The Consolations of Death In Ancient Greek Literature

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "The Consolations of Death In Ancient Greek Literature"

Transcript

1 The Consolations of Death In Ancient Greek Literature By SISTER MARY EVARISTUS, M.A. of THE SISTERS OF CHARITY, HALIFAX, N. S. A DISSERTATION Submitted to the Catholic Sisters College of the Catholic University of America in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy

2 NATIONAU CAPITAL PRESS, INC., WASHINGTON, D. C

3 TABLE OF CONTENTS Page INTRODUCTION. 7 CHAPTER I THE INEVITABLENESS OF DEATH, 10 Universality of death a motive for consolation. Views of death in Homer. Homeric epithets for death. No power can ward off death. Consolation afforded by the thought that it cannot come before the appointed time. Inevitableness of death as depicted in the Lyric Poets, Tragedians, Plato, Lysias, Apollonius Rhodius, ps.- Plutarch, Plutarch. CHAPTER II OTHERS HAVE HAD TO DIE 19 Treatment of τόπος in Homer, οΰ σοι μόνφ. Tragic Poets, Plutarch, ps.-plutarch. Examples of those who have borne sufferings nobly. Extension of τόπος. Even better men have died. CHAPTER III DEATH THE PAYMENT OF A DEBT TO NATURE 26 Should not complain when loan is claimed. Simonides of Ceos. Euripides. Plato. ps.-plutarch. CHAPTER IV DEATH NOT TO BE REGARDED AS UNEXPECTED 28 Nothing ought to appear unexpected. Meditation on death will rob it of its terrors and fears, άπάθβια Sophocles. Euripides, μβλζτη θανάτου of Plato. Socrates' attitude towards death. Plutarch's treatment of τόπος. ps.-plutarch. CHAPTER V DEATH A RELEASE FROM SORROWS. 31 Miseries of life. Homer. Hesiod. Pindar. Inconstancy of Fortune. Crantor. Life a punishment. Better not to have been born. Death a blessing, a remedy for evils. Treatment of τόπος by Tragedians. Story of Xerxes. Views of Epicharmus, Arcesilaus, Hegesias, Alcidamas, Prodicus of Ceos. Consolation for mourners. Used by Socrates, Lucian, ps.-plutarch. Death a peaceful sleep. Socratic argument. Death the end of a journey. Socrates. ps.-plutarch. t

4 The Consolations of Death CHAPTER VI DEATH BEFORE SORROW HAS COME CONSIDERED A BOON. 40 Untimely death. Pathos of early death. Consolation of family ties. Misfortune for parents to survive their children. Those who die early have escaped many misfortunes. Many would have been saved from great calamities if they had met an earlier death. Story of Termaeus of Elysia. "Troilus wept less than Priam." Early death mark of favor of the gods. Not longest life, but most virtuous, is best. Life short compared with eternity. CHAPTER VII DEAD DO NOT SUFFER FROM THE LOSS OF LIFE'S BLESSINGS. 44 Apprehension that the dead feel the loss of the pleasures of this life removed by consolers. Plutarch. Socrates. CHAPTER VIII COMFORT DERIVED FROM GIVING EXPRESSION TO GRIEF.. 45 Crantor's consolation. View taken by Homer. Stoic objection. Uselessness of grief. Used as a consolation in Homer, in Tragic Poets. Archilochus. Letter to Xanthippe. Display of grief unbecoming. Euripides. Plato. ps.-plutarch. Evil effects of grief, μηδβν άγαν. Moderation treated by Plato, Plutarch. Inconsistency of Stoics. Plutarch ad Uxorem. ps.-plutarch. Ίνώθι σαντόν. Grief is not pleasing to the dead. CHAPTER IX CONSOLATION THROUGH RECOLLECTION OF PAST JOYS Memory of past pleasure should help dissipate grief. Recollection of blessings still possessed. Effect of time. CHAPTER X IMMORTALITY OF THE SOUL 57 Belief among the Greeks in a future life. Pindar, Sophocles. Euripides. Vagueness of the idea of immortality. Used as a consolation by Plato, ps.-plato, ps.-plutarch. CHAPTER XI GLORY IN DEATH 60 Renown as an incentive. Death when prosperous. Death in performance of a noble action. Story of Cleobus and Biton. Alcestis. Death for country. Patriotism of Greeks. Effect. Funeral orations. Subject of orations, τόποι of consolation. Children belong pri-

5 In Ancient Greek Literature marily to the state. Iphigenia. Battle song of Tyrtaeus. ps.-platonic Epistle. Demosthenes. Sacrifice of life payment of debt to country. Death of hero increases the glory of the state. Most glorious and noble of deaths. A mark of favor of the gods. Hero receives due rites of burial, imperishable glory, and immortal renown. He leaves a glorious heritage. Patriot is welcomed by his brave ancestors and honored by the gods. State assumes charge of families. Words of comfort from the deceased. CHAPTER XII CONSOLATION APPROPRIATE TO PARTICULAR CIRCUMSTANCES Epicurus. Pericles. Cyrus. Music as a means of consolation. CONCLUSION

6

7 In Ancient Greek Literature 7 INTRODUCTION "The whole life of man is full of griefs, nor is there rest from toils, " 1 exclaims Euripides, and again: "There is no nature of man so obdurate which on hearing thy groans and the long plaints of misery would not let fall the tear." 2 These two sentiments to which Euripides has given expression are the source of a literature of consolation, the beginnings of which are found in the earliest Greek writers, and whose development into a system of topics of consolation adapted to every kind of grief was completed in the classical literature. Thoughts of consolation are supplied by the poets in words of charming sweetness. Many of them the philosophers have borrowed from the poets and clothed in language of sublime gravity. The rhetoricians in turn have added the magnificent impetus of their rhetorical art and formed for this style of writing certain rules. 3 Their development was practically complete by the time of Cicero. Any person, who, in his day, required words of consolation, could have recourse to the charm of the poet, the gravity of the philosopher, and the magnificence of the rhetorician to furnish the material he required. Cicero remarks: "There are particular treatises on banishment, on the ruin of one's country, on slavery, on weakness, on blindness, and on every incident that can come under the name of evil. The Greeks divide these into different treatises and distinct works." 4 The duties of the consoler were also laid down. Plutarch says, "The discourse that ought to come from friends and people disposed to be helpful should be consolation and not mere assent. For we do not in adverse circumstances need people to weep and wail with us like choruses in a tragedy, but people to speak plainly to us and to instruct us.... " B 1 Hipp Hec Cf. Androm. 421; Ores. 299; Hipp. 913; Aeschy., Prom. 240; Ον., El. i, ix. 3 Hieron., Ep. Ix, 5, 8. 4 Tusc. Disp. iii, xxxiv. 6 de Ex. 599B. Cic, T. D. iii, xxxi, thus expresses the same thought Haec igitur ofecia sunt consolantium, tollere aegritudinem funditus, aut sedare, aut detrahere quam plurimunij aut supprimere, nee pati manare longius, aut ad alia mentem traducere. Cf. Stob.,4ii, 113; Mein., iv, p. 349, 1.319, 1.326; Ibid., p. 356, 1.577; p. 357, 1.610, p. 359,1.674.

8 8 The Consolations of Death Death, "the Sleep that is due to all," 6 has, from its universality, been the occasion of more consolatory literature than any of the so-called evils of man. The Homeric age was remarkable for its simplicity. The view taken of life was serious but not pessimistic. Little reflection was made on death, which was considered a necessary evil an evil, however, which should be preferred to a greater evil, an ignoble life. With the development of philosophy the view taken of life assumed a different form. Naturally consequent on this was a change in the view taken of death. The Stoic braved death, even despised it; to him suicide pointed to a means of escape from the miseries of life. To the Epicurean it meant the end of all things. The manner of Socrates' death is explained by his hopes of a future happiness, hopes which contain the germ of the Christian Faith. This changed attitude towards death gave rise to new TOWOL of consolation. Unfortunately a large part of the consolatory writings has been lost. Crantor's Consolatio is especially to be regretted, for it was highly praised by the ancients; a golden book, Cicero calls it; and Panaetius tells Tubero that this book is worth learning by heart. 7 This work found many readers, for it treated of sorrow not as a reprehensible emotion as did the Stoics, but rather as a natural impulse requiring only to be kept within bounds. Cicero used it as the basis of his work, and the ps.-plutarch did the same in his ad Apolloniam. A like fate befell Cicero's Consolatio, 8 a work written to assuage his own grief at the death of his beloved daughter Tullia, in which he collected all the various arguments used by consolers on such occasions. 9 The only critical discussion of this style of literature to which I am indebted has been written by Buresch. 10 This writer has devoted an exhaustive study to the remains of all Consolatory literature down to the Sixth Century A. D. 11 He treats of its 6 Callimachus, Ep. 17. *Cic.,Acad.Q. II,XLIV. 8 The Tusculan Disputations in part supply for the lost Consolatio, for Cicero here repeats much said in his earlier work. *T. D. Ill, XXXI; IV, XXIX. 10 Most notable among the other critics is Skutsch, who has given a full analysis of the Consolatio ad Liviam with a view to fixing its date. Cf. Pauly-Wissowa, Real-Encyclopadie, Stuttgart, 1901, Vol. IV, p Consolationum a Graecis Romanisque Scriptarum Historia Critica, Lipsiae, 1889.

9 In Ancient Greek Literature 9 beginnings, growth and best productions. As above stated, much of the literature of Consolation has been lost. With painstaking fidelity, Buresch has sought out everything in any way suited to restoring the nature and meaning of the lost writings. Many also of the works on this subject remain matter of dispute. He with the same care, has endeavored to establish the authorship or approximate date of these disputed writings. In sketching the field of his research he suggests a further work the gathering together and arranging of the individual arguments and topics of Consolation which ancients have used. The scheme of the present thesis has been the following out of this suggestion of Buresch. No attempt has been made in the present writing to view the subject from a philosophical standpoint. Though this at first suggested itself as a possibility, an investigation of the matter disclosed so vast a field for research that it was necessary to limit the subject to one of its various aspects. Nor have the Latin authors been quoted in the text; though they, especially Cicero and Seneca, might perhaps furnish more abundant material. The reason in this instance, as before, is that by their insertion the scope of the thesis would be unduly extended. These authors are, however, freely referred to in the footnotes. Nor has there been any effort to show that in its fullest sense Consolation is found in something far more exalted than philosophy in Christianity which brings the consciousness of the presence and power of Christ, the dominant feature in religious consolation. The purpose, therefore, of this treatise is the collection, classification, and arrangement in logical order under the different τόποι, of the Consolations of death as expressed in the literature of ancient Greece.

10 10 The Consolations of Death CHAPTER I THE INEVITABLENESS OF DEATH The consideration that death is the common lot of all mankind, the natural consequence of birth, and that man, a creature of a day, 12 as Aeschylus calls him, must yield to it, offers a species of consolation to all. This aspect of death, therefore, is distinctly consolatory and will furnish us the first of the τόποι under which the motives affording consolation will be considered. Examining the passage of Homer in which death is mentioned, we feel constantly that he regarded death as something harsh and evil, 13 the deadly doom which no one who is born escapes. 14 "But swiftly on him came the evil which not one of them could ward off from him although they desired it." 15 "But harsh fate devoured me, the fate which was appointed me when I was born." 16 His favorite epithets for death are severe and stern, as "black fate," "evil destiny," "the fates of black death," "of death that lays men low." 17 These allusions to death readily evoke the image of the κήρ on the Chest of Cypselus described by Pausanius, 18 or of the* Krjpes of the Homeric poem, the Shield of Hercules. With peculiar tenderness and pathos the same poet dwells on the inevitable law of death. This is illustrated in the following passages. The father of gods and men, deliberating whether he would save his favorite Hector from the avenging hands of Achilles, was chided by Athene: "A man who is mortal, doomed long ago by fate, wouldst thou wish to redeem back from ill-boding death." 19 Hera addressed to him the same reproach when he wished to snatch 12 Prom. 253, 546, 944. Cf. Eur., Or. 976; Soph., Antig. 790; Pin., Pyth. vii. 95, viii. 135; Bacchy., iii Cf. Odyss. xi. 488; II. iii Odyss. xxiv. 29. μοϊρ' 6\οή, τήν ου TLS άλβύεται 6s ne γβνηται. Cf. Hesiod, Theog II. xv τάχα δ'αύτψ η\θβ κακόν, το οι ου TIS epvxaxev ιβμβνων περ. 16 II. xxiii. 78. άλλ' ϊμβ μεν κήρ άμφεχανε στυγερή, ή πβρ \άχβ γιγνόμενόν περ. 17 κήρ μέλαινα, κακός μόρος, κήρε$ μέλανος θανάτοιο, et alia. 18 Paus., v. xix II. xxii άνδρα θνητόν εοντα, πάλαι πεπρωμενον atajj, αψ εθελει* θανάτοιο δυσηχεος έξαναλΰσαι.

11 In Ancient Greek Literature 11 his beloved Sarpedon from the "tearful war." 20 And as if to give greater vividness to this impossibility of avoiding Fate we find* "And Eunomus, the augur, yet with all his auguries did not ward off black death; but was vanquished by the hand of the fleet-footed Achilles in the river when he slew the Trojans there and the rest." 21 Although Axylus had entertained all men, yet there was not one to save him from his doom. 22 Nor did the wonderful mace of Ereuthalion 23 or the golden attire of Nastes 24 hold back from them in any wise grievous destruction. "Nor yet did it avail aught to the two sons of Merops that their father beyond all men knew soothsaying and would have hindered them from marching to murderous war: for the fates of black death led them on." 25 Though Abas and Polyidus were sons of Eurydamus, dreamer of dreams, yet he discerned no dreams for them. 26 "Amphiaraus, the rouser of the host, whom Zeus, lord of the aegis, and Apollo loved with all manner of love, yet he reached not the threshold of old age." 27 "For, lo you, death, which is the common lot, the gods themselves cannot avert even from the man they love, when the baleful fate of death that lays men at their length, shall bring him low." 28 "Thou, 20 Ibid. xvi II. ii καί "Εννομος οίωνιστής* akv ουκ οιωνοϊσιν έρϋσατο κηρα μβλαιναν } αλλ' βδάμη ύπδχβρσί ποδώκβος Αίακίδαο kv ποταμφ, δθι πβρ Τρώας κβράϊξβ καί άλλου*. 22 II. vi φίλος δ'ην άνθρώποισΐ ττάντας yap φιλββσκβν όδφ tin οικία ναίων. αλλά ol όΰ τις των ye τδτ* ήρκβσβ Xvypdv okedpov πρόσθβν ύπαντιάσας. 23 II. vii δθ 1 άρ' ου κορύνη οί δλβθρον χραϊσμβ σι,δηρβίη II. ii δ καί χρυσόν 'έχων πό\βμδν δ'ϊ ν ήϋτβ κούρη, νήπιος, ουδέ τι ol το ^έιτηρκεσ* \vypbv δλβθρον, αλλ' έδάμη υπό χ ρσί ποδώκεος ^ Αίακίδαο kv ποταμώ. 25 II. ii τω δέ οί ου τι πβιθέσθην' κήρβς yap ayov μέλανος θανάτοιο. 26 II. ν τοϊς ουκ έρχομένοις δ ykpωv έκρίνατ' όνβίρους, άλλα σφέας κρατερός Αιομήδης έ&νάριξε. 27 Odyss. xv λαοσσδον Άμφιάραον δν πβρί κηρι φί\ ΐ Zeus τ^αίλ^ος καί ΆπδΧλων ταντοίην φιλότητ' ' ούδ' ΐκβτο yήpaoς ουδόν. 28 Ibid. Hi αλλ' η τοι θάνατον μέν δμοΐίον ουδέ θβοι π*ρ καί φί\ω άνδρί δύνανται ά\α\κέμ ν } δππότζ κβν δή μοϊρ' δλοή καθέλχισι τavη\eyέoς θανάτοιο.

12 12 The Consolations of Death too, Achilles, peer of gods, fate will destroy beneath the wall of the noble Trojans." 29 "Son of Atreus, we said that thou of all heroes wast always dear to Zeus, whose joy is in the thunder, seeing that thou wast lord over many great warriors in the land of the Trojans where we Achaeans suffered afflictions. But deadly doom was to visit thee too, which no one who is born avoids." 30 "I accept death... for not the mighty Heracles escaped death, although most dear to Cronian Zeus the king." 31 Although in these passages little is said about consolation directly, yet through all there is a note of fatalism which may at any time become a note of comfort. We find this in the words Sarpedon uses for his own encouragement and to urge on his friend Glaueus in the presence of death. "Ah, friend, if having escaped from this war, we were to be ageless and immortal, neither would I myself fight in the foremost ranks, nor would I send thee into war that gives renown; but now ten thousand fates of death beset us, which it is impossible for a mortal to escape or avoid let us go forward." 32 And again in the words of tenderness with which Thetis endeavors to console Achilles mourning over the body of Patroclus. "My child, the man who lies here we must let be, although we are grieved; for by the will of the god from the beginning was he brought low." 33 Passages similar to these are found where comfort is derived II. xxiii. 80. καί δβ σοι αυτψ μοίρα, Oeols βπιβίκβκ Άχιλλβυ, τβίχβί ΰπο Ύρώων evtiyevkoiv άπόχβσθαι. Cf. Eur., Ale Odyss. xxiv. 28. η τ 1 άρα καί σοι πρώτα παραστήσβσθαι βμβλλβ μοϊρ 1 Όλοι), την ου TLS άλβύβται 6s xe Ύβνηται,. II. xviii κηρα δ' βγω τότβ δίξομαι, οππότβ κβν δή Zeus βθβλη τβλβσαι ήδ αθάνατοι θβοί άλλοι, ούδβ yap ούδβ βίη % Ή.ρακ\ήος φν^ κηρα, 6s 7rep φίλτατος βσκβ Δα Κρονίωνι ανακτι II. χϋ ώ, πβπον, βί μβν yap ττό\βμον ττβρϊ τόvδβφυyόvτ αίβί δη μβκλοιμβν άγήρω τ'άθανάτω τβ βσσβσθ 1, οΰτβ κβν αυτός βνϊ πρώτοισι μαχοίμην οΰτβ κβ σβ στβλλοιμι μάχην es κυδιάνβιραν' νυν δ'βμπης yap κήρβς βφβστασιν θανατοιο μυρίαι, as ουκ βστι φυyelv βροτόν ούδ' ύπαλύξαι, ΐομβν, Cf. Odyss. xvi, 446. II. xix. 8. τ'βκνον βμόν, τούτον μβν βάσομβν άχνύμβνοί πβρ κβϊσθαι, βπβι δη τρώτα θβών Ιοτητι δαμάσθη.

13 In Ancient Greek Literature 13 ifrom the thought that death, though inevitable, cannot come before the time ordained by the gods. "Although we are afflicted we shall not yet go down to the house of Hades before the day of destiny comes." 34 It is this the noble Hector uses to comfort his sorrowing wife. "Dear one, do not grieve excessively. For no men will hurl me into Hades against my fate; but I say no man, either coward or valiant, when once he has been born, has fled from destiny." 35 But nowhere is the pathos of man's mortality expressed with more wonderful power and strength than in the simple words "Even as are the generations of leaves, such are those also of men; the wind scatters the leaves on the earth, but the forest budding brings and produces others in the season of spring: thus the generation of men, one produces and another ceases." 36 Simonides of Ceos was impressed by the Homeric expression when he wrote, "Nothing among men remains eternally lasting. The man of Chios has well said this one best thing, 'like the generation of leaves, such is the race of men.' " 37 Scattered throughout his writings are allusions to this aspect of death. "The strength of man is slight but his troubles are incurable, for a short time labor about labor. Yet unavoidable death threatens him, for an equal share of this is the portion by lot both of the good and the bad." dyss. x Τ Ω φίλοι, ου yap πω καταδυσόμβθ 1, άχνύμβνοί πβρ, eis Άίδαο δόμους, πριν μόρσιμον ήμαρ βπβλθη. 35 II. VI δαιμονίη, μη μοί τι λίην άκαχίζβο θυμφ. ου yap ris μ 1 ύπβρ αϊσαν άνήρ *Άϊδι προϊάφβι. μοϊραν δ'ου τινά φημι πβφυyμβvov βμμβναί ανδρών, ου κακόν, ούδβ μβν βσθλόν, βπήν τα πρώτα ykvt\rai. Cf. II. ix κάτθαν 1 όμως 6 r'aepyos άνήρ 6 τβ πολλά kopycos. Aeschy., Cho. 103; Lysias, Fun. Or. 77; Hor., Od. i. iv. 13;. i. xxviii. 19; ii. iii.21; iii. i. 14; Proper., El. iii. xviii II. vi οϊη πβρ φύλλων yeverj, τοίη 5e και ανδρών. φύλλα τα μβν τ' ανβμος χαμάδίς χββι, άλλα δβ Ο 1 ΰλη τηλβθόωσα φύβί, eapos δ'wiyiyvetai ώρη. ώ$ ανδρών yeverj ή μβν φύβι ή δ, άπoλήyβι. Cf. II. xxi Bergk, iii. Sim. 85 (60). (ούδβν βν ανθρώποισι μ'βνβι χρήμ' βμπβδον αίβί.) βν δβ το καλλιστον Xlos ββιπβν άνήρ. οϊη πβρ φύλλων yβvβή, τοίη δβ και ανδρών. 38 Ibid., 39. (54). 'ανθρώπων ολίγο? μβν κάρτος, άπρακτοι δβ μβληδόνβς,

14 14 The Consolations of Death "Death comes even to the coward." 39 Callinus in his exhortation to battle urges the inevitableness of death as an inspiration tci valor. "For in no wise is it fated that a man should escape^ death, not even if he is of immortal ancestors. Very often escaping the strife of battle and the din of javelins he goes his way, but the, fate of death overtakes him in his home." 40 Demosthenes isj imitating Callinus in the striking passage: "For all mankind the! end of life is death, even if one shutting himself up in a cage protects himself; but it is necessary for brave men to strive always for all honors, placing good hope before them, and to endure courageously whatever the deity ordains." 41 This strain of pathos at the thought of the mortality of man appears frequently in the Odes of Pindar. "All must die." 42 "On the rich and the poor alike the end of death falls." 43 "For equally comes the wave of death and falls on the fameless and the famed" (or on the unexpecting and expectant). 44 "We all in like manner die, although our lots are different." 45 Or as Theognis expresses it, "No one by paying a ransom can escape death or heavy disease or severe old age coming CLLCUVL δε παϋρω πόνος άμψϊ πόνω. δ δ'άφυκτος όμως επικρέμαται θάνατο*, κείνου yap Ισον \άχον μέρος οΐ r'ayadol όστις re κακός Ibid., 65. (106). ό δ'αν θάνατος κίχε καί τον φν^όμαχον. 40 Ibid., iical. 1 (1). 12ff. ού yap πως θάνατον ye cpvyelv εϊμαρμενον εστίν άνδρ\ ούδ'εί πpoyόvωv y yevo* αθανάτων. πόλλάκι δηϊοτητα <pvy<hv καί δοΰπον ακόντων έρχεται, kv δ'οϊκω μοίρα κίχεν θανάτου. 41 de Cor repas μεν yap άπασιν άνθρώποις του βίου θάνατος, καν kv οικίσκω τις αυτόν καθείρξας τηρχι. δεϊ δέ τους άyaθoύς άνδρας kyxeipelv μεν άπασιν άεϊ τοϊς καλοϊς, την άyaθγ^v προβαχχομβνους ελπίδα, φερειν δ'α> ό θεός δίδω yevvaίως. 42 Berkg, i. 01. i. 82. θανεϊν δ'ισιν άvάyκa. Cf. Ibid., iii. Diagoras 2; Anth. Lyr., Phanocles 2; Stob., iii. 118; Cons., ad Liv. 357; Sen., ad Marc xvii; Proper., El. ii. xxviii. 58; Ver., Georg. iii. 67; n Ibid., Nem. vii. 27. άφνεός πενιχρός re θανάτουπόρον σάμα νεονται. Cf. Odyss.. xiii. 59: Pyth., Carm. Aur Ibid., Nem. vii. 44. άλλα κοινόν yap έρχεται κΰμ 1 Ά'ι'δα, πέσε δ'άδόκητον εν καί δοκεοντα. 45 Ibid., Isth. vii. 59. θνάσκομεν yap όμως άπαντες. δαίμων δ* α ίσος.

15 In Ancient Greek Literature 15 upon him." 46 In Anacreon also we find mentioned this necessity of death, but, as in many of the odes of Horace, the motive is rather that of the "carpe diem." 47 There are a number of references in the tragic poets to the inevit ableness of death bringing with it the consolatory reflection that the calamity should be borne with calmness. In Euripides (Hercules Furens 281), Megara, in spite of her own natural repugnance to death, encourages Amphitryo to meet it nobly. "I think it a dreadful thing to die, yet I consider that mortal foolish who strives against necessity. But since we must die, we ought to die not wasted away by fire furnishing laughter to our enemies." 48 " Endure with us death, which nevertheless awaits thee. I call upon thy nobleness, old man; for whoever is eager to escape from misfortunes sent by the gods, he is eager but his eagerness is foolish. For what must be no one will make that it must not be." 49 Under similar circumstances, Euripides (Orestes 1022) shows Orestes reproaching Electra for her groans and tears. "Wilt thou not in silence, ceasing from womanish groans, make up thy mind to what is decreed? These things are indeed lamentable, but yet thou must bear thy present fate." 50 In Euripides' Alcestis (614 if.), Pheres makes use of this 46 Max ούδ' αν αποινα bihovs θάνατον <phyoi ούδε βαρείας vovaovs ούδε κακόν yrjpas επερχόμενον. Cf. Ibid., 1010, 1187; Bergk, ii. Solon, 24. (5.) 7; Ibid., ps.- Phocy. 110; Soph., Antig. 952; Proper., El. iv. xi Bergk, Anac. 38.(24); 43. (25.); 34. (23.); 48. (39.); 50. (36); Cf. Hor., Od. i. xxviii, xxxv; ii. xiv, xviii; iii. xxiv; iv. vii. 48 και το κατθανεϊν δεινόν νομίζω'τφ δ'άναύκαίω τρόπω os αντιτείνει σκαιόν η^ονμαι βρότον. ήμά$ δ 1 } επειδή δει θανεϊν, θνήσκειν χρεών μη πυρϊ καταξανθβντας, εχθροϊσιν yexoov δίδοντας,... Cf. Mull., Democ, frg. 44. ί τόλμα μεθ 1 ημών θάνατον, os μένει σ 1 δμωs. προκάλοϋμεθ 1 evyevetav, ω yepov, σ'εθεν. τ as των θβών yap δστπ εκμοχθεϊ Tvxas, πpόθvμόs εστίν, η προθυμία δ'άφρων. δ χρή yap ούδε^ μη χρεών θήσει ποτέ. Cf. Jodrell's note on necessity, Illus. of Eur. Ale. 259, liii; Campbell, Soph. frg ου aly' άφεϊσα τους yυvaικείoυs yόoυs στερξεπ τα κρανθεντ'; οικτρά μεν τάδ\ αλλ' 6μωs (φερειν a'avay^ ras πapεστώσas τύχα?). Cf. Mein., iv. p

16 16 The Consolations of Death consolation when condoling with Admetus over the loss of his wife. "I come, my son, sympathizing with thee in thy misfortunes, no one will deny that thou hast lost a good and chaste wife. But it is necessary to bear these things although they are hard to bear." 51 And Atossa (Aeschylus, Persians 294 ff.) found in it some alleviation for her grief over the misfortunes which had befallen the Persian army. "This calamity is too great for me to speak or enquire about our sufferings. Nevertheless it is necessary for mortals to endure afflictions when the god sends them." 5 2 The threat of death did not deter Antigone (Sophocles, Antigone 460 ff.) from disobeying the orders of the king and burying her brother. "For I know I must die and why not? Even thougli you had not proclaimed it; and if I die before my day, I count it gain." 53 We have the Chorus, in the same author (Electra 860), reminding Electra in her grief that "death is natural to all mankind," 54 and again (1171): "thou art begotten of a mortal father, Electra, reflect; and mortal is Orestes; do not lament excessively, for to suffer this is owing to us all." 55 The ps.-plato expresses this necessity with even greater emphasis: "Not one of us has been born immortal; nor if this should happen to anyone would he become happy, as it seems to the multitude." 56 And this fact is 51 ηχω χαχοϊσι σοϊσί συ^κάμνων, rkxvov, εσθλης yap, ουδείς άντερεϊ, xal σώφρονος γυναικός ημάρτηχας. άλλα ταΰτα μεν φ'ερειν ανάγκη χαίπερ όντα δϋσφορα Cf. Ibid., 1070; Androm. 1233; η υπερβάλλει yap ήδε σνμφορά, το μήτβ λε (Η μητ 1 ερωτησαι πάθη. όμως δ 1 avayky\ πημονάς βροτοϊς φ'ερειν θεών διδόντων. Cf. Campb., Soph., Frag. 523; Eur., Hec θανουμενη yap εξήδη, τι δ' ου\ χει μη συ κρουχήρυξας. ει δε του χρόνου πρόσθεν θανοϋμαι χερδος αυτ' εyώ λέγω. 54 πάσι θνατοϊς εφυ μόρος. Cf. Sen., Ep cui nasci contigit, mori restat. 55 θνητού πεφυχας πατρός, 'Ηλέκτρα, φρόνει, θνητός δ' 'θρεστης. ώστβ μη λιάν στενέ. (πάσιν yap ημϊν τοϋτ' οφείλεται παθεϊν.) Cf. Diog. La., ii. Anaxag. ix; Xen. x; Cons., ad Liv., 367, 56 Ep. vii. 334E. οότε yap πεφυχεν αθάνατος ημών ουδείς, οΰτ] ει τψ ξυμβαίη, ykvoito αν ευδαίμων, ώς δοχεϊ τοϊ$ πολλοίς:

17 In Ancient Greek Literature 17 borne out by the myth of Tithonus consumed by " cruel immortality" "and longing for the state of happy men who have the power to die." 57 With effective eloquence Lysias introduces in his Epitaphios (77) this motive of consolation. "I do not know why we should grieve over such things. For we are not ignorant that we are all mortal. Why are we afflicted at such events as if one ought not to have expected them? Why support with so much impatience accidents which come from our nature, when we know that death makes no difference between the cowardly and the brave?" 58 In the passages of Apollonius Rhodius, illustrating this point, a close parallel is seen between his turns of thought and even his expressions and those of Homer. "On the same day a pitiless fate there seized Mopsus, son of Ampycus, and he escaped not a bitter doom by his prophecies, for there is no averting of death. " 59 "And here his destined fate smote Idmon, son of Abas, skilled in soothsaying, but his soothsaying did not save him, since necessity led him on to death." 60 "They say that Tiphys, son of Hagnias, died; nor was it his destiny to sail any farther. But a short sickness laid him to rest, there on the spot, far from his native land." 61 "I will dare (the contest)," said Aeson, "even if it is my doom to die, for nothing will fall on man more rigorous than dire necessity." Cf. Tennyson's Tithonus. 58 Άλλα yap ουκ οίδ' 6 τι δει τοιαύτα όλοφύρεσθαι. ου yea ελανθάνομεν ημάς αυτούς 6VT S Θνητοί. ώστε τι δεϊ } α πάλαι, προσεδοκώμβν πείσεσθαι, υπέρ τούτων νυν άχθεσθαι, ή λίαν ούτω βαρέως φ'ερειν επί ταϊς της φύσεως συμφοραϊς, επισταμένους ότι δ θάνατος κοινός καί τοϊς χειρίστους καϊ τοϊς βελτίστοις] Cf. Cic. ad Fam. iv. 5 where Servius Sulpicius extended this reasoning farther and found consolation from beholding the ruins of former magnificent cities, ι Polyb., xxxix Argon, iv "Ενθα καί Άμπυκίδην αύτω kvl ήματι Μόψον νηλειής ελε πότμος ' άδευκεα δ 7 ου φυyεv αϊσαν μαντοσύναις ' ου yap τις άποτροπίη θανάτοιο. 60 Ibid. ii "Εϊ>#α δ' Άβαντιάδην πεπρωμένη ήλασε μοίρα "Ιδμονα, μαντοσύνησι κεκασμενον άλλα μιν ούτι 61 Ibid. ii μαντοσύναι εσάωσαν, επεϊ χρεώ ^ε δα/^αι. % kyvιάδηv Ύϊφυν ^a^eei^ φάτις. οϋδ'ε οι ηεν μοΐρ* ετι ναυτίλλεσθαι έκαστερω. αλλά νυ καϊ τον au^t μινυνθαδίη πάτρης εκάς ευνασε νουσος, 62 Ibid. in τλήσομαι, ει καίμοι ^a^eet^ μόρος. ου yap ετ'άλλο 'piyiov άνθρώποισι κακής επικείσετ 1 άvάyκης^

18 18 The Consolations of Death And when the same hero and his companions killed in mistake tljie hospitable king of the Doliones, bitter grief seized them. "Yet he filled up the measure of his fate; for it is not lawful for mortals to escape from it.'' 63 The author of the Plutarchian Consolation to Apollonius telis his friend that "each one ought to know that not only he himseijf is mortal in his nature, but it is the lot for mortal life and things to be quickly changed into the opposite." 64 "Why is it wonderfu l... if that perishes which by nature is perishable?" 65 "If therefore anyone is angry when he is dying himself, or resents the* death of his children, is it not very plain that he has forgotten that he himself is a man and that he has begotten mortal children? For a man that is sensible cannot be ignorant that man is a mortal creature and born for this, that he must die." 66 In de Tranquilitate Animi, Plutarch dwells on the same thought. "And with regard to things that seem to pain us by their very nature, as sickness and anxieties and the death of friends and children, we should remember that line of Euripides, 'Alas! and why alas? We only suffer what mortals must expect.' For no argument so lays hold of emotion when borne down and dejected as the remembrance of the common and natural necessity to which man is exposed owing to the body, the only part which he gives to fortune; for in his most important and influential part, he is secure." Ibid. i μοϊραν άνβπλησβν. την yap θβμις ουποτ 1 άλυξαι θνητοϊσιν F. χρή yap ου μόνον εαυτόν elh'evai θνητόν όντα την φύσιν, άλλα καί ότι θνητφ avyx^pos εστί βίω καί πpάyμaσι 'ραδίως μβθισταμβνοις προς τουναντίον. 65 Ibid. 106D. τί yap θαυμαστόν... el το φθαρτόν 'έφθαρται; 66 Ibid. 116B. ό ουν ή αυτός μέλλων άποθνήσκβιν ή τέκνων αποθανόντων ύπβpayavaκτώv πώς ου καταφανώς βπιλβλησται Οτι καί αυτός άνθρωπος εστί καί τα τέκνα θνητά *^'εννησεν\ ου yap εστί φρενας 'έχοντοςάνθρωπου ayvoelv ότι ό άνθρωπος ζφον εστί θνητόν ) ούδ' οτι yeyovev εις τό άποθανεϊν C. προς δε τά φύσει δοκοΰντα λυπεϊν, οία νόσοι καί πόνοι και θάνατοι φίλων καί τέκνων, εκείνο τό Ευριπίδειοι* * οΐμοι. τί δ 1 οΐμοι] θνητάτοι πεπόνθαμεν. 1 ουδείς yap ούτω του παθητικού καταφερομενου καί όλισθάνοντας αντιλαμβάνεται λόyoς 7 ως ό της κοινής και φυσικής άνάμνησιν ποιών άvάyκης y η δια τό σώμα μεμ^μενος ό άνθρωπος μόνην ταύτην τη τύχη λαβην δίδωσιν, εν δε τοις κυριωτάτοις καί μ^ίστοις ασφαλής 'έστηκεν. Cf. η. 99.

19 In Ancient Greek Literature 19 CHAPTER II OTHERS HAVE HAD TO DIE This fellowship in misfortune is one of the sources of its greatest alleviation. The reflection that other men have had to die, that others have had to part with friends, helps to soften grief and moderate tears. 68 Hence this reflection furnishes a τόπος closely connected with the preceding one. (The minstrel, singing the story of the misfortunes of the Danaans who had gone to the Trojan yvar, recalled even more vividly to the constant Penelope the memories that were wasting her heart with comfortless sorrow; and she begged him to cease such strains and sing other deeds of gods and men. But Telemachus answered tfiat she should allow the minstrel to gladden their hearts as the spirit moved him, for men prize the song which rings newest in tijieir ears "but let thy heart and mind endure to listen, for not Odysseus only lost in Troy the day of his returning, but other mien also perished." 69 The Chorus, which portrays the pervading sentiment of the action in the dramas, dwells upon this phase of consolation. Repeatedly it reminds Admetus that he is not the only one who has lo$t a noble wife. "Admetus, thou must bear this calamity; for thjsu art not the first nor the last of mortals who has lost an excellent wife." 70 "But puttest thou no bound to thy sorrows? Xhey are heavy to bear but still... endure, thou art not the first man that has lost... thy wife; but different calamities of mortals strike different men." 71 "Thy wife is dead, she left her love behind: what new thing is this? Death has already destroyed 68 Cf. Mullach., Pythag. Frag. 3; Sen., Polyb. i; Cons., ad Liv Odyss. i σοι δ' έπιτολμάτω κραδίη καί θυμός άκούειν' ού yap 'Οδυσσεύς olos απώλεσε νόστιμον ημαρ έν Tpoiy, πολλοί δέ και άλλοι φώτες όλοντο. Cf. Hor., Od. i. xxviii, ii. x, iii. ix. 70 Eur., Ale "Αδμητ 1, h.vk^t\ τάσδε συμφοράς φέρειν ου yap τι πρώτος ' ουδέ λοίσθιος βροτών yυvalκός έσθλης ήμπλακες. 71 Ibid πέρας δε y 1 ουδέν ά^εων τίθης... βαρέα μεν φέρειν, όμως δε.... τλάθ 1 ' ού σύ πρώτος ώλεσας.... yυvalκa ' συμφορά δ 1 έτερους ετέρα πιέζει φανείσα θνατών.

20 20 The Consolations of Death the wives of many." 72 This theme is often introduced by the formula ου σοι μόνω, which at once classifies this τόπος. Such is the consolation offered by the Chorus to Theseus in Euripides, Hippolytus 834 ff. "Not to thee alone, Ο king, have these evils happened, but with many others thou hast lost an excellent wife." 73 Lamenting over the sorrows of Hermione, in Euripides, Andromache 1041 ff., it enumerates the evils that have fallen on Trojans and Greeks. "Not upon thee alone, not upon thy friends have sad griefs fallen." 74 In the same strain it endeavors to comfort Electra, in Sophocles' play of the same name (153 ff.). "Not on thee alone of mortals, Ο child, has grief fallen." 75 And in passionate language it endeavors to console Antigone in that play of Sophocles (944 ff.) by reminding her of mythological examples of similar suffering. "The form of Danae, too, endured to leave the light of heaven in dungeons secured with brass, and concealed in a sepulchral chamber she was bound.... But the power of fate is a marvelous one. Neither happiness, nor war, nor tower, nor black sea-beaten ships, escape it. And the king of the Edonians, the quick-tempered son of Duyas, was imprisoned for his fierce anger, being shut up by Bacchus in a rocky prison; and thus he distills the dreadful fury of his madness, in full force.... By the Cyanean deeps of the double sea, the shores of the Bosphorus, and the (inhospitable) Thracian Salmydessus, where Mars dwells near their cities, saw the accursed wound, inflicted with blindness, on the two sons of Phineus by a cruel stepmother, a wound darkening the wretched balls of their eyes which were 72 Ibid Wave δάμαρ, exine φιλίαν τι vkov τόδβ; TOWOIS ήδη τταρβχυσβν Θάνατος δάμαρτας. 73 ου σοί τάδ\ ώναξ, η\θβ δη μόνω κακά, πο\\ών μετ' αλλ ω δ 1 tl)\eaas κβδνόν \e%os. Cf. Sen., Polyb. xxi. / 74 ουχί σοί μόνα δύσφρονβς βπβπβσον, ου φίλοισι λυπαι' Cf. Helen, 464.! 75 ούτοι σοί μούνα, τβκνον, \ a%os βφάνη βροτών, Cf. Ibid. 289, ω δύσθβον μίσημα, σοι μόνη πατήρ τβθνηκεν; awos S'ourts ev πβνθβι βροτών; where Electra complains to the chorus that her heartless mother repoaches her for grieving for her father.

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

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 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

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

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

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

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

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

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

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

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

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

derivation of the Laplacian from rectangular to spherical coordinates

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

Διαβάστε περισσότερα

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

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

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

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

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

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

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

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

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

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

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

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

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

Calculating the propagation delay of coaxial cable

Calculating the propagation delay of coaxial cable Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric

Διαβάστε περισσότερα

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

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

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

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

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

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

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

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

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

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

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

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

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

2007 Classical Greek. Intermediate 2 Translation. Finalised Marking Instructions

2007 Classical Greek. Intermediate 2 Translation. Finalised Marking Instructions 2007 Classical Greek Intermediate 2 Translation Finalised Marking Instructions Scottish Qualifications Authority 2007 The information in this publication may be reproduced to support SQA qualifications

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

Newborn Upfront Payment & Newborn Supplement

Newborn Upfront Payment & Newborn Supplement GREEK Newborn Upfront Payment & Newborn Supplement Female 1: Το μωρό μου θα ρθει σύντομα, θα πρέπει να κανονίσω τα οικονομικά μου. Άκουσα ότι η κυβέρνηση δεν δίνει πλέον το Baby Bonus. Ξέρεις τίποτα γι

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

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

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

MS 075 Growing old is inevitable, growing up is optional. MS 142 Good friends are worth holding onto.

MS 075 Growing old is inevitable, growing up is optional. MS 142 Good friends are worth holding onto. 68 ίπτυχες ευχετήριες κάρτες 15 x 15 cm, λευκές εσωτερικά, συσκευασµένες µε φάκελο MS 019 Nothing is more beautiful than the love that has weathered the storms of life. MS 036 Life is nothing without friendship.

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

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

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

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013 Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering

Διαβάστε περισσότερα

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

Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ

Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ Πτυχιακή Εργασία Η ΠΟΙΟΤΗΤΑ ΖΩΗΣ ΤΩΝ ΑΣΘΕΝΩΝ ΜΕ ΣΤΗΘΑΓΧΗ Νικόλας Χριστοδούλου Λευκωσία, 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ

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

Αναερόβια Φυσική Κατάσταση

Αναερόβια Φυσική Κατάσταση Αναερόβια Φυσική Κατάσταση Γιάννης Κουτεντάκης, BSc, MA. PhD Αναπληρωτής Καθηγητής ΤΕΦΑΑ, Πανεπιστήµιο Θεσσαλίας Περιεχόµενο Μαθήµατος Ορισµός της αναερόβιας φυσικής κατάστασης Σχέσης µε µηχανισµούς παραγωγής

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

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 3β: Types of Speeches & Strong Language Ιφιγένεια Μαχίλη Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative

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

SAINT CATHERINE S GREEK SCHOOL ΕΛΛΗΝΙΚΟ ΣΧΟΛΕΙΟ ΑΓΙΑΣ ΑΙΚΑΤΕΡΙΝΗΣ

SAINT CATHERINE S GREEK SCHOOL ΕΛΛΗΝΙΚΟ ΣΧΟΛΕΙΟ ΑΓΙΑΣ ΑΙΚΑΤΕΡΙΝΗΣ SAINT CATHERINE S GREEK SCHOOL ΕΛΛΗΝΙΚΟ ΣΧΟΛΕΙΟ ΑΓΙΑΣ ΑΙΚΑΤΕΡΙΝΗΣ WELCOME TO ST. CATHERINE S GREEK SCHOOL! WEEKDAY GREEK SCHOOL - REGISTRATION FORM SCHOOL YEAR 2016-2017 ΑΙΤΗΣΗ ΕΓΓΡΑΦΗΣ ΣΧΟΛΙΚΗ ΧΡΟΝΙΑ

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

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

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

Η αντίσταση στην ανθρωπιστική ψυχοθεραπεία

Η αντίσταση στην ανθρωπιστική ψυχοθεραπεία Η αντίσταση στην ανθρωπιστική ψυχοθεραπεία Σταλίκας Αναστάσιος, Καθηγητής, Πάντειο Πανεπιστήμιο Γιωτσίδη Βασιλική, Διδάκτωρ Κλινικής Ψυχολογίας, Ψυχοθεραπεύτρια. Χριστίνα Σεργιάννη, Διδάκτωρ Κλινικής Ψυχολογίας,

Διαβάστε περισσότερα

SPECIAL VERBS (auxiliary verbs) (βοηθητικά ρήµατα)

SPECIAL VERBS (auxiliary verbs) (βοηθητικά ρήµατα) SPECIAL VERBS (auxiliary verbs) (βοηθητικά ρήµατα) CAN-COULD To βοηθητικό ρήµα can δείχνει: α. δυνατότητα-ικανότητα β. πιθανότητα - άδεια Π.χ. I can lift this box (ικανότητα) can I go out? (άδεια) You

Διαβάστε περισσότερα

þÿ»±íº »¹ Áà  : É º±¹ Ä þÿ Á³ Ä Å : ¼¹± ºÁ¹Ä¹º ±À Ä ¼

þÿ»±íº »¹ Áà  : É º±¹ Ä þÿ Á³ Ä Å : ¼¹± ºÁ¹Ä¹º ±À Ä ¼ Neapolis University HEPHAESTUS Repository School of Health Sciences http://hephaestus.nup.ac.cy Master Degree Thesis 2015 þÿ»±íº »¹ Áà  : É º±¹ Ä þÿ Á³ Ä Å : ¼¹± ºÁ¹Ä¹º ±À Ä ¼ þÿ Ä Æ Á Â, Á ÃÄ Â þÿ Á̳Á±¼¼±

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

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

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

ΔΙΑΘΕΜΑΤΙΚΟ ΠΑΡΑΜΥΘΙ ΧΑΜΕΝΟΙ ΗΡΩΕΣ THE LOST HEROES

ΔΙΑΘΕΜΑΤΙΚΟ ΠΑΡΑΜΥΘΙ ΧΑΜΕΝΟΙ ΗΡΩΕΣ THE LOST HEROES ΔΙΑΘΕΜΑΤΙΚΟ ΠΑΡΑΜΥΘΙ ΧΑΜΕΝΟΙ ΗΡΩΕΣ THE LOST HEROES Μια φορά κι έναν καιρό σε τόπους μακρινούς συναντήθηκαν Once upon a time in far away places οι παλιοί φίλοι φίλοι ο Μπόλεκ, ο Λόλεκ, ο Αστερίξ, ο the

Διαβάστε περισσότερα

ΙΩΑΝΝΗΣ ΛΑΣΚΑΡΗΣ, ΠΗΓΩΝΙΤΗΣ Ή ΣΥΡΠΑΓΑΝΟΣ, Ο ΚΑΛΟΜΙΣΙΔΗΣ

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

Διαβάστε περισσότερα

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

Second Order Partial Differential Equations

Second Order Partial Differential Equations Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y

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 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

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ. Πτυχιακή Εργασία

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

Διαβάστε περισσότερα

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

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education *6301456813* GREEK 0543/03 Paper 3 Speaking Role Play Card One 1 March 30

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

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

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

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

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

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

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

Objectives-Στόχοι: -Helping your Child become a fantastic language learner «Βοηθώντας το παιδί σας να γίνει εξαιρετικό στην εκμάθηση γλωσσών» 6/2/2014

Objectives-Στόχοι: -Helping your Child become a fantastic language learner «Βοηθώντας το παιδί σας να γίνει εξαιρετικό στην εκμάθηση γλωσσών» 6/2/2014 -Helping your Child become a fantastic language learner «Βοηθώντας το παιδί σας να γίνει εξαιρετικό στην εκμάθηση γλωσσών» Dr Caroline Linse Queens University, Belfast, Northern Ireland Objectives-Στόχοι:

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

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

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

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

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

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

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

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

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

Διαβάστε περισσότερα

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

Nuclear Physics 5. Name: Date: 8 (1)

Nuclear Physics 5. Name: Date: 8 (1) Name: Date: Nuclear Physics 5. A sample of radioactive carbon-4 decays into a stable isotope of nitrogen. As the carbon-4 decays, the rate at which the amount of nitrogen is produced A. decreases linearly

Διαβάστε περισσότερα