοί, οὐ χρείαν ἔχετε ὑμῖν γράφεσθαι, καιρος, ου m time, appointed/proper time "With regard to the second advent... the χρονων are the chronological epochs that must elapse, time considered simply with regard to its duration, while the καιρων focus our attention rather on the nature of the time, on the critical events which will take place heralding the coming of the Lord." Morris χρεια, ας f need, want γράφεσθαι Verb, pres pass infin γραφω "There is abundant evidence from the two letters that he had spoken a good deal about the Parousia during his initial preaching... It is widely accepted in modern theology that early Christian teaching was thoroughly eschatological." Morris Verse 2 αὐτοὶ γὰρ ἀκριβῶς οἴδατε ὅτι ἡμέρα κυρίου ὡς κλέπτης ἐν νυκτὶ οὕτως ἔρχεται. ἀκριβως accurately, completely (in the sense of needing no further instruction) οἰδα know, understand ἡμερα κυριου a very ancient expression. Cf. Amos 5: κλεπτης, ου m thief νυξ, νυκτος f night The event is certain but the timing unfathomable. In this sense it will be totally unheralded. Verse 3 ὅταν λέγωσιν Εἰρήνη καὶ ἀσφάλεια, τότε αἰφνίδιος αὐτοῖς ἐφίσταται ὄλεθρος ὥσπερ ἡ ὠδὶν τῇ ἐν γαστρὶ ἐχούσῃ, καὶ οὐ μὴ ἐκφύγωσιν. ὁταν when, whenever, as often as εἰρηνη, ης f peace ἀσφαλεια, ας f security, safety They imagine their situation unshakable. τοτε then, at that time αἰφνιδιος, ον sudden, unexpected ἐφιστημι come up to, approach, appear ὀλεθρος, ου m destruction, ruin ὡσπερ as, even as ὠδιν, ινος f birth-pains, suffering γαστρὶ Noun, dat s γαστηρ, τρος f womb; ἐν γαστρι ἐχω conceive or be pregnant The comparison of a woman in labour focusses not merely on the pain but also on suddenness and inevitability. ἐκθευγω escape Verses 4-11 The themes of night and day continue but are now supplemented by those of darkness and light. "It is not a difficult step from the idea of the day of the Lord to that of walking in the light, from that of the coming of Christ to that of the character of Christian people as 'sons of the light.' The coming of that Day must inspire God's people to live lives appropriate to their calling." Morris Verse 4 ὑμεῖς δέ, ἀδελφοί, οὐκ ἐστὲ ἐν σκότει, ἵνα ἡ ἡμέρα ὑμᾶς ὡς κλέπτης καταλάβῃ, σκότει Noun, dat s σκοτος, ους n darkness, evil κλεπτης see v.2 καταλάβῃ Verb, aor act subj, 3 s καταλαμβανω obtain, seize Not that it will be heralded for them but that they will be prepared. Verse 5 πάντες γὰρ ὑμεῖς υἱοὶ φωτός ἐστε καὶ υἱοὶ ἡμέρας. οὐκ ἐσμὲν νυκτὸς οὐδὲ σκότους πάντες Adjective, m nom pl πας φως, φωτος n light

2 υἱοι φωτος is a Semitic idiom: to be a 'son' of something is for that thing or quality to be characteristic of the person. The added 'sons of the Day' must refer to the Day of the Lord. "Believers find in the Day of the Lord a situation in which they are perfectly at home." Morris A Day in which they live now. νυξ, νυκτος f night οὐδε neither, nor σκοτος, ους n darkness, evil Verse 6 ἄρα οὖν μὴ καθεύδωμεν ὡς οἱ λοιποί, ἀλλὰ γρηγορῶμεν καὶ νήφωμεν. ἀρα οὐν expresses a "logical inference and introduces an inescapable conclusion." Morris καθευδω sleep, be dead λοιπος, η, ον rest, remaining, other "Unbelievers may well 'sleep'; they are spiritually insensitive. But the believer should not take his standards from them... 'Sleep' is natural enough for the sons of the night, but is entirely out of place in the sons of light." Morris γρηγορεω be or keep awake, be alert Cf. Mk 14:38. νηφω be sober, be self-controlled The senses not clouded or drowsy through drink. Verse 7 οἱ γὰρ καθεύδοντες νυκτὸς καθεύδουσιν, καὶ οἱ μεθυσκόμενοι νυκτὸς μεθύουσιν μεθυσκομαι get drunk μεθυω be drunk, drink freely Sleep and drunkenness are characteristic of the night. Verse 8 ἡμεῖς δὲ ἡμέρας ὄντες νήφωμεν, ἐνδυσάμενοι θώρακα πίστεως καὶ ἀγάπης καὶ περικεφαλαίαν ἐλπίδα σωτηρίας νηφω see v.6 The stress is not merely on not getting drunk but on the self-control and alertness that should mark a soldier on duty. ἐνδυω dress, clothe; midd put on, wear The aorist may suggest the idea of a definitive act. On Christian armour, see Rom 13:12f; 2 Cor 6:7; 10:4; Eph 6:13f. θωραξ, ακος m breastplate, chest περικεφαλαια, ας f helmet ἐλπις, ιδος f hope, what is hoped for σωτηρια, ας f salvation Note here the three 'graces' of faith hope and love occupy a central place in the Christian life as is expressed also in 1:3. Here they are the defensive armour of the Christian. Verse 9 ὅτι οὐκ ἔθετο ἡμᾶς ὁ θεὸς εἰς ὀργὴν ἀλλὰ εἰς περιποίησιν σωτηρίας διὰ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ, ἔθετο Verb, 2 aor midd indic, 3 s τιθημι midd put place, set, appoint Cf. Jn 15:16; 1 Tim 2:7; 2 Tim 1:11; 1 Peter 2:8. ὀργη, ης f wrath, anger Cf. 1:10. To appreciate the greatness of our salvation we need to appreciate what we have been saved from as well as what we are saved to. περιποιησις, εως f obtaining, gaining σωτηρια, ας f salvation Verse 10 τοῦ ἀποθανόντος περὶ ἡμῶν ἵνα εἴτε γρηγορῶμεν εἴτε καθεύδωμεν ἅμα σὺν αὐτῷ ζήσωμεν. ἀποθανόντος Verb, aor act ptc, m gen s ἀποθνῃσκω die εἰτε if, whether γρηγορεω see v.6 καθευδω see v.6 The sense here is 'whether we are living or have died' ἁμα adv. at the same time, together ζαω live, be alive "Paul is maintaining that the death of Jesus has brought about a new relationship between God and sinners. Those who are Christ's live with him. There is the thought of that close union which elsewhere is expressed in the pregnant phrase 'in Christ.' This relationship is not disturbed by even such a final and decisive happening as death." Morris Verse 11 διὸ παρακαλεῖτε ἀλλήλους καὶ οἰκοδομεῖτε εἷς τὸν ἕνα, καθὼς καὶ ποιεῖτε. διο therefore, for this reason παρακαλεω exhort, encourage, urge The present tense implies continuous action. ἀλληλων, οις, ους one another οἰκοδομεω build, build up, encourage Implies growth.

3 εἱς τον ἑνα 'one (to) one' is equivalent to ἀλληλους but emphasises the distributive nature of the task each one is to do it and also that it is to be a one-to-one activity as well as communal. καθως καὶ ποιεῖτε "He knows the way in which the Thessalonians were assisting one another, and he commends them for it. But he urges them to go forward on this way. Christians may never relax on the grounds that they have made sufficient progress." Morris Verses Morris suggests that the first groups of Christians would have been organised on the model of the synagogue (cf. Jas 2:2) and would have included a group of elders exercising oversight. Such elders at Thessalonica may have been unused to responsibilities of leadership most of the believers seem to have been from the lower strata of society. Yet they were being required to deal with members who, in the heat of apocalyptic fervour, had given up work and were expecting to live off others. In such a situation there may well have been tension between the leaders and some of the congregation. Verse 12 Ἐρωτῶμεν δὲ ὑμᾶς, ἀδελφοί, εἰδέναι τοὺς κοπιῶντας ἐν ὑμῖν καὶ προϊσταμένους ὑμῶν ἐν κυρίῳ καὶ νουθετοῦντας ὑμᾶς, ἐρωταω ask, request, beg, urge εἰδεναι infin οἰδα (verb perf in form but with present meaning) know Here 'know the worth of', respect κοπιαω work, work hard, labour The single definite article indicates a single group the elders in the church who may not yet have formally borne that title. The following participles may expand and explain the first. προϊστημι be a leader, have authority over The NT is not shy of speaking of leadership within the church, though it does offer a distinctive Christ-centred model. νουθετεω instruct, teach, warn A distinctively Pauline word, cf. Acts 20:31; 1 Cor 4:14. J Behm says that strictly the verb means "to impart understanding (a mind for something)" and further, "It denotes the word of admonition which is designed to correct while not provoking or embittering." Verse 13 καὶ ἡγεῖσθαι αὐτοὺς ὑπερεκπερισσοῦ ἐν ἀγάπῃ διὰ τὸ ἔργον αὐτῶν. εἰρηνεύετε ἐν ἑαυτοῖς. ἡγεομαι think, regard, consider, esteem ὑπερεκπερισσου adv. exceedingly "Hold them in special esteem and affection" Moffatt εἰρηνευω live or be at peace ἑαυτος, ἑαυτη, ἑαυτον reflexive pronoun, himself, herself, itself Both leaders and followers are to be peacemakers (cf. Mk 9:50; Rom 12:18; 2 Cor 13:11). Verse 14 παρακαλοῦμεν δὲ ὑμᾶς, ἀδελφοί, νουθετεῖτε τοὺς ἀτάκτους, παραμυθεῖσθε τοὺς ὀλιγοψύχους, ἀντέχεσθε τῶν ἀσθενῶν, μακροθυμεῖτε πρὸς πάντας. "The address 'brothers' shows that these words are addressed to the whole of the membership and not simply to the leaders... The content of this charge is to look to the needs of certain people in the church. While this would be in a special measure the responsibility of those holding office, it was also something that lay on the shoulders of all (perhaps it was something the leaders should lead others to do). It was (and is) characteristic of the Christian understanding of life that the entire brotherhood is charged with responsibility for all. For Christians care for others is not to be left to any special class of believers." Morris παρακαλεω see v.11 νουθετεω see v.12 ἀτακτος, ον idle, unruly The word is a military term meaning a soldier who is out of step. It came then to mean one who is idle a slacker. παραμυθεομαι comfort, console ὀλιγοψυχος, ον fainthearted, discouraged "The word is well adapted to expressing a tender concern, quite in the spirit of 'a bruised reed he will not break' (Is 42:3)." Morris ἀντεχομαι be loyal to, support ἀσθενης, ες sick, weak, helpless On the responsibility of the strong towards the weak, see esp Rom 14 and 1 Cor 8. μακροθυμεω be patient, wait patiently Verse 15 ὁρᾶτε μή τις κακὸν ἀντὶ κακοῦ τινι ἀποδῷ, ἀλλὰ πάντοτε τὸ ἀγαθὸν διώκετε εἰς ἀλλήλους καὶ εἰς πάντας. ὁραω trans see, observe; intrans make sure, see to

4 κακος, η, ον evil, bad, wrong, harm ἀντι prep with gen for, in place of ἀποδῷ Verb, 2 aor act subj, 3 s ἀποδιδωμι give back, repay Cf. Matt 5:44-45; Rom 12:17. "Revenge is the most natural and instinctive of vices." Denny παντοτε always διωκω seek after, pursue, follow ἀλληλων, οις, ους one another "Our Master, for our salvation, endured patiently the insults and injuries of wicked men. He, the Just, died for the unjust. In both these ways his example is important for his people. As the servant is not greater than his Lord, we must expect the same kind of treatment, and therefore we must expect to be called on to show the same kind of patience under provocation. And since he came to die for sinful people, we must expect that our meekness is to be by way of ministering to the needs of the sinful also." Morris Verse 16 πάντοτε χαίρετε, "The New Testament does not give us a picture of believers as people who are always screwing themselves up to the point of doing unpleasant things in the service of their God but rather those who are glad to live out the implications of their faith... He is not writing about a joy that Christians produce by their own efforts. It is natural for people to be happy when things go well for them. But it is not this natural joy, dependent on circumstances, that is the special characteristic of Christians. It is the joy that comes from being 'in Christ.' Thus it is that the New Testament contains so many exhortations to joyful living startlingly many, if we fix our attention on the outward circumstances of the early Christian communities. Persecution was always threatening and often actual. Believers were usually in straitened circumstances and compelled to work hard for their living. Their lot can rarely have been other than hard. But if we fasten our attention on these things, we put our emphasis in the wrong place. They thought more of their Lord than of their difficulties, more of their spiritual riches in Christ than of their poverty on earth, more of their glorious future when their Lord should come again than of their unhappy past. So the note of joy rings through the New Testament, and so Paul, who himself knew what it was to rejoice in difficult circumstances (Acts 16:25; Rom 5:3; Col 1:24), can say 'Be joyful always' (cf. Phil 4:4), and speak of Christians as 'sorrowful, yet always rejoicing' (2 Cor 6:10)." Morris Verse 17 ἀδιαλείπτως προσεύχεσθε, ἀδιαλειπτως ceaselessly, without ceasing προσευχομαι pray "Continuing prayer is the continuing expression... of dependence... Again and again in Paul's letters (and especially in these two letters to the Thessalonians) the apostle interjects little prayers into his argument. Prayer was as natural to Paul as breathing. At any time he was likely to break off his argument or to sum it up by a prayer. In the same way he looks for the Thessalonians to live lives with such an attitude of dependence on God that they will easily and naturally move into the words of prayer on all sorts of occasions, great and small, grave and festive" Morris Verse 18 ἐν παντὶ εὐχαριστεῖτε τοῦτο γὰρ θέλημα θεοῦ ἐν Χριστῷ Ἰησοῦ εἰς ὑμᾶς. εὐχαριστεω thank, give thanks "When we come to realise that God's hand is in all things, we learn to give thanks for all things." Morris θελημα, ατος n will, wish, desire Cf. 4:3. "'For this is the will of God...' almost certainly refers to the three injunctions" [of vv 16-18] Morris Verse 19 τὸ πνεῦμα μὴ σβέννυτε, σβεννυμι extinguish, put out "The use of the Greek negative μη with the present imperative here denotes a command to cease from doing something already in process and not simply a warning to avoid this kind of thing in the future." Morris Morris suggests that the reference is to the behaviour Paul has written to them about, which quenches the Spirit and results in loss of spiritual power and joy. Verse 20 προφητείας μὴ ἐξουθενεῖτε προφητεια, ας f prophecy, preaching, the gift of prophecy ἐξουθενεω despise, treat with contempt Verse 21 πάντα δὲ δοκιμάζετε, τὸ καλὸν κατέχετε, δοκιμαζω test, examine, prove κατεχω hold fast, keep, restrain

5 "The point of this injunction, then, is that the Thessalonians are asked to apply tests. There are things that appear on the surface to be good. There are manifestations that claim to come from God. Such are not simply to be accepted at their face value, for it is not part of Christian simplicity to be credulous. All things must be tested. And not simply tested, but accepted wholeheartedly or rejected decisively as a result of the test. 'Hold on to' denotes the firm acceptance of the good. There must be no half measures." Morris Verse 22 ἀπὸ παντὸς εἴδους πονηροῦ ἀπέχεσθε. εἰδος, ους n visible form, appearance πονηρος, α, ον evil, bad, wicked πονηρου here can be either a noun or an adjective, the phrase meaning either 'every appearance of evil' or 'every evil appearance'. In either case the meaning is the same. ἀπεχω midd. abstain from, avoid Verse 23 Αὐτὸς δὲ ὁ θεὸς τῆς εἰρήνης ἁγιάσαι ὑμᾶς ὁλοτελεῖς, καὶ ὁλόκληρον ὑμῶν τὸ πνεῦμα καὶ ἡ ψυχὴ καὶ τὸ σῶμα ἀμέμπτως ἐν τῇ παρουσίᾳ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ τηρηθείη. εἰρηνη, ης f peace ἁγιάσαι Verb, aor act opt, 3 s ἁγιαζω sanctify, make holy ὁλοτελης, ες wholly, in every part The work carries the sense of completeness, 'to perfection'. ὁλοκληρος, ον sound, whole, complete ψυχη, ης f self, inmost being, life, 'soul' σωμα, τος n body Sanctification involves the whole person. ἀμεμπτως Adv (from ἀμεμπτος) blamelessly παρουσια, ας see 2:19 τηρηθείη Verb, aor pass opt, 3 s τηρεω keep, observe, maintain Verse 24 πιστὸς ὁ καλῶν ὑμᾶς, ὃς καὶ ποιήσει. πιστος, η, ον faithful, reliable Paul is confident that his prayer will be answered. "Because he is the faithful One, and because he is the One who has called them, the Thessalonians may know that he will do perfectly all that is involved in their call. It is profoundly satisfying to the believer that in the last resort what matters is not his feeble hold on God, but God's strong grip on him (cf. John 10:28-29)." Morris Verse 25 Ἀδελφοί, προσεύχεσθε περὶ ἡμῶν. προσευχομαι pray Paul needed their prayer as much as they needed his. Verse 26 ἀσπάσασθε τοὺς ἀδελφοὺς πάντας ἐν φιλήματι ἁγίῳ. ἀσπαζομαι greet, welcome φιλημα, τος n kiss ἁγιος, α, ον holy The meaning is 'give everyone a kiss from me.' Verse 27 ἐνορκίζω ὑμᾶς τὸν κύριον ἀναγνωσθῆναι τὴν ἐπιστολὴν πᾶσιν τοῖς ἀδελφοῖς. ἐνορκιζω place (someone) under a solemn charge (in the name of) Morris links this strong term to such passages as 2: "Apparently some of the Thessalonians had said that he had no real love for them, and if he had wished to do so, he would have been able to return. That he had not done so showed him to have his affections elsewhere. In this situation the ideal thing would have been for Paul to have returned. But his circumstances made this impossible; he had to use this letter as a substitute. Accordingly it was important not only that it should come before the notice of all, but also that it be seen plainly to be intended to come before the notice of all. In this way his care for them all would be manifest." Morris The first person singular may suggest that this is the point where Paul himself took up the pen. ἀναγνωσθῆναι Verb, aor pass infin ἀναγινωσκω read, read in public worship ἐπιστολη, ης f letter Verse 28 ἡ χάρις τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ μεθʼ ὑμῶν. χαρις, ιτος f grace, unmerited favour

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

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

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

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

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

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

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

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

Notes on the Greek New Testament Week 69 1 Thessalonians 4:9-5:28

Notes on the Greek New Testament Week 69 1 Thessalonians 4:9-5:28 Notes on the Greek New Testament Week 69 1 Thessalonians 4:9-5:28 Day 341: 1 Thessalonians 4:9-14 Verse 9 Περὶ δὲ τῆς φιλαδελφίας οὐ χρείαν ἔχετε γράφειν ὑµῖν, αὐτοὶ γὰρ ὑµεῖς θεοδίδακτοί ἐστε εἰς τὸ ἀγαπᾶν

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

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

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

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

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

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

Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο

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

Διαβάστε περισσότερα

LESSON 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

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

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

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

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

Διαβάστε περισσότερα

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

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

2 Thessalonians 3. Greek

2 Thessalonians 3. Greek Book Chapter Verse Interlinear English Word # in 2 Thess Greek # of letters # of words Numeric value 140301 00548 ΤΟ 2 370 140301 finally 00549 ΛΟΙΠΟΝ 6 310 140301 pray 00550 ΠΡΟΣΕΥΧΕΣΘΕ 11 1674 140301

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Living and Nonliving Created by: Maria Okraska

Living and Nonliving Created by: Maria Okraska Living and Nonliving Created by: Maria Okraska http://enchantingclassroom.blogspot.com Living Living things grow, change, and reproduce. They need air, water, food, and a place to live in order to survive.

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

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

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

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

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

Συστήματα Διαχείρισης Βάσεων Δεδομένων

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

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

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

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

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

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

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

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

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

Μηχανική Μάθηση Hypothesis Testing

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

Διαβάστε περισσότερα

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

ST5224: Advanced Statistical Theory II

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

Διαβάστε περισσότερα

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

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

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

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

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

Διαβάστε περισσότερα

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

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

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

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

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1 Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the

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

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

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

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

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

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

The Apostle Paul, Servant of Christ WELCOME Lorin Cranford

The Apostle Paul, Servant of Christ WELCOME Lorin Cranford WELCOME Lorin Cranford Page 1 Notes Here: Page 2 Notes here: Session Eighty-nine Taken from chapter nine of the book Emphasis on the writing ministry of Paul Learning Goals: 1. Learning what Paul wrote

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

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

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

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

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

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

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

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

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

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

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

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

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΠΕΛΟΠΟΝΝΗΣΟΥ

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

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ. Πτυχιακή Εργασία

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ. Πτυχιακή Εργασία ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία ΣΤΑΣΕΙΣ ΚΑΙ ΣΥΜΠΕΡΙΦΟΡΕΣ ΝΟΣΗΛΕΥΤΩΝ ΚΑΙ ΦΟΙΤΗΤΩΝ ΝΟΣΗΛΕΥΤΙΚΗΣ ΣΕ ΣΧΕΣΗ ΜΕ ΤΟ ΣΤΙΓΜΑΤΙΣΜΟ ΑΣΘΕΝΩΝ ΜΕ HIV Μιλτιάδους Γιώργος Λεμεσός

Διαβάστε περισσότερα

Fractional Colorings and Zykov Products of graphs

Fractional Colorings and Zykov Products of graphs Fractional Colorings and Zykov Products of graphs Who? Nichole Schimanski When? July 27, 2011 Graphs A graph, G, consists of a vertex set, V (G), and an edge set, E(G). V (G) is any finite set E(G) is

Διαβάστε περισσότερα

Πτυχιακή Εργασία. Παραδοσιακά Προϊόντα Διατροφική Αξία και η Πιστοποίηση τους

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

Διαβάστε περισσότερα

Please be sure that your kid memorized the song. Students homework -Pg.2: Read the song and the translation 3 times.

Please be sure that your kid memorized the song. Students homework -Pg.2: Read the song and the translation 3 times. 1 Name: Ms. Mesimeri Homework Δευτέρα Section: Τράβα μπρος Trava embros Parents homework -Print this homework packet. During the next two weeks we will mainly deal with the song «Trava ebros. Students

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

Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get)

Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get) Νόμος περί Αναπηριών 2006 (Disability Act 2006) Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get) Greek Νόμος περί Αναπηριών

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

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

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

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

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

Αγγλική Τουριστική Ορολογία

Αγγλική Τουριστική Ορολογία ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα Αγγλική Τουριστική Ορολογία Ενότητα 8: Exercises Κουτσογιάννη Ευαγγελία Τμήμα Διοίκηση Επιχειρήσεων Άδειες Χρήσης Το παρόν εκπαιδευτικό

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

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

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