Χρονολόγηση. Γεωγραφικός εντοπισμός Constantinopole, Istanbul. Τοπογραφικός εντοπισμός Blachernai region IΔΡΥΜA ΜΕΙΖΟΝΟΣ ΕΛΛΗΝΙΣΜΟΥ. 1.

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Χρονολόγηση. Γεωγραφικός εντοπισμός Constantinopole, Istanbul. Τοπογραφικός εντοπισμός Blachernai region IΔΡΥΜA ΜΕΙΖΟΝΟΣ ΕΛΛΗΝΙΣΜΟΥ. 1."

Transcript

1 Περίληψη : The basilica of the Virgin Mary of Blachernai became the most popular Constantinopolitan pilgrimage shrine of Theotokos. Its erection was traditionally attributed to Pulcheria and Emperor Maurice; it seems, however, that it was erected by Justin I ( ). Earlier mentions of pilgrimage shrine of the Virgin Mary of Blachernai probably referred to the chapel (Soros), where the maphorion (the holy veil) of the Virgin was kept after its translation from Palestine in the 460s. Until the 7 th century the basilica stood outside the city walls, since the Theodosian enclosure was not extending as far as the region of Blachernai; thus, the fact the the church was spared during the Avar siege in 626 was considered a miracle. The lifting of the Avar siege, which was attributed to a miraculous intervention of Theotokos, was associated with Virgin Mary of Blachernai (the Virgin Vlachernitissa). During the following centuries, the Virgin Vlacernitissa came to be considered as the city s divine protector par excellence. The church was entirely destroyed by a fire in 1070; by 1077 it had already been rebuilt. This second building was destroyed, again by fire, in The existing church is dated to the mid-19 th century. Χρονολόγηση 2 nd half of the 5 th c Γεωγραφικός εντοπισμός Constantinopole, Istanbul Τοπογραφικός εντοπισμός Blachernai region 1. Introduction The cult of Theotokos held a central place in the religious life of Constantinople. Already from the 7 th century Constantinople became, according to C. Mango s expression, Theotokoupolis (=city of Virgin Mary), with an ever growing emphasis on Virgin s cult which is also apparent in the effort to gather relics of hers in the capital. In one of his orations in 624/625, Theodore Synkellos mentions the density of churches and chapels dedicated to Theotokos, situated almost in every public building, palace or religious foundation. 1 The most important pilgrimage shrine of Theotokos at Constantinople was the church of Blachernai. 2 In reality, it was a complex including the basilica (it is also mentioned as the Great Church in the De Cerimoniis), the Hagia Soros, where Virgin s maphorion was kept, as well as other holy relics, and a bath edifice, the so-called lousma (λού[σ]μα). 3 The date of the structure is uncertain. Earlier, the basilica was believed to have been founded by the empress Pulcheria; 4 however, more recent research attributes the erection of the basilica to Justin I ( ). The Soros was most probably an older structure than the basilica, whereas its erection was associated with the translation of the maphorion from a village near Nazareth to Constantinople, in the last years of Leo s I reign ( ). Blachernai was a quarter on the shores of Golden Horn, lying outside the enceinte of Theodosian land walls. Breezy and woody region, it was a fine suburb where some wealthy Romans built their mansions. Furthermore, at Blachernai there was natural spring of mineral water, which was used for baths, to which healing qualities were attributed at some point by the 5 th century. such qualities, connected with the local Virgin s cult The monument. Architectural description The appearance of this early-byzantine monument is partially known by descriptions, since the monument itself has not been preserved. Procopios describes it (around 554), as a three-aisled basilica, with two colonnades made of Parian marble. It was a structure of overwhelming dimensions, with 50 m. length. During the repairing-works that took place under Justin II ( ), two niches were added, on the northern and the southern wall of the initial building, so as to form a transept visible in the groundplan. 6 The basilica had a narthex and galleries accessible through a staircase, as well as an ambo and a solea. On the gallery there was a chapel Δημιουργήθηκε στις 12/2/2017 Σελίδα 1/12

2 and a chamber. To the south of the bema there was a small skeuophylakion (sacristy). 7 It seems that the bath edifice was located to the south of the basilica, towards the Palace. To the southeast of the basilica there was the shrine of Hagia Soros. This edifice probably predated the basilica, and was circular in groundplan. 8 The Hagia Soros was not just a chapel, since it was a building of significant dimensions, with a separate narthex, to which a chamber behind the basilika's skeuophylakion gave access. The Soros also included a triclinus for the emperor. 9 Beneath the Altar of the Soros there was a reliquary, to which the sources are referring as episkepsis (ἐ πίσκεψις). 10 From other sources we learn that inside the Soros there was an ambo, 11 which means that the place was intended from the beginning to host holy services. In all probability it had a gallery as well with a chapel and a metatorion (a changing room). Via the triclinus a pass with a staircase gave access from the Soros to the Blacharnai palace The history of the Virgin Mary of Blachernai 3.1. The date of the basilica In the earlier bibliography the basilica of Blachernai was believed to have been founded by the empress Pulcheria and her husband Maurice ( ) between the years This attribution was based on the testimony of ample later sources. 13 Nevertheless, Procopios records it as a Justin s I edifice ( ). Under Justin II the basilica acquired its trancept that gave it a cruciform shape, a work that is attested in two epigrams of the Anthologia Palatina (1.2-3); In the second of these epigrams, founder of the church appears again Justin I. 14 According to C. Mango, these two testimonies are clearer and more reliable than the imprecise information we collect from later sources, and thus, we must consider the chronology that places the monument's erection in the years of Justin I safe enough The Hagia Soros and the tradition related to Pulcheria The eukterion (place of worship) of Blachernai already existed there in the year 475, when Verina, Leo s I wife ( ) and Basiliskos sister ( ), against whom he had turned after his accession to the throne, sought refuge there. However, the building in question must have been the Soros and not the basilica, which is a later addition, as we have seen. 16 The foundation of the Soros is associated with the translation of Virgin s maphorion from Nazareth to Constantinople, during the decade of 460. Neither is Pulcheria s role believed to be certain regarding the erection of this older edifice. According to C. Mango, the Soros was built by Verina during the last years of Leo s reign. Verina s relation to the Soros and the foundation at Blachernai generally passes in silence in the written sources. The later tradition, repeated among others by Theophanes, associates Pulcheria s name not only with Virgin Mary of Blachernai, but with the Virgin Mary of Chalkoprateia as well, 17 attributing, thus, to this empress an important role in the introduction and the consolidation of the Virgin s cult at Constantinople: because both of these churches, not only were dedicated to Theotokos, but they also sheltered, supposedly or not, important relics of Theotokos: the holy girdle (Virgin Mary of Chalkoprateia) and the maphorion (Virgin Mary of Blachernai). Nevertheless, the evidence on Virgin Mary of Chalkoprateia imply that it was rather a foundation of Verina than of Pulcheria. As far as the relic of the holy girdle is concerned, it is a tradition of uncertain origin and in any case subsequent to the one referring to the maphorion; however, since the moment it made its appearance, in the beginnings of the 8 th century, it has been usually associated with the story of maphorion; 18 after the fall and the sack of Constantinople by the knights of the Fourth Crusade, a fragment of the holy girdle was supposedly kept in the Virgin Mary of Blachernai. 19 In relation to the decoration of the Hagia Soros, some testimonies have been preserved about two of its decorative scenes: the first one was probably covering the apse conch and portrayed the figure of enthroned Theotokos, flanked by the emperor Leo I, Verina and their daughter Ariadne. Verina was pictured in a posture of veneration, with her grand-son Leo in her arms. The second scene (or a big portable icon, it is not clear) was found in the diakonikon and depicted Theotokos flanked by two angels and two saints, John Prodromos and Conon. In a posture of prayer were depicted the patrikioi Galbius and Candidus, who transferred, according to the Δημιουργήθηκε στις 12/2/2017 Σελίδα 2/12

3 tradition, Virgin s maphorion to Constantinople The glory of the shrine Until the beginnings of the 6 th century, the pious foundation of the Virgin Mary of Blachernai seems to have already rose to prominence as a place of miraculous healings an attribute connected with the relic of the maphorion as well as with the spring on that spot) and this reputation eventually urged Justin I to built a grand basilica at Blachernai, which remained the largest Constantinopolitan church of Theotokos in dimensions. Always according to C. Mango, it is probable that the foundation of the Soros church and the translation of the maphorion to Constantinople were connected with Monophysitic cycles of the capital city, a hypothesis based on the testimony of the sources referring to the origin of the two patrikioi, of Galbius and Candidus. In that case, the erection of a splendid church by Justin I could have been interpreted as an effort to associate the already famous relic with the Orthodox tradition. This may explain as well the evolution, during later times, of the tradition connecting the translation of the maphorion and the foundation of the church at Blachernai with the pious Orthodox empress Pulcheria. 21 Under Justin II ( ) the basilica was renovated and acquired a cross shaped ground-plan. A large number of clergy served at the temple, which was second only to the clergy of Hagia Sophia. In 588 the emperor Maurice established a weekly patronal feast at the church of Blachernai, while a Novel of Herakleios ( ) ordained the reduction of the number to 74 persons: presbyters, 18 deacons, 6 deaconesses, 8 subdeacons, 20 lectors, 4 chanters and 6 doorkeepers. According to Theodore Synkellos, by the 7 th century Blachernitissa was already considered as the most important oikos of the Virgin at the capital. 23 In 1070 the church of the Virgin Mary of Blachernai was destroyed by fire 24 and was restored by the emperors Romanos IV (Diogenes) ( ) and Michael VII Doukas ( ). The new building most probably followed the previous basilicawith-transept plan. From de Clavijo s description we are informed that it was a three-aisled basilica with an attic window, without dome, with superb inner decoration. 25 In 1434, short before the Fall of Constantinople the church was burnt down for the second time. After 1434 only the place of the holy fountain remained intact, while afterwards, in 1453, the wider region came within the Ottomans sphere of authority. Traces of the edifice were visible until the middle of the 16 th century, but soon afterwards they disappeared as well. 26 In 1867 the land belonged to the property of a Turk. It was bought by the guild of Constantinople s furriers, which erected a small shrine around the hagiasma (holy spring). 27 Gradually, as the time passed the Patriarchate of Constantinople erected new buildings, giving to the area its present form. The church was decorated with paintings in 1964, depicting themes from the pilgrim s history. 4. The Virgin Mary of Blachernai as Constantinople s divine protector 4.1. Akathistos Hymn It is not clear when the Virgin Mary of Blachernai was first considered Constantinople s divine protector. It seems, however, that it was an evolution predating the great siege of Constantinople by the Avars in According to the tradition, during the siege of 626 the patriarch of Constantinople Sergios ( ) walked in procession holding the maphorion (and/ or the icon of Theotokos Blachernitissa) around the city and on its walls, encouraging thus its not numerous defenders. A little later, while the Avars tried with small boats (monoxyla) to get Persian reinforcements ferried across, from the opposite Asian shore, a storm burst out which destroyed their fleet and forced them to abandon the siege. After the raising of the siege the entire people of Constantinople gathered at the church of the Virgin Mary of Blachernai, where a thanks-giving agrypnia (vigilance) was performed. During the vigilance the Akathistos Hymn was chanted, which according to the tradition was supposed to have been composed the same day by patriarch Sergios, 29 in an act of gratitude for rescuing the city. The event has been depicted on the inner side of the latest edifice. Δημιουργήθηκε στις 12/2/2017 Σελίδα 3/12

4 This tradition is later; the narrations closest to the 7 th -century events record neither the procession (litany) of Virgin s icon (there are some narrations recording a certain acheiropoietos icon of Christ and a Virgin s icon situated on the western walls) nor the storm inflicted upon the Avars. 30 As far as the maphorion is concerned, in reality it had already been transferred in 623 from the Virgin Mary of Blachernai, which remained extramural, in order not to run any danger during the siege. However, already the 7 th -century sources attributed the raising of the siege of 626 to a miracle of Theotokos Blachernitissa, whose vision supposed to have appeared before the khagan of the Avars and to have put him to flight. An epigram of George Pisides in the Palatine Anthology praises Virgin Mary of Blachernai for protecting the city from the barbarians. To the Virgin s miraculous intervention was attributed as well the rescue of Constantinople during the sieges of and by the Arabs; the Akathistos Hymn had been associated with the raising of the second siege. Finally, the siege of the Rus in 860 was ended thanks to a storm disastrous for the enemy fleet, attributed to the fact that patriarch Photios sank into the waters Virgin s maphorion. Generally speaking, between the 6 th and the 9 th century Theotokos was distinguished as Constantinople s par excellence supernatural protector; in this belief central place possessed the shrine of the Virgin Mary at Blachernai The miraculous icon of Theotokos Blachernitissa In the 11 th century, the historian Michael Attaleiates referring to Virgin s icon that Romanos IV Diogenes had brought along with him in his campaign against the Seljuks, defined it as the one of Blachernitissa, the miraculous icon from the church of Blachernai. 32 The first time a Virgin s icon that was associated with military campaign dates already to the beginnings of the 7 th century, during Herakleios campaign against Phokas ( ), however until the 11 th century Virgin s icons regarding military events were not defined due to specific names. The iconographic type of Theotokos which is defined as Blachernitissa on coins and seals portrays Theotokos with her hands raised, in a gesture of entreaty; the variation of Virgin Orans with Christ-Child in bust, within a medallion in front of her chest is also called Blachernitissa, as well as Episkepsis. Finally, an 11 th -century icon from the Sinai monastery portrays Theotokos holding Christ-Child, according to the Eleousa type, but is defined as Blachernitissa. 33 Obviously Virgin s icons such as the above-mentioned ones were found in the shrine of the Virgin Mary at Blachernai, but it is hard to define which one of them was considered to be the miraculous one associated with the celebration of triumphs and the protection of the city. A description of Leo the Deacon about Virgin s icon that John I Tzimiskes used during his triumph in 971, after his victory over the Bulgarians, seems to fit in with the type that we call today Eleousa, while other sources as well point out that such an icon, believed to be miraculous, was kept inside the church of Blachernai. 34 Besides, from the 12 th century on another icon of Theotokos, that of Hodegetria, very close to the Eleousa type from an iconographical viewpoint, became the par excellence palladium of Constantinople. This icon, for which also existed the legend of being made by the hands of the Evangelist Luke, was connected with illuminations of the Akathistos Hymn on 14 th -century manuscripts, while each year it was been carried to the palace of Blachernai from the Palm Sunday until Easter Sunday. 35 The close relation of these two Theotokos icons, associated both with Constantinople s supernatural protection, becomes clear on the Virgin of the Tretyakov gallery (fig. 3), a Constantinopolitan icon of 1130 according to the Eleousa type, that was gifted to the prince of Kiev and believed to possess Blachernitissa s qualities, while it was from the 15 th century onwards that its attribution to the Evangelist Luke commenced, following the example of Hodegetria icon of Constantinople Theotokos Blachernitissa The Great Panagia of the city In Byzantine and post-byzantine liturgical pattens (panagiaria), as well as in 14 th -15 th -c. paintings and mosaics in the apses of the bema, we find quite often representations of the Theotokos in the type of Blachernitissa inscribed Great Panagia. In relation to this observation it is worth-mentioning that, monasteries under the name Great Panagia 37 existed already during the 10 th century at Athens and at Irtakion, near Kyzikos. However, the use of the epithet associated with the imperial cult point to Constantinople, because it was there that many monuments were venerated under the title Great ; ti was also there that Theotokos Blachernitissa was originally considered as the city s divine protector. 38 Δημιουργήθηκε στις 12/2/2017 Σελίδα 4/12

5 It is very probable that the Great Panagia constituted the every-day name of the shrine of the Virgin Mary at Blachernai, because besides the relation of the iconographic types between Great Panagia and Blachernitissa, we may suppose that this name was used as a way to denote the church at Blachernae and differentiate it from other, smaller churches at Byzantine Constantinople dedicated to the Mother of God. Furthermore, besides its size, the Virgin Mary of Blachernai was, as we have said, by far the most celebrated church of Theotokos at Constantinople, which, already before the 7 th century, had been associated with miraculous healings. 39 In addition, the existence of other extramural churches dedicated to Blachernitissa, mainly at Ravenna and the Greek mainland, most probably urged the Byzantines to ascribe the name "Great Panagia" to the original Virgin Mary of Blachernai (meaning the church). 40 Following the course of this hypothesis, we may think that the "Acolouthia of the lifting of the Panagia" ("Panagia" was for the first time celebrated at the church of Blachernai, since the scenes of the Great Panagia are related to the imperial ideology, whereas we are not obliged to associate this Eucharistic rite ceremony exclusively with monastic refectories in the 10 th c. 41 Thus, we can not exclude the possibility that the "Acolouthia of the lifting of the Panagia" had been introduced exactly at Blachernai, by far the most important Constantinopolitan church among those dedicated to Theotokos, since the clergy serving there possessed the statue and the power, because of its close relations with the imperial court, to introduce novelties in the Divine Liturgy. During the last centuries of the empire s decline (14 th -15 th c.), at churches under the jurisdiction of the archbishop of Ohrid appeared frescoes with the inscription ΜΕΓΑΛΗ ΠΑΝΑΓΙΑ (the Great Panagia), that, besides the spread of this iconographic type, perhaps they attest an effort to promote the Archbishopric as the guardian of the liturgical tradition under threat, at the decayed capital, by non Christian presumptive conquerors. 42 On the other hand, the naming Great Panagia which accompanies many a variation of Blachernitissa s imagery inside encolpia, medallions and objects of personal use in general, could be associated with the fame of the Virgin Mary of Blachernai miraculous cult mainly in relation to healings; it acquired, thus, during the post-byzantine period an apotropaic and soteriological nature, and not so much an Eucharistic one. 1. Θεόδωρος Σύγκελλος, Theodore Syncellus, In depositionem pretiosae vestis, in Combefis, F. (ed.), Novum auctarium, vol. II. Historia haeresis monotheliarum santaque in eam sextae Synodi actorum vindiciae (Paris 1648), pp , for the relics see esp. p Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II] (Split-Vatican City 1998), p. 61. Mango, C., "Η Κωνσταντινούπολη ως Θεοτοκούπολη", in: Μήτηρ Θεού. Απεικονίσεις της Παναγίας στη βυζαντινή Τέχνη (Benaki Museum, Athens 2000), pp Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II] (Split-Vatican City 1998), p Mercati, G., Due nove memorie di S. Maria delle Blacherne, in: Atti della Pontificia Accademia Romana di Archeologia. Memorie, Ser. 3, vol. 1 (Roma 1923/24), p. 26 ff. Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II], (Split-Vatican City 1998), p. 63, fig Ebersolt, J., Sanctuaires de Byzance (Paris 1921), p. 44 ff. Janin, R. Le géographie ecclésiastique de l empire Byzantine, I: Le siège de Constantinople et le Patriarchat Oecuménique, 3: Les églises et les monastères (Paris 21969), pp Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II] (Split-Vatican City 1998), p Προκόπιος, Περι κτισμάτων, J. Haury (ed.), G. Wirth (corr.) Procopii Cesariensis Opera Omnia, IV: De aedificiis (Leipzig 1964), I Θεοφάνης, Χρονογραφία, de Boor, C. (ed.) Theophanis Chronographia (Leipzig 1883), p Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za Δημιουργήθηκε στις 12/2/2017 Σελίδα 5/12

6 starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II], (Split-Vatican City 1998), p. 63, fig1. 8. «... περιφερής ή σφαιροειδής νεώς», Νικηφόρος Κάλλιστος Ξανθόπουλος, Εκκλησιαστική Ιστορία, ed. J.P. Migne, Patrologiae cursus completus Series Greca 147, col. 45D, 69C. 9. Janin, R. Le géographie ecclésiastique de l empire Byzantine, I: Le siège de Constantinople et le Patriarchat Oecuménique, 3: Les églises et les monastères (Paris 21969), p Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II], (Split-Vatican City 1998), p Grumel, V. Sur l Episkepsis des Blachernes, Échos d Orient 29 (1930), pp «Βίος αγίου Ανδρέα του δια Χριστόν σαλού», Migne, J.P. (ed.) Patrologiae cursus completus Series Greca 111, col. 848C. 12. Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II], (Split-Vatican City 1998), p. 63. See as well Κωνσταντίνος Πορφυρογέννητος, Περι Βασιλείου τάξεως Ι 27, A. Vogt (ed.), Constantin VII Porphyrogénète, Le livre des Cérémonies vol. 1 (Paris 1935), p For the relevant sources see Janin, R. Le géographie ecclésiastique de l empire Byzantine, I: Le siège de Constantinople et le Patriarchat Oecuménique, 3: Les églises et les monastères (Paris 21969), p. 161 note 11. See as well Νικηφόρος Κάλλιστος Ξανθόπουλος, Εκκλησιαστική Ιστορία, XV.14, Migne, J.P. (ed.), Patrologiae cursus completus Series Greca 147, col. 41D-44A. 14. Παλατινή Ανθολογία, Beckby, H., (ed.) Anthologia Greca I (Munich 21965), epigr. 2 and 3; Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II], (Split-Vatican City 1998), p Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II], (Split-Vatican City 1998), p Βίος Δανιήλ Στυλίτου, Delehaye, H., (ed.) "Vita Danielis stylitae", Analecta Bollandiana 32 (1913), p Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II], (Split-Vatican City 1998), pp Θεοφάνους Χρονογραφία, De Boor, C. (ed.) Theophanis Chronographia (Lipsiae 1883), pp. 102 and Mango, C., "Η Κωνσταντινούπολη ως Θεοτοκούπολη", in: Μήτηρ Θεού. Απεικονίσεις της Παναγίας στη βυζαντινή Τέχνη, (Benaki Museum, Athens2000), p. 19. For a more detailed critical presentation of the traditions with regard to Pulcheria s role in the foundation of the Virgin Mary of Blachernai and the translation of the maphorion to Constantinople see Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II] (Split-Vatican City 1998), pp The last report of this holy relic is an anonymous Russian pilgrim to Constantinople between the years 1424 and We are unaware of what happened to this piece of the Timia Zone after Thus, the only surviving piece is the one kept in the Holy Monastery of Vatopaidi, where it ended up after a very adventurous way. 20. Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II] (Split-Vatican City 1998), pp Especially for the wall mosaic on the apse conch see Grabar, A., L'iconoclasme byzantin. Dossier archéologique (Paris 21984), pp. 29, 54 Mango, C., The art of the Byzantine Empire Sources and documents (London ), pp Mango, C., The Origins of the Blachernae Shrine at Constantinople, in: Cambi, N., Marin, E., (eds.), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju (Split, Poreč ) [Acta XIII Congressus Internationalis Archaeologiae Christianae II] (Split-Vatican City 1998), Δημιουργήθηκε στις 12/2/2017 Σελίδα 6/12

7 pp Konidaris, J. (ed.), «Die Novellen des Kaisers Herakleios», Fontes Minores 5 (1982), pp. 68, Θεόδωρος Σύγκελλος, Theodore Syncellus, In depositionem pretiosae vestis, in Combefis, F. (ed.), Novum auctarium, vol. II. Historia haeresis monotheliarum santaque in eam sextae Synodi actorum vindiciae (Paris 1648), p Angelidi, C.- Papamastorakis T., «Picturing the spiritual protector: from Blachernitissa to Hodegetria», in Vassilaki, M. (ed.), Images of the Mother of God. Perceptions of the Theotokos in Byzantium (Ashgate 2005), p Μιχαήλ Ατταλειάτης, Ιστορία, ed. I. Bekker (CSHB, Bonn 1853), p Janin, R., Le géographie ecclésiastique de l empire Byzantine, I: Le siège de Constantinople et le Patriarchat Oecuménique, 3: Les églises et les monastères (Paris 21969), p. 168, with a reference to Ruy Gonzalez de Clavijo, Historia del Gran Tamorlan (Madrid 1782), p Gyllius, P., De topographia Constantinopoleos (Lyon 1561), IV.5, p Πασπάτης, Α. Γ., Βυζαντιναί μελέται (Constantinople 1877), p Mango, C., "Η Κωνσταντινούπολη ως Θεοτοκούπολη", in: Μήτηρ Θεού. Απεικονίσεις της Παναγίας στη βυζαντινή Τέχνη (Benaki Museum, Athens 2000), pp The tradition associating the Akathistos hymn with the siege of 626 goes back already to the 10 th century, see Angelidi, C.- Papamastorakis T., «Picturing the spiritual protector: from Blachernitissa to Hodegetria», in Vassilaki M. (ed.), Images of the Mother of God. Perceptions of the Theotokos in Byzantium (Ashgate 2005), p. 212 and note The 7 th -century sources are a poem of George of Pisidia, Perusi, A. (ed.), Giorgio di Pisidia Poemi (Studia Patristica et Byzantina 7, Freising 1960), pp ; a homily attributed to Theodore Synkellos, Makk, F., Traduction et commentaire de l homélie écrite probablement par Théodore le Syncelle sur le siege de Constantinople en 626 (Opuscula Byzantina III, Szeged 1975); and an excerpt in the Chronicle Paschale, ed. L. Dindorf (CSHB, Bonn 1832), pp See Pentcheva, B.V., «The supernatural protector of Constantinople: the Virgin and her icons in the tradition of the Avar siege», Byzantine and Modern Greek Studies 26 (2002), pp. 5-12, for the 7 th -century sources, and pp , for the middle Byzantine sources concerning the event and the formation of the later tradition. 31. Mango, C., "Η Κωνσταντινούπολη ως Θεοτοκούπολη", in: Μήτηρ Θεού. Απεικονίσεις της Παναγίας στη βυζαντινή Τέχνη (Benaki Museum, Athens 2000), pp. 22-3; Angelidi, C.- Papamastorakis T., «Picturing the spiritual protector: from Blachernitissa to Hodegetria», in Vassilaki M. (ed.), Images of the Mother of God. Perceptions of the Theotokos in Byzantium (Ashgate 2005), p Μιχαήλ Ατταλειάτης, Ιστορία, ed. I. Bekker (CSHB, Bonn 1853), p Patterson-Ševčenko, N., «Vigin Blachernitissa», in Kazhdan, A. (editor-in-chief), The Oxford Dictionary of Byzantium 3 (Oxford-New York 1991), pp Angelidi, C.- Papamastorakis T., «Picturing the spiritual protector: from Blachernitissa to Hodegetria», in Vassilaki M. (ed.), Images of the Mother of God. Perceptions of the Theotokos in Byzantium (Ashgate 2005), pp Patterson-Ševčenko, N., «Vigin Hodegetria», in Kazhdan, A. (editor-in-chief), The Oxford Dictionary of Byzantium 3 (Oxford-New York 1991), pp For the succession of Blachernitissa by Hodegetria on the role of capital s palladium see Angelidi, C.- Papamastorakis T., «Picturing the spiritual protector: from Blachernitissa to Hodegetria», in Vassilaki M. (ed.), Images of the Mother of God. Perceptions of the Theotokos in Byzantium (Ashgate 2005), pp For this theme see Мутафов, Е. «ΜΗΤΗΡ ΘΕΟΥ Η ΜΕΓΑΛΗ ΠΑΝΑΓΙΑ поява, разпространение, варианти и хипотези. ΠΡΟΛΕΓΟΜΕΝΑ», Mediaevalia Christiana 2.C. (2008) (forthcoming). Δημιουργήθηκε στις 12/2/2017 Σελίδα 7/12

8 38. On coins dated to the years of Michael VIII Palaiologos (1259/ ) and of Andronikos II Palaiologos ( ), as well as on illuminated manuscripts from the 14 th c., behind Virgin s figure are depicted on the ground the walls and the towers of Constantinople. See Грозданов, Ц., Студии за Охридския живопис (Скопjе 1990), pp , fig. 50 and p. 51 with previous bibliography. 39. Those writers that record the miracles are Theodore Synkellos, Theodore Syncellus, In depositionem pretiosae vestis, in: Combefis, F. (ed.), Novum auctarium, vol. II. Historia haeresis monotheliarum santaque in eam sextae Synodi actorum vindiciae (Paris 1648), pp , as well as George Pisides in the Palatine Anthology, Beckby, H., (ed.), Anthologia Greca 1 (Munich ), 121, col. 6-9: «ἐ νταῦ θα κρουνοὶ σαρκικῶν καθαρσίων καὶ ψυχικῶν λύτρωσις ἀγνοημάτων ὅσαι γάρ εἰ σι τῶν παθῶν περιστάσεις, βλύζει τοσαύτας δωρεὰς τῶν θαυμάτων.». 40. In medieval Thessalonica as well we observe such a contrast. The church of the Virgin Mary Acheiropoietos of the 5 th c. is called «μέγας ναός» by the bishop of Thessalonica Eustathios in his «Ιστορία άλωσης της Θεσσαλονίκης από τους Νορμανδούς» a work of the year 1185, underestimating in a way all the other notable churches of the city, namely Hagia Sophia and Saint Demetrios. In the 15 th c. Saint Symeon of Thessalonica also calls the Acheiropoietos «Μέγα ναό της Θεοτόκου» eventually in contrast to the Nea Panagia, built upon the foundations of a 12 th -century Virgin s monastery. 41. Геров, Г., Б. Пенкова, Р. Божинов, Стенописите на Роженския манастир (София. 1993), p. 137 with previous bibliography about the theme of the divine service in question and its celebration at the Balkan monasteries. 42. In the 14 th c. Byzantium experienced a period of decay, during which the empire s neighbors tried to acquire some precious objects and valuable symbols. Even the Bulgarian chronographers of Tsar John Alexander s court ( ) made an attempt to name Veliko Tŭrnovo New Reigning City and Third Rome. See accordingly Тъпкова-Заимова, В., Търново между Ерусалим, Рим и Цариград, Търновска книжовна школа, 4, Културно развитие на българската държава ХІІ ь-хіvь (София 1985), pp By the Nomokanon of Stefan Dušan in 1334 the Archbishopric of Ohrid became autonomous and the archbishop Nikolaos in 1347 called himself Archbishop of Bulgaria. Because of its religious significance Ohrid was named the Zion of the Bulgarians or the Jerusalem of the Bulgarians. Βιβλιογραφία : Restle M., Istanbul-Bursa-Edirne-Iznik. Baudenkmäler und Museen, Reclams Kunstführer, Stuttgart 1976 Janin R., La géographie ecclésiastique de l empire byzantin, Ι. Le Siège de Constantinople et le Patriarcat Oecuménique 3: Les églises et les monastères, 2, Paris 1969 Mathews T.F., The Byzantine Churches of Istanbul. A Photographic Survey, University Park London 1976 Müller-Wiener W., Bildlexikon zur Topographie Istanbuls, Byzantion Konstantinupolis Istanbul bis zum Beginn d. 17. Jhs., Tübingen 1977 Van Millingen A., Byzantine Churches in Constantinople, Their History and Architecture, London 1912, repr Freely J., Summner-Boyd H., Byzantinische Kirche in Istabul: Literaturchinweise, München Istanbul 1975 Hotz W., Byzanz, Konstantinopel, Istanbul. Handbuch der Kunstdenkmaler, Darmstadt 1971 Kleiss W., Topographisch-Archaölogischer Plan von Istanbul, Tübingen 1965 Odenthal J., Istanbul, DuMont Kunst-Reisefuhrer, Köln 1990 Rice D.T., Hirschmer J., Kunst aus Byzanz, München 1959 Δημιουργήθηκε στις 12/2/2017 Σελίδα 8/12

9 Wulzinger K., Byzantinische Baudenkmaler zu Konstantinopel, Osnabruck 1973, Mittelmeerlander und Orient, Sammlung wissenschaftl, Studien, Band 1 Mango C., "The Origins of the Blachernae Shrine at Constantinople", Cambi, N. Marin, E. (eds), Radovi XIII Međunarodnog Kongresa za starokršćansku arheologiju ΙΙ (Split, Poreč ), Pontificio Istituto di Archeologia Cristiana, Split Vatican City 1998, Ebersolt J., Sanctuaires de Byzance, Paris 1921 Dünden B., Istanbul Ansiklopedisi, Türkiye Ekonomik ve Toplumsal Tarih Vakfi, vol. 6, 7, Istanbul 1993 Mango C., "Η Κωνσταντινούπολη ως Θεοτοκούπολη", Μήτηρ Θεού. Απεικονίσεις της Παναγίας στη βυζαντινή τέχνη, Μουσείο Μπενάκη, Αθήνα 2000, Кондаков Н. П., Иконография Богоматери, vol. ІІ, Москва 1998 Patterson-Ševčenko N.P., "Icons in Liturgy", Dumbarton Oaks Paper, 45, 1991, Pentcheva B.V., "The supernatural protector of Constantinople: the Virgin and her icons in the tradition of the Avar siege", Byzantine and Modern Greek Studies, 26, 2002, 2-41 Angelidi C., Papamastorakis Τ., "Picturing the spiritual protector: from Blachernitissa to Hodegetria", Vassilaki M. (ed.), Images of the Mother of God. Perceptions of the Theotokos in Byzantium, Ashgate 2005, Patterson-Ševčenko N.P., "Vigin Blachernitissa", Kazhdan, A. (ed.), Oxford Dictionary of Byzantium 3, Oxford-New York 1991, Δικτυογραφία : Cup (steatite paten) of Pulcheria panagiarion 14th c. Xeropotamou Monastery, Mount Athos Γλωσσάριo : acheiropoietos Icon, usually of Christ, which-according to the legend-was non-hand made. Several legends concerning acheiropoietes icons appeared in Byzantium since the 6th c. and refer to objects which miraculously preserved the imprint of the face or the body of Christ, after having come in contact with Him. The most famous is the Holy Mandylion of Eddesa. During the middle byzantine period most of those acheiropoietes icons of Christ are forgotten, though many legends emerged concerning acheiropoietes icons of saints. ambo The elevated pulpit used for preaching in the church nave. bema The area at east end of the naos in Byzantine churches, containing the altar, also referred to as the presbetery or hierateion (sanctuary). In these area take place the Holy Eucharist. Eleousa An icon type of Virgin Mary. She is depicted holding the Child, bending her head so as to touch his cheek with hers, while Jesus puts his arm around her neck. galea galea (from γαλαίος, swordfish, ) a term introduced first by Leo VI to denote light, rapid dromones powered probably by one bank of oars. They were commonly used as messenger ships or for reconnaissance in enemy waters. Hodegetria Δημιουργήθηκε στις 12/2/2017 Σελίδα 9/12

10 Iconographic type of the Virgin Mary. The Virgin is depicted standing, slightly turning to the right of the viewer, holding in her arms the infant Jesus. The type was named so after an allegedly thaumaturgic icon of the Virgin Mary kept in the monastery of Hodegoi in Constantinople. khan (Ilkhan), khagan This title was used in Turkic and Mongolian languages to designate the supreme ruler. The Byzantines used it to refer to the rulers of the Avars, Khazars, Turks and Bulgarians. maphorion A women's garment covering the head and shoulders and sometimes reaching down to the feet. In Byzantium maphorion was the name of the Virgin's outer veil. According to the christian tradition it was preserved by apostle Thomas after the Dormition and 4-5 centuries afterwards it was transfered to Constantinople and deposited at the church of Blachernai. It was one of the most important relics gathered in Constantinople. narthex A portico or a rectangular entrance-hall, parallel with the west end of an early Christian basilica or church. niche Semi-circular recess on the surface of the wall. skeuophylakion ( Treasure house or sacristy) A particular area or room in the churches for keeping vestments and the church furnishings, sacred vessel. Usually take place in the diakonikon, south (at right) from the central apse with the altar. solea A wide and oblong elevated passageway in front of the central opening of the chancel screen that reached until the ambo; there stood the deacons and the lectors during the Service. three-aisled basilica An oblong type of church internally divided into three aisles: the middle and the two side aisles. The middle aisle is often lighted by an elevated clerestory. In the Early Byzantine years this type of church had huge dimensions. Πηγές Theodore Syncellus, In depositionem pretiosae vestis, in: Combefis, F. (ed.) Novum auctarium, vol. II. Historia haeresis monotheliarum santaque in eam sextae Synodi actorum vindiciae (Paris 1648), pp Makk, F., Traduction et commentaire de l homélie écrite probablement par Théodore le Syncelle sur le siege de Constantinople en 626 (Opuscula Byzantina III, Szeged 1975). J. Haury (ed.), G. Wirth (corr.), Procopii Cesariensis Opera Omnia, IV: De aedificiis (Leipzig 1964), I De Boor, C. (ed.), Theophanis Chronographia (Leipzig 1883), pp. 102, 105, 244, Dindorf L. (ed.), Chronicon Paschale 1 (Corpus Scriptorum Historiae Byzantinae, Bonn 1832), pp Anthologia Palatina, ed. H. Beckby, Anthologia Graeca 1 (Munich ), nos. 2, 3, 120, 121. De Cerimoniis Ι 27, ed. A. Vogt, Constantin VII Porphyrogénète, Le livre des Cérémonies vol. 1 (Paris 1935), p Bekker, I. (ed.), Michaelis Attaliotae Historia (Corpus Scriptorum Historiae Byzantinae, Bonn 1853), pp. 138, 153. Βίος Δανιήλ Στυλίτου, Delehaye, H., (ed.) ʺVita Danielis stylitaeʺ, Analecta Bollandiana 32 (1913), p «Βίος αγίου Ανδρέα του δια Χριστόν σαλού», Migne, J.P. (ed.) Patrologiae cursus completus Series Greca 111, col. 848C. Νικηφόρος Κάλλιστος Ξανθόπουλος, Εκκλησιαστική Ιστορία, ed. J.P. Migne, Patrologiae cursus completus Series Greca 147, col. 41D 44A, 45D, 69C. Δημιουργήθηκε στις 12/2/2017 Σελίδα 10/12

11 Gyllius, P., De topographia Constantinopoleos (Lyon 1561), IV.5, p Mango, C., The art of the Byzantine Empire Sources and documents (London ), pp Παραθέματα 1. The remodeling of the basilica of Blachernai by Justin II (2.) Ἐν ταῖς ἁψῖσι τῶν Βλαχερνῶν Θεῖος Ἰουστῖνος, Σοφίης πόσις, ᾧ πόρε Χριστὸς (1) πάντα διορθοῦσθαι καὶ κλέος ἐν πολέμοις, μητρὸς ἀπειρογάμοιο δόμον σκάζοντα νοήσας, σαθρὸν ἀποσκεδάσας τεῦξέ μιν ἀσφαλέως. (3.) Εἰς τὸ αὐτὸ ἐν ταῖς αὐταῖς Ὁ πρὶν Ἰουστῖνος περικαλλέα δείματο νηὸν (1) τοῦτον μητρὶ Θεοῦ κάλλεϊ λαμπόμενον ὁπλότερος δὲ μετ αὐτὸν Ἰουστῖνος βασιλεύων κρείσσονα τῆς προτέρης ὤπασεν ἀγλαΐην. Anthologia Palatina 2 and 3, H. Beckby (ed.), Anthologia Graeca I (Munich ). 2. Epigramms by George Pisides for Virgin Mary of Blachernai (120.) Ἐν Βλαχέρναις ἴαμβοι οἱ βάρβαροι δὲ προσβαλόντες τῇ πόλει, αὐτὴν στρατηγήσασαν ὡς εἶδον μόνην, (10) ἔκαμψαν εὐθὺς τοὺς ἀκαμπεῖς αὐχένας. (121.) Εἰς τὸν αὐτὸν ναόν ἐνταῦθα κρουνοὶ σαρκικῶν καθαρσίων καὶ ψυχικῶν λύτρωσις ἀγνοημάτων ὅσαι γάρ εἰσι τῶν παθῶν περιστάσεις, βλύζει τοσαύτας δωρεὰς τῶν θαυμάτων. ἐνταῦθα νικήσασα τοὺς ἐναντίους (10) ἀνεῖλεν αὐτοὺς ἀντὶ λόγχης εἷσ ὕδωρ τροπῆς γὰρ ἀλλοίωσιν οὐκ ἔχει μόνην, Χριστὸν τεκοῦσα καὶ κλονοῦσα βαρβάρους. Anthologia Palatina, and , H. Beckby (ed.), Anthologia Graeca 1 (Munich ). 3. The icon of Blachernitissa in the campaigns of the Byzantine emperors... τὴν πάνσεπτον εἰκόνα τῆς πανυμνήτου δεσποίνης θεοτόκου τῆς, Βλαχερνιτίσσης, ἥτις εἰώθει τοῖς πιστοῖς βασιλεῦσιν ἐν ἐν στρατείαις ὡς ἀπροσμάχητον ὅπλον συνεκστρατεύεσθαι... Bekker, I. (ed.), Michaelis Attaliotae Historia (CSHB, Bonn 1853), p Δημιουργήθηκε στις 12/2/2017 Σελίδα 11/12

12 4. The wall mosaic of Leo I and Verina in the Soros After the demise of [Galbius and Candidus], the said emperor Leo and his most pious spouse Veronica honored in a fitting fashion the holy garment of Our Lady the Mother of God by dedicating to her a church with all glory and veneration... The same emperors beloved of God and Christ set up in the ciborium of the [bema] an image, all of gold and precious stones, in which image [are represented] Our Lady the immaculate Mother of God seated on a throne and on either side of her Leo and Veronica, the latter holding her own [grand]son, the young emperor Leo, as she falls before Our Lady the Mother of God, and also their daughter Ariadne. This image has stood from that time onward above the bema of the holy Soros. Cod. Paris gr. 1447, fol , English trans. Mango, C., The art of the Byzantine Empire Sources and documents (London ), p Δημιουργήθηκε στις 12/2/2017 Σελίδα 12/12

Παναγία Βλαχερνών. Περίληψη : Χρονολόγηση. Γεωγραφικός εντοπισμός IΔΡΥΜA ΜΕΙΖΟΝΟΣ ΕΛΛΗΝΙΣΜΟΥ. 1. Εισαγωγή

Παναγία Βλαχερνών. Περίληψη : Χρονολόγηση. Γεωγραφικός εντοπισμός IΔΡΥΜA ΜΕΙΖΟΝΟΣ ΕΛΛΗΝΙΣΜΟΥ. 1. Εισαγωγή Για παραπομπή : Moutafov Emmanuel,, 2008, Περίληψη : Η βασιλική της Παναγίας των Βλαχερνών αναδείχθηκε στο πιο δημοφιλές προσκύνημα της Θεοτόκου στην Κωνσταντινούπολη. Η ίδρυσή της αποδιδόταν παραδοσιακά

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

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

Η εκκλησία του Τιμίου Σταυρού βρίσκεται στην περιοχή Τροόδους, στο χωριό Πελέντρι. Η ύπαρξη του οποίου μαρτυρείται από τα τέλη του 12ου αιώνα.

Η εκκλησία του Τιμίου Σταυρού βρίσκεται στην περιοχή Τροόδους, στο χωριό Πελέντρι. Η ύπαρξη του οποίου μαρτυρείται από τα τέλη του 12ου αιώνα. Νεφέλη Μιχαήλ Α6 Η εκκλησία του Τιμίου Σταυρού βρίσκεται στην περιοχή Τροόδους, στο χωριό Πελέντρι. Η ύπαρξη του οποίου μαρτυρείται από τα τέλη του 12ου αιώνα. Από το 1985 περιλαμβάνεται, στον κατάλογο

Διαβάστε περισσότερα

ΓΕΩΜΕΣΡΙΚΗ ΣΕΚΜΗΡΙΩΗ ΣΟΤ ΙΕΡΟΤ ΝΑΟΤ ΣΟΤ ΣΙΜΙΟΤ ΣΑΤΡΟΤ ΣΟ ΠΕΛΕΝΔΡΙ ΣΗ ΚΤΠΡΟΤ ΜΕ ΕΦΑΡΜΟΓΗ ΑΤΣΟΜΑΣΟΠΟΙΗΜΕΝΟΤ ΤΣΗΜΑΣΟ ΨΗΦΙΑΚΗ ΦΩΣΟΓΡΑΜΜΕΣΡΙΑ

ΓΕΩΜΕΣΡΙΚΗ ΣΕΚΜΗΡΙΩΗ ΣΟΤ ΙΕΡΟΤ ΝΑΟΤ ΣΟΤ ΣΙΜΙΟΤ ΣΑΤΡΟΤ ΣΟ ΠΕΛΕΝΔΡΙ ΣΗ ΚΤΠΡΟΤ ΜΕ ΕΦΑΡΜΟΓΗ ΑΤΣΟΜΑΣΟΠΟΙΗΜΕΝΟΤ ΤΣΗΜΑΣΟ ΨΗΦΙΑΚΗ ΦΩΣΟΓΡΑΜΜΕΣΡΙΑ ΕΘΝΙΚΟ ΜΕΣΟΒΙΟ ΠΟΛΤΣΕΧΝΕΙΟ ΣΜΗΜΑ ΑΓΡΟΝΟΜΩΝ-ΣΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΣΟΜΕΑ ΣΟΠΟΓΡΑΦΙΑ ΕΡΓΑΣΗΡΙΟ ΦΩΣΟΓΡΑΜΜΕΣΡΙΑ ΓΕΩΜΕΣΡΙΚΗ ΣΕΚΜΗΡΙΩΗ ΣΟΤ ΙΕΡΟΤ ΝΑΟΤ ΣΟΤ ΣΙΜΙΟΤ ΣΑΤΡΟΤ ΣΟ ΠΕΛΕΝΔΡΙ ΣΗ ΚΤΠΡΟΤ ΜΕ ΕΦΑΡΜΟΓΗ ΑΤΣΟΜΑΣΟΠΟΙΗΜΕΝΟΤ

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

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

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

«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

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

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

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

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

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

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

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

Χρονολόγηση. Γεωγραφικός εντοπισμός Constantinople, Istanbul

Χρονολόγηση. Γεωγραφικός εντοπισμός Constantinople, Istanbul Περίληψη : The monument is located near the church of Hagia Sophia. It was one of the most important churches dedicated to the Virgin Mary in the early Byzantine Constantinople. Today it preserves only

Διαβάστε περισσότερα

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ

ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ

Διαβάστε περισσότερα

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

Θέμα διπλωματικής εργασίας: «Από το «φρενοκομείο» στη Λέρο και την Ψυχιατρική Μεταρρύθμιση: νομικό πλαίσιο και ηθικοκοινωνικές διαστάσεις»

Θέμα διπλωματικής εργασίας: «Από το «φρενοκομείο» στη Λέρο και την Ψυχιατρική Μεταρρύθμιση: νομικό πλαίσιο και ηθικοκοινωνικές διαστάσεις» ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΕΣ ΙΑΤΡΙΚΗΣ & ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΤΜΗΜΑΤΑ ΝΟΜΙΚΗΣ & ΘΕΟΛΟΓΙΑΣ ΔΙΑΤΜΗΜΑΤΙΚΟ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ «ΣΥΓΧΡΟΝΕΣ ΙΑΤΡΙΚΕΣ ΠΡΑΞΕΙΣ: ΔΙΚΑΙΙΚΗ ΡΥΘΜΙΣΗ ΚΑΙ ΒΙΟΗΘΙΚΗ

Διαβάστε περισσότερα

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

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΦΙΛΟΛΟΓΙΑΣ

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

Διαβάστε περισσότερα

Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author.

Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author. Κάθε γνήσιο αντίγραφο φέρει υπογραφή του συγγραφέα. / Each genuine copy is signed by the author. 2012, Γεράσιμος Χρ. Σιάσος / Gerasimos Siasos, All rights reserved. Στοιχεία επικοινωνίας συγγραφέα / Author

Διαβάστε περισσότερα

ΓΗΠΛΧΜΑΣΗΚΖ ΔΡΓΑΗΑ ΑΡΥΗΣΔΚΣΟΝΗΚΖ ΣΧΝ ΓΔΦΤΡΧΝ ΑΠΟ ΑΠΟΦΖ ΜΟΡΦΟΛΟΓΗΑ ΚΑΗ ΑΗΘΖΣΗΚΖ

ΓΗΠΛΧΜΑΣΗΚΖ ΔΡΓΑΗΑ ΑΡΥΗΣΔΚΣΟΝΗΚΖ ΣΧΝ ΓΔΦΤΡΧΝ ΑΠΟ ΑΠΟΦΖ ΜΟΡΦΟΛΟΓΗΑ ΚΑΗ ΑΗΘΖΣΗΚΖ ΔΘΝΗΚΟ ΜΔΣΟΒΗΟ ΠΟΛΤΣΔΥΝΔΗΟ ΥΟΛΖ ΠΟΛΗΣΗΚΧΝ ΜΖΥΑΝΗΚΧΝ ΣΟΜΔΑ ΓΟΜΟΣΑΣΗΚΖ ΓΗΠΛΧΜΑΣΗΚΖ ΔΡΓΑΗΑ ΑΡΥΗΣΔΚΣΟΝΗΚΖ ΣΧΝ ΓΔΦΤΡΧΝ ΑΠΟ ΑΠΟΦΖ ΜΟΡΦΟΛΟΓΗΑ ΚΑΗ ΑΗΘΖΣΗΚΖ ΔΤΘΤΜΗΑ ΝΗΚ. ΚΟΤΚΗΟΤ 01104766 ΔΠΗΒΛΔΠΧΝ:ΑΝ.ΚΑΘΖΓΖΣΖ ΗΧΑΝΝΖ

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

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

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

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

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΣΥΓΚΡΙΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΓΚΡΑΤΗΤΙΚΗΣ ΙΚΑΝΟΤΗΤΑΣ ΟΡΙΣΜΕΝΩΝ ΠΡΟΚΑΤΑΣΚΕΥΑΣΜΕΝΩΝ ΣΥΝΔΕΣΜΩΝ ΑΚΡΙΒΕΙΑΣ

Διαβάστε περισσότερα

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

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

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

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

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

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

Τμήμα Πολιτικών και Δομικών Έργων

Τμήμα Πολιτικών και Δομικών Έργων Τμήμα Πολιτικών και Δομικών Έργων Πτυχιακή Εργασία: Τοπογραφικό διάγραμμα σε ηλεκτρονική μορφή κεντρικού λιμένα Κέρκυρας και κτιρίου νέου επιβατικού σταθμού σε τρισδιάστατη μορφή και σχεδίαση με AutoCAD

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

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

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

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ιπλωµατική Εργασία του φοιτητή του τµήµατος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Ηλεκτρονικών

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

ΠΑΡΑΜΕΤΡΟΙ ΕΠΗΡΕΑΣΜΟΥ ΤΗΣ ΑΝΑΓΝΩΣΗΣ- ΑΠΟΚΩΔΙΚΟΠΟΙΗΣΗΣ ΤΗΣ BRAILLE ΑΠΟ ΑΤΟΜΑ ΜΕ ΤΥΦΛΩΣΗ

ΠΑΡΑΜΕΤΡΟΙ ΕΠΗΡΕΑΣΜΟΥ ΤΗΣ ΑΝΑΓΝΩΣΗΣ- ΑΠΟΚΩΔΙΚΟΠΟΙΗΣΗΣ ΤΗΣ BRAILLE ΑΠΟ ΑΤΟΜΑ ΜΕ ΤΥΦΛΩΣΗ ΠΑΝΕΠΙΣΤΗΜΙΟ ΜΑΚΕΔΟΝΙΑΣ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΚΠΑΙΔΕΥΤΙΚΗΣ ΚΑΙ ΚΟΙΝΩΝΙΚΗΣ ΠΟΛΙΤΙΚΗΣ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΠΑΡΑΜΕΤΡΟΙ ΕΠΗΡΕΑΣΜΟΥ ΤΗΣ ΑΝΑΓΝΩΣΗΣ- ΑΠΟΚΩΔΙΚΟΠΟΙΗΣΗΣ ΤΗΣ BRAILLE

Διαβάστε περισσότερα

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

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

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

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

ΔΙΑΜΟΡΦΩΣΗ ΣΧΟΛΙΚΩΝ ΧΩΡΩΝ: ΒΑΖΟΥΜΕ ΤΟ ΠΡΑΣΙΝΟ ΣΤΗ ΖΩΗ ΜΑΣ!

ΔΙΑΜΟΡΦΩΣΗ ΣΧΟΛΙΚΩΝ ΧΩΡΩΝ: ΒΑΖΟΥΜΕ ΤΟ ΠΡΑΣΙΝΟ ΣΤΗ ΖΩΗ ΜΑΣ! ΔΙΑΜΟΡΦΩΣΗ ΣΧΟΛΙΚΩΝ ΧΩΡΩΝ: ΒΑΖΟΥΜΕ ΤΟ ΠΡΑΣΙΝΟ ΣΤΗ ΖΩΗ ΜΑΣ! ΘΥΜΑΡΑ Μ. Μ. 11 Ο Γυμνάσιο Πειραιά, Δ/νση Β/Θμιας Εκπ/σης Πειραιά e-mail: margthym@yahoo.gr ΠΕΡΙΛΗΨΗ Το πρόγραμμα της διαμόρφωσης των σχολικών

Διαβάστε περισσότερα

Περίληψη : Χρονολόγηση. Γεωγραφικός εντοπισμός Trebizond, Pontos IΔΡΥΜA ΜΕΙΖΟΝΟΣ ΕΛΛΗΝΙΣΜΟΥ

Περίληψη : Χρονολόγηση. Γεωγραφικός εντοπισμός Trebizond, Pontos IΔΡΥΜA ΜΕΙΖΟΝΟΣ ΕΛΛΗΝΙΣΜΟΥ Περίληψη : The Church of St. Anne, the earliest Christian church of Trebizond, was internally decorated with paintings made between the 12 th and the 15 th century. The 12 th century paintings are the

Διαβάστε περισσότερα

Πανεπιστήμιο Πειραιώς Τμήμα Πληροφορικής Πρόγραμμα Μεταπτυχιακών Σπουδών «Πληροφορική»

Πανεπιστήμιο Πειραιώς Τμήμα Πληροφορικής Πρόγραμμα Μεταπτυχιακών Σπουδών «Πληροφορική» Πανεπιστήμιο Πειραιώς Τμήμα Πληροφορικής Πρόγραμμα Μεταπτυχιακών Σπουδών «Πληροφορική» Μεταπτυχιακή Διατριβή Τίτλος Διατριβής Επίκαιρα Θέματα Ηλεκτρονικής Διακυβέρνησης Ονοματεπώνυμο Φοιτητή Σταμάτιος

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

ΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3:

ΠΕΡΙΕΧΟΜΕΝΑ. Κεφάλαιο 1: Κεφάλαιο 2: Κεφάλαιο 3: 4 Πρόλογος Η παρούσα διπλωµατική εργασία µε τίτλο «ιερεύνηση χωρικής κατανοµής µετεωρολογικών µεταβλητών. Εφαρµογή στον ελληνικό χώρο», ανατέθηκε από το ιεπιστηµονικό ιατµηµατικό Πρόγραµµα Μεταπτυχιακών

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

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

"ΦΟΡΟΛΟΓΙΑ ΕΙΣΟΔΗΜΑΤΟΣ ΕΤΑΙΡΕΙΩΝ ΣΥΓΚΡΙΤΙΚΑ ΓΙΑ ΤΑ ΟΙΚΟΝΟΜΙΚΑ ΕΤΗ 2011-2013"

ΦΟΡΟΛΟΓΙΑ ΕΙΣΟΔΗΜΑΤΟΣ ΕΤΑΙΡΕΙΩΝ ΣΥΓΚΡΙΤΙΚΑ ΓΙΑ ΤΑ ΟΙΚΟΝΟΜΙΚΑ ΕΤΗ 2011-2013 ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΚΡΗΤΗΣ ΣΧΟΛΗ ΔΙΟΙΚΗΣΗΣ ΚΑΙ ΟΙΚΟΝΟΜΙΑΣ ΤΜΗΜΑ ΛΟΓΙΣΤΙΚΗΣ ΚΑΙ ΧΡΗΜΑΤΟΟΙΚΟΝΟΜΙΚΗΣ Επιμέλεια Κρανιωτάκη Δήμητρα Α.Μ. 8252 Κωστορρίζου Δήμητρα Α.Μ. 8206 Μελετίου Χαράλαμπος Α.Μ.

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

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

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

Διαβάστε περισσότερα

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

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

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΥΨΗΛΩΝ ΤΑΣΕΩΝ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΥΨΗΛΩΝ ΤΑΣΕΩΝ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΥΨΗΛΩΝ ΤΑΣΕΩΝ Διπλωµατική Εργασία Της Φοιτήτριας του Τµήµατος Ηλεκτρολόγων

Διαβάστε περισσότερα

Ακαδημαϊκός Λόγος Εισαγωγή

Ακαδημαϊκός Λόγος Εισαγωγή - In this essay/paper/thesis I shall examine/investigate/evaluate/analyze Γενική εισαγωγή για μια εργασία/διατριβή Σε αυτήν την εργασία/διατριβή θα αναλύσω/εξετάσω/διερευνήσω/αξιολογήσω... To answer this

Διαβάστε περισσότερα

Η ΠΡΟΣΩΠΙΚΗ ΟΡΙΟΘΕΤΗΣΗ ΤΟΥ ΧΩΡΟΥ Η ΠΕΡΙΠΤΩΣΗ ΤΩΝ CHAT ROOMS

Η ΠΡΟΣΩΠΙΚΗ ΟΡΙΟΘΕΤΗΣΗ ΤΟΥ ΧΩΡΟΥ Η ΠΕΡΙΠΤΩΣΗ ΤΩΝ CHAT ROOMS ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ Ι Ο Ν Ι Ω Ν Ν Η Σ Ω Ν ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ & ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : ΑΤΕΙ Ιονίων Νήσων- Λεωφόρος Αντώνη Τρίτση Αργοστόλι Κεφαλληνίας, Ελλάδα 28100,+30

Διαβάστε περισσότερα

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

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

ΔΗΜΟΚΡΙΤΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΡΑΚΗΣ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΑΓΩΓΗΣ

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

Διαβάστε περισσότερα

Business English. Ενότητα # 9: Financial Planning. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων

Business English. Ενότητα # 9: Financial Planning. Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ Ανώτατο Εκπαιδευτικό Ίδρυμα Πειραιά Τεχνολογικού Τομέα Business English Ενότητα # 9: Financial Planning Ευαγγελία Κουτσογιάννη Τμήμα Διοίκησης Επιχειρήσεων Άδειες Χρήσης Το παρόν εκπαιδευτικό

Διαβάστε περισσότερα

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

6.1. Dirac Equation. Hamiltonian. Dirac Eq.

6.1. Dirac Equation. Hamiltonian. Dirac Eq. 6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2

Διαβάστε περισσότερα

Démographie spatiale/spatial Demography

Démographie spatiale/spatial Demography ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΙΑΣ Démographie spatiale/spatial Demography Session 1: Introduction to spatial demography Basic concepts Michail Agorastakis Department of Planning & Regional Development Άδειες Χρήσης

Διαβάστε περισσότερα

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

Ακαδημαϊκός Λόγος Εισαγωγή

Ακαδημαϊκός Λόγος Εισαγωγή - Σε αυτήν την εργασία/διατριβή θα αναλύσω/εξετάσω/διερευνήσω/αξιολογήσω... Γενική εισαγωγή για μια εργασία/διατριβή In this essay/paper/thesis I shall examine/investigate/evaluate/analyze Για να απαντήσουμε

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

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

Μεταπτυχιακή εργασία : Μελέτη της εξέλιξης του προσφυγικού οικισμού της Νέας Φιλαδέλφειας με χρήση μεθόδων Γεωπληροφορικής.

Μεταπτυχιακή εργασία : Μελέτη της εξέλιξης του προσφυγικού οικισμού της Νέας Φιλαδέλφειας με χρήση μεθόδων Γεωπληροφορικής. ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ Σχολή Αγρονόμων & Τοπογράφων Μηχανικών ΜΕΤΑΠΤΥΧΙΑΚΟ ΠΡΟΓΡΑΜΜΑ ΓΕΩΠΛΗΡΡΟΦΟΡΡΙΙΚΗ Μεταπτυχιακή εργασία : Μελέτη της εξέλιξης του προσφυγικού οικισμού της Νέας Φιλαδέλφειας με

Διαβάστε περισσότερα

Other Test Constructions: Likelihood Ratio & Bayes Tests

Other Test Constructions: Likelihood Ratio & Bayes Tests Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

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

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

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics

Fourier Series. MATH 211, Calculus II. J. Robert Buchanan. Spring Department of Mathematics Fourier Series MATH 211, Calculus II J. Robert Buchanan Department of Mathematics Spring 2018 Introduction Not all functions can be represented by Taylor series. f (k) (c) A Taylor series f (x) = (x c)

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

LESSON 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

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

Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας

Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας ΤΕΙ ΚΑΒΑΛΑΣ ΠΑΡΑΡΤΗΜΑ ΔΡΑΜΑΣ ΤΜΗΜΑ ΑΡΧΙΤΕΚΤΟΝΙΚΗΤΟΠΙΟΥ Αστικές παρεμβάσεις ανάπλασης αδιαμόρφωτων χώρων. Δημιουργία βιώσιμου αστικού περιβάλλοντος και σύνδεση τριών κομβικών σημείων στην πόλη της Δράμας

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

Physical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible.

Physical DB Design. B-Trees Index files can become quite large for large main files Indices on index files are possible. B-Trees Index files can become quite large for large main files Indices on index files are possible 3 rd -level index 2 nd -level index 1 st -level index Main file 1 The 1 st -level index consists of pairs

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

«Έντυπο και ψηφιακό βιβλίο στη σύγχρονη εποχή: τάσεις στην παγκόσμια βιομηχανία».

«Έντυπο και ψηφιακό βιβλίο στη σύγχρονη εποχή: τάσεις στην παγκόσμια βιομηχανία». ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΙΟΝΙΩΝ ΝΗΣΩΝ ΤΜΗΜΑ ΔΗΜΟΣΙΩΝ ΣΧΕΣΕΩΝ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑΣ Ταχ. Δ/νση : ΑΤΕΙ Ιονίων Νήσων- Λεωφόρος Αντώνη Τρίτση Αργοστόλι- Κεφαλληνίας, Ελλάδα 28100, +30

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: Understanding and Written Response

Advanced Subsidiary Unit 1: Understanding and Written Response Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes

Διαβάστε περισσότερα

ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ

ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΤΜΗΜΑ ΠΟΛΙΤΙΚΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΔΟΜΟΣΤΑΤΙΚΗΣ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ Η ΣΥΜΒΟΛΗ ΤΩΝ ΔΟΜΙΚΩΝ ΕΠΙΦΑΝΕΙΩΝ ΣΤΟ ΦΥΣΙΚΟ ΦΩΤΙΣΜΟ ΤΩΝ ΘΑΛΑΜΩΝ ΝΟΣΗΛΕΙΑΣ ΑΜΠΛΙΑΝΙΤΗ ΑΛΙΚΗ ΣΤΑΜΑΤΟΠΟΥΛΟΥ ΣΤΑΥΡΟΥΛΑ

Διαβάστε περισσότερα

ΜΕΤΑΠΤΥΧΙΑΚΗ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «ΘΕΜΑ»

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

Διαβάστε περισσότερα

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

TMA4115 Matematikk 3

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

Διαβάστε περισσότερα

ΣΤΥΛΙΑΝΟΥ ΣΟΦΙΑ Socm09008@soc.aegean.gr

ΣΤΥΛΙΑΝΟΥ ΣΟΦΙΑ Socm09008@soc.aegean.gr ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΚΟΙΝΩΝΙΟΛΟΓΙΑΣ ΜΕΤΑΠΤΥΧΙΑΚΟ ΠΡΟΓΡΑΜΜΑ ΣΠΟΥΔΩΝ «ΕΡΕΥΝΑ ΓΙΑ ΤΗΝ ΤΟΠΙΚΗ ΚΟΙΝΩΝΙΚΗ ΑΝΑΠΤΥΞΗ ΚΑΙ ΣΥΝΟΧΗ» ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ Θέμα: Διερεύνηση των απόψεων

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΚΑΛΩΝ ΚΑΙ ΕΦΑΡΜΟΣΜΕΝΩΝ ΤΕΧΝΩΝ ΤΜΗΜΑ ΚΑΛΩΝ ΤΕΧΝΩΝ ΜΕΤΑΠΤΥΧΙΑΚΟ ΠΡΟΓΡΑΜΜΑ ΣΤΗΝ ΙΣΤΟΡΙΑ ΚΑΙ ΘΕΩΡΙΑ ΤΗΣ ΤΕΧΝΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΚΑΛΩΝ ΚΑΙ ΕΦΑΡΜΟΣΜΕΝΩΝ ΤΕΧΝΩΝ ΤΜΗΜΑ ΚΑΛΩΝ ΤΕΧΝΩΝ ΜΕΤΑΠΤΥΧΙΑΚΟ ΠΡΟΓΡΑΜΜΑ ΣΤΗΝ ΙΣΤΟΡΙΑ ΚΑΙ ΘΕΩΡΙΑ ΤΗΣ ΤΕΧΝΗΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΚΑΛΩΝ ΚΑΙ ΕΦΑΡΜΟΣΜΕΝΩΝ ΤΕΧΝΩΝ ΤΜΗΜΑ ΚΑΛΩΝ ΤΕΧΝΩΝ ΜΕΤΑΠΤΥΧΙΑΚΟ ΠΡΟΓΡΑΜΜΑ ΣΤΗΝ ΙΣΤΟΡΙΑ ΚΑΙ ΘΕΩΡΙΑ ΤΗΣ ΤΕΧΝΗΣ Αφήγηση και εθνική ταυτότητα: Η Κυπριακή Συλλογή στο Εθνικό

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

ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ ΜΕ ΘΕΜΑ : «ΑΜΦΙΣΒΗΤΗΣΕΙΣ ΟΡΙΩΝ ΓΕΩΤΕΜΑΧΙΩΝ ΔΙΑΔΙΚΑΣΙΑ ΕΠΙΛΥΣΗΣ ΜΕΣΩ ΔΙΚΑΣΤΙΚΩΝ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΩΝ.»

ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ ΜΕ ΘΕΜΑ : «ΑΜΦΙΣΒΗΤΗΣΕΙΣ ΟΡΙΩΝ ΓΕΩΤΕΜΑΧΙΩΝ ΔΙΑΔΙΚΑΣΙΑ ΕΠΙΛΥΣΗΣ ΜΕΣΩ ΔΙΚΑΣΤΙΚΩΝ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΩΝ.» ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕIO ΣΧΟΛΗ ΑΓΡΟΝΟΜΩΝ & ΤΟΠΟΓΡΑΦΩΝ ΜΗΧΑΝΙΚΩΝ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ ΜΕ ΘΕΜΑ : «ΑΜΦΙΣΒΗΤΗΣΕΙΣ ΟΡΙΩΝ ΓΕΩΤΕΜΑΧΙΩΝ ΔΙΑΔΙΚΑΣΙΑ ΕΠΙΛΥΣΗΣ ΜΕΣΩ ΔΙΚΑΣΤΙΚΩΝ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΩΝ.» ΕΠΙΒΛΕΠΟΥΣΑ: Χ.

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

Η ΨΥΧΙΑΤΡΙΚΗ - ΨΥΧΟΛΟΓΙΚΗ ΠΡΑΓΜΑΤΟΓΝΩΜΟΣΥΝΗ ΣΤΗΝ ΠΟΙΝΙΚΗ ΔΙΚΗ

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

Διαβάστε περισσότερα

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 1: Elements of Syntactic Structure Το περιεχόμενο του μαθήματος διατίθεται με άδεια

Διαβάστε περισσότερα