Was Innovation unwanted in Byzantium?

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Was Innovation unwanted in Byzantium?"

Transcript

1 Apostolos Spanos, University of Agder Working paper, to be published in: Ingela Nilsson & Paul Stephenson (eds.), Byzantium Wanted: The Desire and Rejection of an Empire, Uppsala 2013 [Studia Byzantina Upsaliensia, vol. 15]. ABSTRACT: A well-established thesis in Byzantine studies is that Byzantium was a conservative civilization, negative if not hostile to innovation. This general idea influenced the study of innovation in Byzantium, which has been presented by modern scholars as either absent or as being decisively opposed to. After a presentation of some preliminary questions on the use of terms as innovation in modern historical writing this article examines the use of Byzantine terms related to the concept of innovation in Byzantine lexicographical, historiographical and theological texts. The comparison of these works to ancient Greek ones demonstrates that the Byzantines continued using words and concepts as innovation, novelty etc. in a way similar to that used by their predecessors. Furthermore, the article demonstrates that the Byzantines probably had more than one understandings of innovation and were not negative towards innovation as such.

2 2 In memory of Tomas Hägg It is often said that Byzantium and the Byzantines were negative, if not inimical and hostile, to innovation 1. Albeit not thoroughly studied 2 and contradicted, directly or not, by a number of modern studies 3, the notion of Byzantium as a static and changeless civilization has influenced a great number of historians, who have presented the Byzantine understanding of innovation in negative light, particularly in the fields of politics and religion, where the Byzantines are supposed to have perceived innovation as rebellion and heresy correspondingly 4. But, really, did the Byzantines have one and only one understanding of innovation? Were they negative or sceptical towards innovation as such? And furthermore, did they evaluate innovation in a way that was originally their own? 5 I would like to thank Prof. Emer. Jonny Holbek (University of Agder) for having shared with me thoughts on innovation, types of innovation and innovation in Byzantium; this essay would not be the same without our discussions, which I am deeply grateful for. I am also thankful to Prof. Benoît Godin (INRS, Montreal) and Dr. Vasileios Syros (Finnish Centre of Political Thought & Conceptual Change), for their comments, corrections and criticisms. 1 See for example the entry on innovation in the Oxford Dictionary of Byzantium: The Byzantines did not appreciate innovation and claimed to have stuck to tradition. Imitation or repetition of the standard authorities was praiseworthy. [ ] Reforms were usually couched in terms of the restoration of the past rather than of innovation. [ODB, ed. A. P. Kazhdan [et al.], Vols. 1 3 (Oxford, 1991), here vol. 2: 997]. 2 See A. Spanos, To Every Innovation Anathema (?). Some preliminary thoughts on the study of Byzantine Innovation, in Mysterion, strategike og kainotomia. Et festskrift til ære for Jonny Holbek, ed. H. Knudsen, J. Falkenberg, K. Grønhaug & Å. Garnes (Oslo, 2010), See, e.g., A. R. Littlewood (ed.), Originality in Byzantine Literature, Art and Music. A Collection of Essays (Oxford, 1995); A. P. Kazhdan & A. W. Epstein, Change in Byzantine Culture in the Eleventh and Twelfth Centuries (Berkeley, 1985); A. Ödekan, E. Akyürek, N. Necipoğlu (eds.), First International Sevgi Gonul Byzantine Studies Symposium. Change in the Byzantine World in the Twelfth and Thirteenth Centuries (Istanbul, 2010). 4 See for example ODB 3: 997: More often the word [kainotomia] was used in a broader sense of novelty and breach of tradition and applied predominantly to heretical doctrines or even rebellions. 5 This paper will not enter in the discussion of whether the Byzantines had a notion of innovation similar to our own, a problem that still waits for an ad hoc study.

3 3 This paper aims at answering these questions by studying Byzantine sources 6. After some preliminary reflections on the study of innovation in historical writing, it looks briefly at the Byzantine explanation of innovation in Byzantine lexica. Then it considers if the Byzantine understanding of innovation in politics, that is to say innovation as rebellion, was as monolithic as modern scholarship seems to believe. Finally, it deals with innovation in theology, or, according to modern historians, innovation as heresy. While studying innovation as rebellion and as heresy, the paper employs ancient Greek sources, to examine whether the Byzantines understood innovation in politics and religion in a way different than that of the Ancient Greeks. Innovation in Historical Writing A classical definition of innovation presents the modern concept of the term as any idea, practice, or material artifact perceived to be new by the relevant unit of adoption 7. By focusing on the crucial role of the adoptive unit in the process (and eventually the result) of any innovation, this definition points to the main problem of the historical study of innovation, namely the oversimplification of the relation between innovation(s) and unit(s) of adoption 8. To make the point clear: by speaking about Byzantine innovation in general the historian creates and applies a unit of adoption (Byzantium or the Byzantine civilization) that was enormous both in space (at its largest from present Middle East to Spain and from the Danube to North Africa) and time (from the fourth to the fifteenth century). Furthermore, and this is the most important in our case, this superstructure, inhabited by a big number of 6 As the sources studied are not more than a drop in the ocean of Byzantine literature, the thoughts presented here could not be anything but preliminary. 7 G. N. Zaltman, R. B. Duncan & J. Holbek, Innovations and Organizations (New York, 1973), 10; cf. E. M. Rogers, Diffusion of Innovations, (New York, 1995 [1962]), 11. Let it be noted that the term innovation is used in the rest of my text in its modern meaning, while when referring to the Byzantine understanding of innovation, I am using the two words mainly used by the Byzantines themselves, namely kainotomia and neoterismos. 8 Some of the questions related to the use of concepts as innovation, novelty, invention and the like in historical writing are to be studied in an ad hoc paper in preparation, in collaboration with Jonny Holbek, under the working title: Historical Innovation: Rethinking the Concept of Innovation in Historical Writing.

4 4 peoples, completely different between them and with varying interests and sets of concerns and priorities, is supposed to have been homogeneous enough to have articulated one and only one understanding of what innovation was. Even more, it is also supposed to have had and applied the same criteria on which new ideas, practices or artefacts were to be accepted as positive innovations and which were to be rejected as negative or even dangerous. While speaking about innovation in Byzantium, or any other civilization, a historian should consider the civilization as a mega-system encompassing countless units of various types, as to name but a few the state, the church, the emperor, the army, the society in general, various local societies and social groupings, local aristocracies, or monastic communities. A new idea, for example a theological doctrine, or a new practice, let us say a fiscal system, could be accepted or enforced by the central government and opposed by the church or the society. An innovative law could be accepted by the state and the largest part of the society but opposed by the big landowners or the nobility. An innovation could be rejected right after its first appearance to be accepted later, by the same or another unit of adoption, or could be introduced to just one of the cities or the provinces of the empire (that is to say: to one unit of adoption) to be adopted later by some other provinces or the whole empire. Another problem in the historical study of innovation is that modern scholarship presents, more often than not, concepts as originality, novelty, invention and the like as synonyms to innovation 9, something that may easily lead to perplexity and wrong conclusions. These concepts are not identical, neither in modern times nor in a historical perspective. To make this clear by focusing only on originality: it is not of axiomatic truth that every innovation by default is an original idea, practice or artefact. There are cases, where an 9 One example will suffice: Summing up the anthology Originality in Byzantine Literature, Art and Music, A. Cutler realizes that the authors of the papers that precede this treat originality variously as a synonym for creativity, invention, or innovation [A. Cutler, Originality as a Cultural Phenomenon, in Littlewood, Originality, 203].

5 5 innovation indicates simply the creative use or realization of an old idea, or a newly imported or transplanted idea or practice, that was originally invented or set up by another unit, as for example an individual, a group, a state, a civilization etc. (it is also possible that two of more old ideas add up to an innovation). The adaptation of this(-ese) old idea(s) and its appropriation, transformation or reinvention by the new unit may be so differentiating that the new product or practice becomes an innovation, even though the idea it is based on is not original. Another point should be added: unlike what is usual in other fields, in historical writing innovation is used as an unambiguous concept, without any reference to the various types of innovation 10. Due to the scope and the limitations of this paper, there is space enough to refer, by way of example, to only two distinct types of innovation, namely the radical and incremental innovations. Radical innovations require a high degree of new knowledge and skills and they introduce fundamental and, at least sometimes, revolutionary changes. Incremental innovations may be achieved with a low degree of new knowledge and they introduce minor improvements or simple adjustments in current ideas 11 (it should be noted though that a series of incremental innovations might result in a radical innovation). The aphorisms on an antiinnovative Byzantium in modern scholarship refer most probably to Byzantium s scepticism towards radical innovation, particularly in politics and religion. Even though, a study of sources of various types demonstrate that the Byzantines were not hostile to innovation as such, neither to radical not to incremental innovations. 10 Zaltman et al., Innovations and Organizations, 17 32, present a typology based on whether an innovation is: (a) programmed or non-programmed, (b) instrumental or ultimate, and (c) radical or not. On types of innovation see also N. King & N. Anderson, Managing Innovation and Change: A Critical Guide for Organizations (London, 2002), ; G. Zaltman & N. Lin, On the Nature of Innovations, American Behavioral Scientist 14 (1971) ; R. D. Dewar & J. E. Dutton, The Adoption of Radical and Incremental Innovations: An Empirical Analysis, Management Science 32 (1986) ; H. W. Chesbrough & D. J. Teece, Organizing for Innovation: When Is Virtual Virtuous?, Harvard Business Review 80 (2002) See Dewar & Dutton, The Adoption of Radical and Incremental Innovations,

6 6 Innovation in Byzantine Lexicography The study of Byzantine texts and lexica 12 shows that the Byzantines used mainly two words for innovation: kainotomia (καινοτοµίία) and neoterismos (νεωτερισµόός) 13. The verb to innovate occurs in Byzantine lexicographical sources as kainotomein (καινοτοµεῖν), neoterizein (νεωτερίίζειν) and kainourgein (καινουργεῖν). Modern scholarship seems to accept that the Byzantines used all these words in the same meaning; and, mainly, in a negative way. But was it so? The largest surviving Byzantine lexicon was composed in the fifth sixth century and is attributed to Hesychios 14. This lexicon defines the verb kainotomein in a neutral way: to innovate: to make/do something new (Καινοτοµῆσαι καινὸν ποιῆσαι) 15. This definition appears in a number of later Byzantine lexica, deriving from or influenced by that of Hesychios, who adds that the word also means the opening of a new mining field (Καινοτοµεῖν καινὴν λατοµίίαν τέέµνειν) 16. An innovator (kainourgekos) is someone who works/produces new things (Καινουργηκόότα νέέα πράάγµατα ἐργασάάµενον) 17. The verb neoterizein is presented as having a different meaning from kainotomein; while kainotomein is defined as making new things, neoterizein has the meaning of doing new things (Νεωτερίίζει καινὰ πράάττει) 18. A lexicon ascribed to the fifth-century patriarch of Alexandria Cyril ( ), under the title Συναγωγήή, also presents the verbs kainotomein and neoterizein as not having exactly the same meaning. Kainotomein is described 12 On Byzantine lexicography see K. Alpers, Lexikographie. B. I III, Historisches Wörterbuch der Rhetorik (Tübingen, 2001), ; K. Alpers, Griechische Lexikographie in Antike und Mittelalter, in Welt der Information, ed. Hans-Albrecht Koch (Stuttgart, 1990), The word kainourgema (καινούύργηµα) was also used, but not very often. 14 Ed. Moritz Schmidt, 5. vols (Jena, ); a part of the lexicon is edited by K. Latte, Hesychii Alexandrini Lexicon, vols. I (A Δ) II (E O) (Copenhagen, ). 15 Hesychii Alexandrini Lexicon, ed. Latte, II, Hesychii Alexandrini Lexicon, ed. Latte, II, 394. The definition is not originally Byzantine, as it appears for example in Xenophon, De vectigalibus, tr. Marchant, 4: Hesychii Alexandrini Lexicon, ed. Latte, II, Hesychii Alexandrini Lexicon, ed. Latte, II, 708.

7 7 as working/producing something new (Καινοτοµεῖ καινουργεῖ), while neoterizein as doing new things (νεωτερίίζει καινὰ πράάττει) 19. Somebody who deals with neoterismos, a neoteropoios, is characterized as rebel, tyrant, plotter (Νεωτεροποιόός ἀντάάρτης, τύύραννος, ἐπιθέέτης) 20. The great ninth-century Byzantine statesman, scholar and patriarch of Constantinople Photios ( and ) composed a lexicon, where he presents kainotomia, neoterizein, and neoteropoios in exactly the same way to Cyril of Alexandria (Καινοτοµεῖ καινουργεῖ 21 ; Νεωτερίίζει: καινὰ πράάττει; and Νεωτεροποιόός: ἀντάάρτης τύύραννος ἐπιθέέτης 22 ). The tenth-century Etymologicum Gudianum presents kainotomia as something changed against the rules and the laws of nature (Kαινοτοµίία, ἔστι πράάγµα, παρὰ τοὺς τῆς φύύσεως ὅρους καὶ νόόµους παρηλλαγµέένον) 23. This definition is most probably from the corollary of a theological understanding of kainotomia, that is to say the Incarnation of Christ, which took place exactly against the rules and the laws of nature 24. The so-called Souda Lexicon, a compilation of lexica, etymologika and other sources, most probably produced around 1000, explains the verb kainotomein as to produce/work something new, relating it to politics (Καινοτοµεῖ 19 Synagoge. Συναγωγὴ λέέξεων χρησίίµμων. Texts of the Original Version and of MS: B, ed. Ian C. Cunningham (Berlin New York, 2003), 282 and Synagoge, ed. Cunningham, Photii patriarchae lexicon, ed. C. Theodoridis, vol. ΙΙ (Ε Μ) (Berlin New York, 1998), 348, nr. 68. The lexicon also includes an entry on the infinitive kainotomein, which presents the literal meaning of the word in mining, identically to the lexicon by Hesychios: mainly to cut fresh into a mine (καινοτοµεῖν καινὴν λατοµίίαν τέέµνειν κυρίίως; ibid., nr. 59). 22 Φωτίίου τοῦ πατριάάρχου λέέξεων συναγωγήή, ed. Porson (Cambridge, 1822), 1: Etymologicum Graecae linguae Gudianum et alia grammaticorum scripta e codicibus manuscriptis nunc primum edita, ed. F. W. Sturz (Leipzig, 1818), See, for example, the definition of kainotomia as the Incarnation of Christ in the entry of a thirteenthcentury lexicon wrongly attributed Ioannes Zonaras (12th c.). This lexicon presents innovation as what is by any means changed against the common nature and not identified in anything to the human custom. It is necessary to get a deep knowledge of this term because of those who misunderstand the innovation in Christ. Because although he innovated nature by being born without semination, after his birth and as he was growing, quite much (of the features) of his body he did not have in innovation but in sameness to us, with only the exception of sin [=Τὸ κατὰ πάάντα τρόόπον παρηλλαγµέένον τῆς κοινῆς φύύσεως, καὶ ἐν µηδενὶ τῇ τῶν ἀνθρώώπων συνηθείίᾳ ἐξοµοιούύµενον. Τοῦτον δὲ τὸν ὅρον ἀναγκαῖον ἐπίίστασθαι διὰ τοὺς κακῶς νοοῦντας τὴν καινοτοµίίαν ἐν Χριστῷ. Εἰ γὰρ ἐκαινοτόόµησε τὴν φύύσιν ἀσπόόρως γεννηθεὶς, ἀλλ ὅµως µετὰ τὸν τόόκον τὴν αὔξησιν τῆς ἡλικίίας, καὶ τὰ πολλὰ τὰ ἐν τῷ σώώµατι οὐ κατὰ καινοτοµίίαν ἔσχεν, ἀλλὰ καθ ὁµοιόότητα ἡµῶν χωρὶς ἁµαρτίίας. Pseudo-Zonaras, Lexicon, ed. Tittmann, (Leipzig, 1808): 1154]. [Translations are mine, unless noted otherwise.]

8 8 αἰτιατικῇ. καινουργεῖ. ὅτι τὸ καινοτοµεῖν ἐπὶ τοῦ ἄρχειν) 25. In the entry on the lyric poet Melanippides the verb kainotomein is used in a way that reminds of the modern use of the verb to innovate, as the lexicon reads that Melanippides innovated a lot in the composition of the dithyramb 26. The noun kainotomia is also listed in Souda, without any explanation. Souda presents the verb neoterizei as doing something new (Νεωτερίίζει: καινὰ πράάττει) 27. It also includes a passage by Thucydides under the entry neoterizein 28, and explains neoterismos as rebellion and neoteropoios in exactly the same way to Cyril and Photios, as rebel, tyrant, plotter (Nεωτερισµόός: ἀνταρσίία and Nεωτεροποιόός: ἀντάάρτης, τύύραννος, ἐπιθέέτης) 29. All the studied lexica present kainotomia and kainotomein in a neutral way, not reflecting any negative understanding of the term. An argumentum ex silentio may be added here, as a number of other Byzantine lexica and etymologica that have been examined, do not include an entry on our innovation-terms ; this probably demonstrates that the lexicographers did not find the words worthy of an explanation, as they should I am tempted to think if kainotomia was generally understood as something negative, or even dangerous or harmful. This is, more or less, the case for the verb neoterizein as well, while neoterismos is clearly presented as a negative change, or effort to change or alter, usually of the political order or existing regime. 25 Suidae Lexicon, ed. A. Adler, 5 vols. (Leipzig, ), Κ Μελανιππίίδης, [...] ὃς ἐν τῇ τῶν διθυράάµβων µελοποιΐα ἐκαινοτόόµησε πλεῖστα (Suidae Lexicon, ed. Adler, M 454). Let it be noted that in this entry the verb kainotomein is used in the same meaning as in the lexica of Hesychios, Cyril and Photios studied above. 27 Suidae Lexicon, ed. Adler, Ν «Νεωτερίίζειν. Θουκυδίίδης τῆς ἡµέέρας τὸ πνῖγος ἐλύύπει, νύύκτες δὲ µετοπωριναὶ καὶ ψυχραὶ τῇ µεταβολῇ ἀσθέένειαν ἐνεωτέέριζον. ὁ δὲ βάάρβαρος οὐδὲ ἐπὶ τὴν νεωτερίίζουσαν τὰ πράάγµατα τύύχην ἔσχεν ἀνενεγκεῖν τὴν αἰτίίαν, ὡς ἂν ἔννοµόόν τινα καὶ ὕπαιθρον ἀγωνισάάµενος µάάχην» (Suidae Lexicon, ed. Adler, Ν 244). Cf. Thycydides, Historiae, ed. Jones & Powell (Oxford, 1942), (τῆς ἡµέέρας ἐνεωτέέριζον) and Eunapius, Fragmenta historica, ed. Dindorf (Leipzig, 1870), 226 (ὁ δὲ βάάρβαρος µάάχην)]. 29 Suidae Lexicon, ed. Adler, Ν 245, 247. The words are also used in this sense when employed in other entries of the lexicon.

9 9 Thus, we may say that the study of the verbs kainotomein and neoterizein and their derivatives in Byzantine lexica does not support the theory of a sclerotic negative understanding of innovation in Byzantium. Furthermore, they demonstrate that in Byzantine lexicography the words kainotomia and neoterismos do not have the same meaning, since kainotomia is presented in a neutral way, while neoterismos includes negative meanings, as for example that of rebellion or sedition. This is also confirmed by the study of the words on those who introduce kainotomiai and neoterismoi: the word kainotomos (καινοτόόµμος), is not evaluated as so important to be honoured by an entry, while a neoteristes (νεωτεριστὴς) is presented only negatively as «rebel, tyrant, plotter». To examine this deduction further, let us turn to Byzantine historiography and theology. Innovation in Byzantine Political Life According to modern scholarship, in the field of politics the Byzantines understood innovation as rebellion, revolt, or revolution. One of the main arguments for that, expressed in the Oxford Dictionary of Byzantium, is a text by the eleventh-century Byzantine scholar, Michael Psellos. In his Chronographia (Χρονογραφίία), Psellos comments on a revolt against the emperor Michael V ( ), writing that «by the majority the act was understood as an irrational innovation» 30. But is this passage representative of the hostile tendency of the Byzantines towards innovation? First of all, the argument does not pay attention to a word that is of importance, namely the word irrational, or senseless (ἄλογος). The fact that Psellos uses this adjective to define the kind of innovation means that in the Byzantine mentality of his time there were also rationally founded, or non-senseless, innovations. 30 «Τοῖς µὲν οὖν πολλοῖς καινοτοµίία τις ἄλογος τὸ πραττόόµενον ἔδοξεν» [Michel Psellos: Chronographie ou histoire d'ʹun siècle de Byzance ( ), ed. E. Renault, vols I II (Paris, ), 5.27]. E.R.A. Sewter translates: To most of the others it seemed a senseless revolt ; E.R.A. Sewter (trans.), Fourteen Byzantine Rulers (New York, 1966), 139 (the translation is free online at This text is used as an argument for the Byzantine understanding of kainotomia as revolt in ODB 2: 997.

10 10 Furthermore, Psellos uses kainotomia and kainotomein no less that twelve times in his Χρονογραφίία, in a variety of meanings; he refers, for example, to innovations by the divine justice 31 or by the emperor himself 32. In another text, his encomium on the patriarch of Constantinople Constantine Leichoudes ( ), he praises the patriarch for having opened for him the path to education; the verb used by Psellos for opening the way is kainotomein. 33 A number of other passages from various periods demonstrates that Byzantium also had developed a positive understanding of innovation in politics. I could refer, for example, to Anna Comnena and her Alexias, where she commends her father Alexius I ( ) as introducing kainotomiai, writing that if anyone were to reckon the art of ruling as a science and a kind of high philosophy, as if it were the art of all arts and the science of all sciences, then he would certainly admire my father as a skilful scientist and artist for having invented [kainotomounta] those new titles and functions in the Empire «Λέέξω, ὡς ἂν οἷόός τε ὦ, ὁπόόσα µετὰ τὴν τῆς βασιλίίδος ὑπερορίίαν ἡ θείία δίίκη τῷ τε καιρῷ καὶ τοῖς πράάγµασιν ἐκαινοτόόµησεν» (= I will tell, to the best of my ability, an account of all those things that the Divine Justice innovated in relation to time and the sircumstances; Chronographie, ed. Renault, 5.24; Sewter, Fourteen Byzantine Rulers, 137 translates: At all events, to the best of my ability, I will tell my story an account of all those strange happenings that followed the empress s exile, events that Divine Justice brought to pass at this moment in history). 32 Even if the evaluation of the kainotomia is here clearly negative, it could not be understood as rebellion and the like: «ᾬοντο δὲ µηδὲ τοὺς ἐν τῇ Πόόλει τῷ βασιλεῖ προσθήήσεσθαι, τούύτοις δὲ ἀντιστήήσεσθαι, δι ὀργῆς τε τὸν αὐτοκράάτορα ἔχοντας, ἐπειδὴ καὶ καινοτοµεῖν τι κατ αὐτῶν ἤρξατο, καὶ τὴν προεδρίίαν αὐτοῦ δυσχεραίίνοντας, καὶ βουλοµέένους στρατιώώτην ἰδεῖν αὐτοκράάτορα, σφῶν τε προκινδυνεύύοντα καὶ τὰς ἐπιδροµὰς τῶν βαρβάάρων ἀνείίργοντα» (Besides, they were under the impression that the inhabitants of Constantinople would not remain loyal; they expected no opposition there, because the emperor had made himself unpopular by introducing reforms which curbed the liberty of the citizens. The people loathed him as a ruler and wanted to see a soldier-emperor, a man who would endanger his own life on their behalf and put an end to barbarian incursions; Chronographie, ed. Renault, 6.104; translated by Sewter, Fourteen Byzantine Rulers, ). 33 Αὐτόός γάάρ µοι τὴν τῆς παιδείίας ὁδὸν πρὸ τῶν ἄλλων ἐκαινοτόόµησας (Encomium in patriarchem Constantinum Leichudem, ed. in K. N. Sathas, Ἐπιτάάφιοι Λόόγοι, vol. 4 [Bibliotheca Graeca Medii Aevi (1874)], 420). Psellos also uses positively kainotomia in theology; see, for example, footnotes 45 and 46). 34 Eἰ γάάρ τις εἰς ἐπιστήήµην καίί τινα ὑπερτάάτην φιλοσοφίίαν ἀνάάγοι τὴν βασιλείίαν ὥσπερ τέέχνην οὖσαν τεχνῶν καὶ ἐπιστήήµην ἐπιστηµῶν, θαυµάάσαιτο ἂν καὶ τὸν ἐµὸν πατέέρα οἷόόν τινα ἐπιστήήµονάά τε καὶ ἀρχιτέέκτονα τὰ ὑπὸ τὴν βασιλείίαν καινοτοµοῦντα καὶ πράάγµατα καὶ ὀνόόµατα [Annae Comnenae Alexias, ed. A. Kambylis and D. R. Reinsch (Corpus Fontium Historiae Byzantinae. Series Berolinensis XL/1, Berlin New York, 2001) 96; transl. by Elizabeth A. Dawes (London, 1928),

11 11 To depart from the eleventh century, let us recall Pseudo-Kodinos and his Treatise on the Dignities and Offices (De officiis, composed between 1347 and 1368), where he makes clear that it is possible to the emperors to kainotomein unhindered, both in functions and titles 35. Let us note that in all these cases where the concept of innovation is used in a neutral or positive way the verb expressing the concept is kainotomein and not neoterizein. Thus, it could be argued that the positive understanding of innovation in politics was expressed with the use of the word kainotomein and its derivatives, while neoterizein was almost always, if not always, used for negative, not accepted radical changes in political life and state organization. But was this negative understanding of neoterismos as rebellion, revolt or revolution an originally Byzantine understanding? Or was it something the Byzantines inherited by their predecessors? A study of ancient sources demonstrates that a negative understanding of neoterizein and neoterismos in political thinking existed at least from the fifth century BC. One may refer, for example, to Plato 36, Aristotle 37, or Demosthenes 38. Almost half a millennium later, the great biographer Plutarch (c AD) uses the word in the same negative meaning, for example in his available free online at last accessed 2 October 2012]. 35 Ἔξεστι δὲ καὶ τοῖς βασιλεῦσι καινοτοµεῖν καὶ πράάγµατα καὶ ὀνόόµατα ἀκωλύύτως [Pseudo- Kodinos. Traité des offices, ed. J. Verpeaux (Paris, 1966), 135]. 36 «Αἰτίίαν δὴ ἔσχον ὑπὸ τῶν ἑτέέρων, κἂν µὴ ἐπιθυµῶσι νεωτερίίζειν, ὡς ἐπιβουλεύύουσι τῷ δήήµῳ καίί εἰσιν ὀλιγαρχικοίί (=And thereupon the charge is brought against them by the other party, though they may have no revolutionary designs, that they are plotting against the people, and it is said that they are oligarchs)» (Plato, The Republic, trans. Shorey, 8.565b). 37 «Δεῖ δὲ τοιούύτους εἶναι τοὺς ἀρχοµέένους πρὸς τὸ πειθαρχεῖν καὶ µὴ νεωτερίίζειν ( unfriendliness in the subject classes is a good thing with a view to their being submissive to authority and not making revolution)» (Aristotle, Politica, tr. Rackham, 1262b). 38 «Ἔστι γὰρ ἐν ταῖς συνθήήκαις ἐπιµελεῖσθαι τοὺς συνεδρεύύοντας καὶ τοὺς ἐπὶ τῇ κοινῇ φυλακῇ τεταγµέένους ὅπως ἐν ταῖς κοινωνούύσαις πόόλεσι τῆς εἰρήήνης µὴ γίίγνωνται θάάνατοι καὶ φυγαὶ παρὰ τοὺς κειµέένους ταῖς πόόλεσι νόόµους, µηδὲ χρηµάάτων δηµεύύσεις, µηδὲ γῆς ἀναδασµοίί, µηδὲ χρεῶν ἀποκοπαίί, µηδὲ δούύλων ἀπελευθερώώσεις ἐπὶ νεωτερισµῷ» (=For it is provided in the compact that it shall be the business of the delegates at the Congress and those responsible for public safety to see that in the states that are parties to the peace there shall be no executions and banishments contrary to the laws established in those states, no confiscation of property, no partition of lands, no cancelling of debts, and no emancipation of slaves for purposes of revolution) [Demosthenes, Περὶ τῶν πρὸς Ἀλέέξανδρον συνθηκῶν, 17.15; ed. Dilts, Demosthenis orationes (Oxford 2002), p. 203; transl. Demosthenes. I. Olynthiacs, Philippics, Leptines I XVII, XX. With an English translation by J. H. Vince, (Cambridge & London, 1930), 473].

12 12 biography of the second king of Rome, Numa Pompilius ( BC) 39. To the evidence given by Greek sources we may add an argumentum related to the Roman precursors of the Byzantines: in Latin sources the concept of revolution may be expressed as novae res (=new things), that is to say radical changes, or neoterismoi. Innovation in Byzantine Religion When it comes to the Byzantine understanding of innovation in religion, modern scholarship demonstrates that the word kainotomia is used in Byzantine theology mainly in relation to: (a) the mystery of the Incarnation of Christ and (b) radical changes in dogma, which were not in accordance to the official doctrines and teachings of the Church. 40 Innovation as unacceptable changes in dogma is presented clearly in the so-called Synodikon of Orthodoxy, a liturgical document produced in the period between 843 and The study of Byzantine theological and religious texts reveals a good number of passages, where kainotomia is used in this meaning. But was this use of the word representative of the Byzantine understanding and evaluation of innovation in religion? A good number of theological texts shows clearly that innovation is anathematized when it reflects drastic changes in faith and/or the ecclesiastical traditions and practices, when these changes are not accepted by the Church; this means that the understanding of 39 «Oὔτε γὰρ πόόλεµος οὔτε στάάσις οὔτε νεωτερισµὸς περὶ πολιτείίαν ἱστόόρηται Νοµᾶ βασιλεύύοντος (For there is noe record either of war, or faction, or political revolution while Numa was king)» [Plutarch'ʹs lives, ed. and tr. Perrin, vol. 1 (Cambridge, 1914) ]. The sentence is quoted by the Byzantine historian Ioannes Zonaras in his Epitomae Historiarum, ed. L. Dindorf, 2: This is, once again, an oversimplification of the study of innovation, as innovation in religion could be studied from many different viewpoints. One may focus on innovations in religion as theory (belief, theology) and as practice (ritual). Another possibility could be to study innovation in religions as independent systems of cognitive beliefs or as systems that function within one or more wider cultures which host them. Related aspects are discussed in C. Disbrey, Innovation and Tradition in Religion (Aldershot, 1994). 41 One example could be enough: Τοὺς παραχαράάττοντας τὰς ἀποστολικὰς καὶ πατρικὰς καὶ συνοδικὰς παραδόόσεις τῆς ἐκκλησίίας καὶ ἄλλο τι καινοτοµοῦντας ἢ ἐπινοοῦντας κατὰ τῆς πίίστεως, ἀνάάθεµα (=To those falsifying the traditions of the apostles and the fathers and the councils of the Church, and any other thing innovating or excogitating against faith, anathema); J. Gouillard, Le Synodikon de l Orthodoxie. Édition et Commentaire, Travaux et Memoires 2 (1967) 313.

13 13 innovation is not different from that in the Byzantine lexica, the making/doing something new, the opening of new paths. The problem for the Church was that novelties in specific fields or with specific content were not acceptable, as they would threaten its foundations. The discussion, for instance, on Christology was not just a theoretical debate but directly connected to the salvation of the human being. Thus, the innovation of Arius on Jesus as created by the Father was not to be accepted. At the same time, the innovative theologies of the homoousios and the triune God were accepted by the First Ecumenical Council, becoming thus doctrines of the church. The opinion that the Byzantine Church was not hostile to any innovation in theology as such may be strengthened by an argument the modern scholarship agrees on, namely that the Byzantine Church understood as we have seen previously the Incarnation of Christ as a kainotomia. 42 And this was an innovation understood in a very positive way. The Synodikon of Orthodoxy demonstrates this clearly by anathematizing those who do not believe in this kainotomia. 43 It should be noted here that in the passages studied, the Incarnation is presented as kainotomia, not neoterismos, which may indicate that Byzantine theology was acutely aware of the specific differences between kainotomia, which could be either positively of negatively evaluated, and neoterismos, which was always a negative change in doctrine or practice this should be studied on the basis of a sufficient amount of sources. Apart from that, Christianity seems to have understood itself, from the very beginning, as a religion that should express the innovative change from the antique world. When it comes to its theology, Christianity s fundamental doctrine is not completely new: gods and deities coming down to earth, getting killed and being resurrected were known before Christ. But the 42 Let us refer here to the Chrysostomic καινοτοµοῦνται φύύσεις, και Θεὸς ἄνθρωπος γίίνεται (=Natures are innovated, and God becomes a man; In sancta lumina, PG 36: 348). 43 Τοῖς [ ] λόόγοις διαλεκτικοῖς [ ] ἐπὶ τῆς ὑπὲρ φύύσιν καινοτοµίίας τῶν δύύο φύύσεων τοῦ Θεοῦ καὶ ἀνθρώώπου λογοµαχεῖν πειρωµέένοις, ἀνάάθεµα (=To those who by conversational words try to argue against the over the principles of nature kainotomia of the two natures of God, anathema); Gouillard, Le Synodikon de l Orthodoxie, 57.

14 14 Christian dogma of the one and only God being at the same time one nature and three persons is as innovative as one can get in Antiquity, not only in theology but also in philosophy. The same may be said for the doctrine on afterlife, which was not original, but was vested in the Christian world a new content and meaning. Thus, we may say that Byzantine theology seems not to have been hostile to the concept of innovation as such. Otherwise, we would never get neither the theology nor the practices originated during two very important theological controversies in Byzantium, namely Iconoclasm and Hesychasm. Iconoclasm (ca ) has been seen, studied and understood from diverse perspectives and points of view: political, ecclesiastical, economic, and theological. For the purpose of the present paper, let us focus on only one dimension of it: the iconoclastic part of the church (and, of course, the state) represents a conservative understanding of the ritual and the ecclesiastical practice; during the iconoclastic debate they upheld the unbroken and continuous tradition which existed between the views they expressed and the teachings of Christ, the Apostles, and the Fathers of the Church, in contrast to the false and innovative doctrine of their opponents 44. The iconophiles, on the other hand, supported the veneration of icons, which was indeed an innovation (by any means, including the painting s technique and style). After some 150 years of turbulence and persecutions of the iconophiles by the iconoclasts, the innovative veneration of the icons evolved into the official dogma of the Church as a result of the Council of Nicaea (843). Thus, the way was open to new innovations within painting and the production of icons, as for example with the production of the so-called narrative icons, from the twelfth century onwards 45. Hesychasm (14 th c.) is the last great theological controversy in the Byzantine world, related to a specific practice of monastic praying, which 44 L. Brubaker, Icons and Iconomachy, in A Companion to Byzantium, ed. Liz James (Chichester, 2010), 331 (emphasis added). 45 See P. Chatterjee, Narrating Sanctity: The Narrative Icon in Byzantium and Italy (PhD thesis, University of Chicago, 2007).

15 15 according to the theologian Gregory Palamas ( ) and his followers led to the physical experience of the divine energy, through the so-called silent prayer (the word Hesychasm derives from the Greek ἡσυχίία, silence). It is through this debate that new doctrines, as for example the distinction between the divine essence and the divine energies, were canonized as dogma, in the Council of Constantinople in 1351, even if they have been previously refuted by parts of the church (the patriarchate of Antioch for example) as innovations. Once more, an innovative new understanding and argumentation won the battle. Apart from these two great eras of theological innovations one could also refer to passages from other periods, as for example Psellos arguing that faith equal to a grain of mustard seed removes mountains and innovates [kainotomei] the impossible 46, or that it is not the apostle Paul who first innovates [kainotomei] the third heaven, as he bases himself on the Bible 47. Let us now try again to compare the Byzantine understanding of innovation in theology to the understanding of the ancient Greeks. Was innovation in theology and philosophy always acceptable before Byzantium? Religion in ancient Greece was not as systematic and doctrinal as in Byzantium. Its ethical system was not so dominating as the Christian one and the priesthood had neither the authority nor the power to intervene in the political and social life as the Byzantine church did. Furthermore, polytheism facilitated, one should think, the introduction of new gods, new ideas and new doctrines, in contradiction to the religious Byzantine state and society, where the powerful and conservative church could prevent innovations in theology and religious practices. But was it so? The famous trial, indictment and death of Socrates probably shows otherwise. Let us not forget that the Athenian philosopher was sentenced to death for corrupting the youth, not 46 Πίίστις ἑοικυῖα κόόκκῳ σινάάπεως ὄρη µεθιστάάνει καὶ καινοτοµεῖ τὰ ἀµήήχανα [Michaelis Pselli orationes hagiographicae, ed. E.A. Fisher, (Stuttgart, 1994), 300 (=Oratio in decollationem Ioannis Baptistae, v )]. 47 Τὸν δὲ τρίίτον τοῦτον οὐρανὸν οὐ πρῶτος καινοτοµεῖ ὁ ἀπόόστολος, ἀλλὰ τοῖς τῆς γραφῆς ἀποχρώώµενος ῥήήµασι καὶ τρίίτον φησὶν οὐρανὸν [Michaelis Pselli theologica, ed. P. Gautier (Stuttgart, 1994), opusculum 27].

16 16 believing in the established gods of the city and introducing new gods in Athens 48. One could hardly avoid thinking that the last accusation in reality means innovating in religion, a negative evaluation of which is thus shown as much older than Byzantium, at least in specific cases (as was also the case in Byzantium). Conclusions Taking into consideration everything presented above on the use and the meanings of our innovation-terms in Byzantine lexicography, historiography and theology (even if in an infinitesimal sample), we may deduce that the Byzantine understanding of innovation was not as monolithic as argued in prior scholarship. The first striking element is that in Byzantine thinking kainotomia and neoterismos seem not to have exactly the same meaning. While kainotomia was understood in both a positive and a negative way, neoterismos seems to have been evaluated mainly, if not only, negatively. Even if this should be studied on the basis of more sources, we may at this stage say that neoterizein seems to have been closer related to undertaking or attempting something against well established traditions, customs or conventions, while kainotomein also has the meaning of changing the status quo in a way that leads to positive results or, at least, does not harm the unit of adoption. As to the overall Byzantine understanding of innovation: there were of course fields in which most Byzantines understood innovation as something negative. In other fields, though, innovation was not only accepted, but also appreciated and encouraged. Furthermore, skepticism towards innovation, or 48 See for example Plato s Apologia Socratis: Σωκράάτη φησὶν ἀδικεῖν τούύς τε νέέους διαφθείίροντα καὶ θεοὺς οὓς ἡ πόόλις νοµίίζει οὐ νοµίίζοντα, ἕτερα δὲ δαιµόόνια καινάά (=It states that Socrates is a wrongdoer because he corrupts the youth and does not believe in the gods the state believes in, but in other new spiritual beings; Apologia Socratis, ed. and tr. Fowler, 24b c), and Xenophon s Memorabilia: Ἡ µὲν γὰρ γραφὴ κατ αὐτοῦ τοιάάδε τις ἦν Ἀδικεῖ Σωκράάτης οὓς µὲν ἡ πόόλις νοµίίζει θεοὺς οὐ νοµίίζων, ἕτερα δὲ καινὰ δαιµόόνια εἰσφέέρων ἀδικεῖ δὲ καὶ τοὺς νέέους διαφθείίρων [=The indictment against him was to this effect: Socrates is quilty of rejecting the gods aknowledged by the state and of bringing in strange deities; he is also guilty of corrupting the youth; Xenophontis Memorabilia, tr. E. C. Marchant, 1.1].

17 17 at least certain kinds (probably: types?) of innovation, or innovation is specific fields, seems to have existed long before Byzantium, as the study of ancient Greek sources may demonstrate 49. The widespread modern evaluation of Byzantium as anti-innovative could be proven wrong by the study of various innovations in Byzantine architecture 50 (one should need no more than studying the pendentives of Hagia Sophia), military techniques and practices 51 (the Greek fire being a very good example, even if not the only), technology (see for example the fifthcentury mechanical sundial treasured today at the British Museum of Science 52, or the famous tenth-century hydraulic systems of the imperial palace described by Liutprand of Cremona 53 ), painting (the narrative icon), theology (see above, on Iconoclasm and Hesychasm), or music 54. Thus, we may conclude that the modern thesis on innovation having been more or less unwanted in Byzantium is contradicted by a great number of sources of various types. Hence, one can assume that this thesis is a result of (a) a minimal study of the Byzantine understanding (or understandings?) of innovation and (b) neglect of a principle in innovation studies that almost every innovation meets resistance, whose power depends on the specific characteristics and valence of the adoptive unit (whether, for example, the majority of its members are receptive and amenable to adopting new ideas and changes) 55. So, one is tempted to think that since innovation seems not to have been unwanted in Byzantium, it is most probably the study of Byzantine innovation that has not been so far very wanted by modern scholarship. 49 See B. Godin (with the collaboration of Pierre Lucier), Innovation and Conceptual Innovation in Ancient Greece, Project on the Intellectual History of Innovation Working Paper No 14, (INRS/Montreal, 2012). 50 R. Ousterhout, Beyond Hagia Sophia: Originality in Byzantine Architecture, in Littlewood, Originality, See E. N. Luttwak, The Grand Strategy of the Byzantine Empire (Cambridge, 2009). 52 J. V. Field & M. T. Wright, Gears from the Byzantines: A Portable Sundial with Calendrical Gearing, Annals of Science 42 (1985) See P. Squartiti (transl.), The complete Works of Liudprand of Cremona (Washington D.C., 2007), Miloš Velimirović, Originality and Innovation in Byzantine Music, in Littlewood, Originality, See for example the chapter Resistance to change in King & Anderson, Managing Innovation and Change,

18 18 Bibliography 1. Sources Anna Comnena, The Alexias, ed. and tr. Elizabeth A. Dawes (London, 1928). Anna Comnena, Annae Comnenae Alexias, ed. A. Kambylis and D. R. Reinsch [Corpus Fontium Historiae Byzantinae. Series Berolinensis XL/1] (Berlin New York, 2001). Aristotle, Politics, tr. H. Rackham (Cambridge & London, 1932 [repr. 1998], vol. 21). Demosthenes, Περὶ τῶν πρὸς Ἀλέέξανδρον συνθηκῶν, ed. M. R. Dilts, Demosthenis orationes, vol. 1 (Oxford 2002), ; transl. Demosthenes. I. Olynthiacs, Philippics, Leptines I XVII, XX. With an English translation by J. H. Vince, (Cambridge & London, 1930; repr. 1989). Etymologicum Graecae linguae Gudianum et alia grammaticorum scripta e codicibus manuscriptis nunc primum edita, ed. F. W. Sturz (Leipzig, 1818). Eunapius, Fragmenta historica, ed. L. Dindorf, Historici Graeci minores, vol. 1 (Leipzig, 1870), Gouillard Jean, Le Synodikon de l Orthodoxie. Édition et Commentaire, Travaux et Memoires 2 (1967) Hesychios, Hesychii Alexandrini Lexicon, ed. K. Latte, vols. I (A Δ) II (E O) (Copenhagen, ). Hesychios, Hesychii Alexandrini Lexicon, ed. Moritz Schmidt, 5. vols (Jena, ). Hesychios, Ioannes Zonarae Epitomae Historiarum, ed. L. Dindorf, vols. 1 3, (Leipzig, ). John Chrysostom, In sancta lumina, PG 36: Michael Psellos, Encomium in patriarchem Constantinum Leichudem, ed. K. N. Sathas, Ἐπιτάάφιοι Λόόγοι, vol. 4 [Bibliotheca Graeca Medii Aevi (1874), ]. Michael Psellos, Michaelis Pselli orationes hagiographicae, ed. E.A. Fisher, (Stuttgart, 1994). Michael Psellos, Michaelis Pselli theologica, ed. P. Gautier (Stuttgart, 1994). Michael Psellos, Michel Psellos: Chronographie ou histoire d'ʹun siècle de Byzance ( ), ed. E. Renault, vols I II (Paris, [repr. 1967]). Photios, patriarch, Photii patriarchae lexicon, ed. C. Theodoridis, vol. ΙΙ (Ε Μ) (Berlin New York, 1998). Photios, patriarch, Synagoge. Συναγωγὴ λέέξεων χρησίίµμων. Texts of the Original Version and of MS: B, ed. Ian C. Cunningham (Berlin New York, 2003). Photios, patriarch, Φωτίίου τοῦ πατριάάρχου λέέξεων συναγωγήή, ed. R. Porson, pts. 1 2 (Cambridge, 1822). Plato, Apologia Socratis, ed. A. E. Taylor and tr. H. N. Fowler, Euthyphro; Apology; Crito; Phaedo; Phaedrus (London Cambridge, 1914 [repr. 1953]),

19 19 Plato, The Republic, tr. P. Shorey, (Cambridge London, 1935 [repr. 1946]). Plutarch, Plutarch'ʹs lives, ed. B. Perrin, vol. 1 (Cambridge, Mass., 1914 [repr. London: W. Heinemann 1967]), Pseudo-Kodinos, Pseudo- Kodinos. Traité des offices, ed. J. Verpeaux (Paris, 1966). Pseudo-Zonaras, Iohannis Zonarae lexicon ex tribus codicibus manuscriptis, ed. J.A.H. Tittmann, 2 vols. (Leipzig, 1808). Sewter E.R.A. (trans.), Fourteen Byzantine Rulers (New York, 1966). Suidae Lexicon, ed. A. Adler, 5 vols. (Leipzig, ). Squartiti Paolo (transl.), The complete Works of Liudprand of Cremona (Washington D.C., 2007). Thucydides, Historiae, ed. H. S. Jones & J. E. Powell (Oxford, 1942). Xenophon, De vectigalibus, ed. E. C: Marchant, Xenophontis opera omnia, vol. 5 (Oxford, 1920 [repr. 1969]). Xenophon, Xenophontis Memorabilia, tr. E. C. Marchant (Cambridge London, 1923). 2. Secondary literature Alpers Klaus, Griechische Lexikographie in Antike und Mittelalter, in Welt der Information, ed. Hans-Albrecht Koch (Stuttgart, 1990), Alpers Klaus, Lexikographie. B. I-III, in Historisches Wörterbuch der Rhetorik (Tübingen, 2001), Brubaker Leslie, Icons and Iconomachy, in A Companion to Byzantium, ed. Liz James (Chichester, 2010), Chatterjee Paroma, Narrating Sanctity: The Narrative Icon in Byzantium and Italy (PhD thesis, University of Chicago, 2007). Chesbrough Henry W. & David J. Teece, Organizing for Innovation: When Is Virtual Virtuous?, Harvard Business Review 80 (2002) Dewar Robert D. & Jane E. Dutton, The Adoption of Radical and Incremental Innovations: An Empirical Analysis, Management Science 32 (1986) Disbrey Claire, Innovation and Tradition in Religion (Aldershot, 1994). Field Judith V. & Michael T. Wright, Gears from the Byzantines: A Portable Sundial with Calendrical Gearing, Annals of Science 42 (1985) Godin Benoît (with the collaboration of Pierre Lucier), Innovation and Conceptual Innovation in Ancient Greece, Project on the Intellectual History of Innovation Working Paper No. 14, (INRS/Montreal, 2012). Kazhdan Alexander P. [et al.], Oxford Dictionary of Byzantium, Vols. 1 3 (Oxford, 1991).

20 20 Kazhdan Alexander P. & Ann W. Epstein, Change in Byzantine Culture in the Eleventh and Twelfth Centuries (Berkeley, 1985). King Nigel & Neil J. Anderson, Managing Innovation and Change. A Critical Guide for Organizations (London, 2002). Littlewood Antony R. (ed.), Originality in Byzantine Literature, Art and Music. A Collection of Essays (Oxford, 1995). Luttwak Edward N., The Grand Strategy of the Byzantine Empire (Cambridge, 2009). Ödekan Ayla, Engin Akyürek & Nevra Necipoğlu (eds.), First International Sevgi Gonul Byzantine Studies Symposium. Change in the Byzantine World in the Twelfth and Thirteenth Centuries (Istanbul, 2010). Rogers Everett M., Diffusion of Innovations, (New York 1995 [1962]). Spanos Apostolos, To Every Innovation Anathema (?). Some preliminary thoughts on the study of Byzantine Innovation, in Mysterion, strategike og kainotomia. Et festskrift til ære for Jonny Holbek, ed. H. Knudsen, J. Falkenberg, K. Grønhaug & Å. Garnes (Oslo, 2010), Zaltman Gerald N., Robert B. Duncan & Jonny Holbek, Innovations and Organizations (New York 1973). Zaltman Gerald & Nan Lin, On the Nature of Innovations, American Behavioral Scientist 14 (1971)

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

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

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

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

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

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

It is often said that Byzantium and the Byzantines were negative, if not inimical

It is often said that Byzantium and the Byzantines were negative, if not inimical 2 Was innovation unwanted in Byzantium? Apostolos Spanos In memory of Tomas Hägg It is often said that Byzantium and the Byzantines were negative, if not inimical and hostile, to innovation.1 Albeit not

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

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

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

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

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

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

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

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

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

Διαβάστε περισσότερα

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

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

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

Lecture 2. Soundness and completeness of propositional logic

Lecture 2. Soundness and completeness of propositional logic Lecture 2 Soundness and completeness of propositional logic February 9, 2004 1 Overview Review of natural deduction. Soundness and completeness. Semantics of propositional formulas. Soundness proof. Completeness

Διαβάστε περισσότερα

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

ΚΑΘΟΡΙΣΜΟΣ ΠΑΡΑΓΟΝΤΩΝ ΠΟΥ ΕΠΗΡΕΑΖΟΥΝ ΤΗΝ ΠΑΡΑΓΟΜΕΝΗ ΙΣΧΥ ΣΕ Φ/Β ΠΑΡΚΟ 80KWp

ΚΑΘΟΡΙΣΜΟΣ ΠΑΡΑΓΟΝΤΩΝ ΠΟΥ ΕΠΗΡΕΑΖΟΥΝ ΤΗΝ ΠΑΡΑΓΟΜΕΝΗ ΙΣΧΥ ΣΕ Φ/Β ΠΑΡΚΟ 80KWp ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΜΕΤΑΔΟΣΗΣ ΠΛΗΡΟΦΟΡΙΑΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΛΙΚΩΝ ΚΑΘΟΡΙΣΜΟΣ ΠΑΡΑΓΟΝΤΩΝ ΠΟΥ ΕΠΗΡΕΑΖΟΥΝ ΤΗΝ ΠΑΡΑΓΟΜΕΝΗ ΙΣΧΥ

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

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 1 State vector space and the dual space Space of wavefunctions The space of wavefunctions is the set of all

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

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ Μελέτη των υλικών των προετοιμασιών σε υφασμάτινο υπόστρωμα, φορητών έργων τέχνης (17ος-20ος αιώνας). Διερεύνηση της χρήσης της τεχνικής της Ηλεκτρονικής Μικροσκοπίας

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

Πειραματικό Λύκειο Αναβρύτων, 2012

Πειραματικό Λύκειο Αναβρύτων, 2012 «Ήδη από τον 3 ο π.χ. αιώνα η μνήμη της ανθρωπότητας στη Μεσόγειο λειτουργεί στα ελληνικά» (Jean Sirinelli, Τα παιδιά του Αλεξάνδρου, μετάφρ. Σ. Μπίνη-Σωτηροπούλου, εκδ. Σ. Ι. Ζαχαρόπουλος, 2001, σ. 157.)

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

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

ΤΕΧΝΟΛΟΓΙΚΟ ΕΚΠΑΙΔΕΥΤΙΚΟ ΙΔΡΥΜΑ ΠΕΛΟΠΟΝΝΗΣΟΥ

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

Διαβάστε περισσότερα

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

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

Chapter 29. Adjectival Participle

Chapter 29. Adjectival Participle Chapter 29 Adjectival Participle Overview (29.3-5) Definition: Verbal adjective Function: they may function adverbially or adjectivally Forms: No new forms because adverbial and adjectival participles

Διαβάστε περισσότερα

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

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

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

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

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

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

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

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

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

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

«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

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

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

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

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

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

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

Capacitors - Capacitance, Charge and Potential Difference

Capacitors - Capacitance, Charge and Potential Difference Capacitors - Capacitance, Charge and Potential Difference Capacitors store electric charge. This ability to store electric charge is known as capacitance. A simple capacitor consists of 2 parallel metal

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

Περίληψη (Executive Summary)

Περίληψη (Executive Summary) 1 Περίληψη (Executive Summary) Η παρούσα διπλωματική εργασία έχει ως αντικείμενο την "Αγοραστική/ καταναλωτική συμπεριφορά. Η περίπτωση των Σπετσών" Κύριος σκοπός της διπλωματικής εργασίας είναι η διερεύνηση

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

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

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

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

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ 0 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ ΥΓΕΙΑΣ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ Επιβλέπων Καθηγητής: Δρ. Βασίλειος Ραφτόπουλος ΔΙΕΡΕΥΝΗΣΗ ΤΗΣ ΣΤΑΣΗΣ ΤΩΝ ΝΟΣΗΛΕΥΤΩΝ ΓΙΑ ΤΗΝ ΕΥΘΑΝΑΣΙΑ Ονοματεπώνυμο:

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

ICTR 2017 Congress evaluation A. General assessment

ICTR 2017 Congress evaluation A. General assessment ICTR 2017 Congress evaluation A. General assessment -1- B. Content - 2 - - 3 - - 4 - - 5 - C. Speakers/ Presentations/ Sessions - 6 - - 7 - D. Posters/ Poster sessions E. Organisation and coordination

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

CRASH COURSE IN PRECALCULUS

CRASH COURSE IN PRECALCULUS CRASH COURSE IN PRECALCULUS Shiah-Sen Wang The graphs are prepared by Chien-Lun Lai Based on : Precalculus: Mathematics for Calculus by J. Stuwart, L. Redin & S. Watson, 6th edition, 01, Brooks/Cole Chapter

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

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

Διαβάστε περισσότερα

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

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

Νέες ρωγµές στην γερµανική ηγεµονία. (New rifts in the German hegemony) Μαυροζαχαράκης Εµµανουήλ Πολιτικός Επιστήµονας

Νέες ρωγµές στην γερµανική ηγεµονία. (New rifts in the German hegemony) Μαυροζαχαράκης Εµµανουήλ Πολιτικός Επιστήµονας Νέες ρωγµές στην γερµανική ηγεµονία. (New rifts in the German hegemony) Μαυροζαχαράκης Εµµανουήλ Πολιτικός Επιστήµονας Mavrozacharakis Emmanouil Political Scientist Abstract Greek Η προσφυγική κρίση που

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

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

Μηχανική Μάθηση Hypothesis Testing

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

Διαβάστε περισσότερα

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

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

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

[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

Διπλωματική Εργασία. Μελέτη των μηχανικών ιδιοτήτων των stents που χρησιμοποιούνται στην Ιατρική. Αντωνίου Φάνης

Διπλωματική Εργασία. Μελέτη των μηχανικών ιδιοτήτων των stents που χρησιμοποιούνται στην Ιατρική. Αντωνίου Φάνης Διπλωματική Εργασία Μελέτη των μηχανικών ιδιοτήτων των stents που χρησιμοποιούνται στην Ιατρική Αντωνίου Φάνης Επιβλέπουσες: Θεοδώρα Παπαδοπούλου, Ομότιμη Καθηγήτρια ΕΜΠ Ζάννη-Βλαστού Ρόζα, Καθηγήτρια

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

Solutions to Exercise Sheet 5

Solutions to Exercise Sheet 5 Solutions to Eercise Sheet 5 jacques@ucsd.edu. Let X and Y be random variables with joint pdf f(, y) = 3y( + y) where and y. Determine each of the following probabilities. Solutions. a. P (X ). b. P (X

Διαβάστε περισσότερα

ΔΘΝΗΚΖ ΥΟΛΖ ΓΖΜΟΗΑ ΓΗΟΗΚΖΖ

ΔΘΝΗΚΖ ΥΟΛΖ ΓΖΜΟΗΑ ΓΗΟΗΚΖΖ Ε ΔΘΝΗΚΖ ΥΟΛΖ ΓΖΜΟΗΑ ΓΗΟΗΚΖΖ Κ ΔΚΠΑΗΓΔΤΣΗΚΖ ΔΗΡΑ ΣΜΖΜΑ : Σνπξηζηηθήο Οηθνλνκίαο θαη Αλάπηπμεο (ΣΟΑ) ΣΔΛΗΚΖ ΔΡΓΑΗΑ Θέκα: Σνπξηζκφο θαη Οηθνλνκηθή Κξίζε Δπηβιέπσλ : Νηνχβαο Λνπθάο πνπδάζηξηα : Σζαγθαξάθε

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

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

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

Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ

Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ Η ΔΙΑΣΤΡΕΥΛΩΣΗ ΤΗΣ ΕΛΛΗΝΙΚΗΣ ΓΛΩΣΣΑΣ ΜΕΣΩ ΤΩΝ SOCIAL MEDIA ΤΗΝ ΤΕΛΕΥΤΑΙΑ ΠΕΝΤΑΕΤΙΑ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΤΗΣ ΑΝΑΣΤΑΣΙΑΣ-ΜΑΡΙΝΑΣ ΔΑΦΝΗ Τμήμα Δημοσίων Σχέσεων & Επικοινωνίας Τεχνολογικό Εκπαιδευτικό Ίδρυμα Ιονίων

Διαβάστε περισσότερα

NBER WORKING PAPER SERIES MAKING THE MOST OF CAPITAL IN THE 21ST CENTURY. Peter H. Lindert. Working Paper

NBER WORKING PAPER SERIES MAKING THE MOST OF CAPITAL IN THE 21ST CENTURY. Peter H. Lindert. Working Paper NBER WORKING PAPER SERIES MAKING THE MOST OF CAPITAL IN THE 21ST CENTURY Peter H. Lindert Working Paper 20232 http://www.nber.org/papers/w20232 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue

Διαβάστε περισσότερα

ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΠΟΛΙΤΙΚΩΝ ΜΗΧΑΝΙΚΩΝ. «Θεσμικό Πλαίσιο Φωτοβολταïκών Συστημάτων- Βέλτιστη Απόδοση Μέσω Τρόπων Στήριξης»

ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΠΟΛΙΤΙΚΩΝ ΜΗΧΑΝΙΚΩΝ. «Θεσμικό Πλαίσιο Φωτοβολταïκών Συστημάτων- Βέλτιστη Απόδοση Μέσω Τρόπων Στήριξης» ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΠΟΛΙΤΙΚΩΝ ΜΗΧΑΝΙΚΩΝ ΤΟΜΕΑΣ ΑΝΘΡΩΠΙΣΤΙΚΩΝ & ΚΟΙΝΩΝΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΚΑΙ ΔΙΚΑΙΟΥ «Θεσμικό Πλαίσιο Φωτοβολταïκών Συστημάτων- Βέλτιστη Απόδοση Μέσω Τρόπων Στήριξης» Διπλωματική

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

PARTIAL NOTES for 6.1 Trigonometric Identities

PARTIAL NOTES for 6.1 Trigonometric Identities PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot

Διαβάστε περισσότερα

3.4 Αζηίεξ ημζκςκζηήξ ακζζυηδηαξ ζημ ζπμθείμ... 64 3.4.1 Πανάβμκηεξ πνμέθεοζδξ ηδξ ημζκςκζηήξ ακζζυηδηαξ... 64 3.5 οιαμθή ηςκ εηπαζδεοηζηχκ ζηδκ

3.4 Αζηίεξ ημζκςκζηήξ ακζζυηδηαξ ζημ ζπμθείμ... 64 3.4.1 Πανάβμκηεξ πνμέθεοζδξ ηδξ ημζκςκζηήξ ακζζυηδηαξ... 64 3.5 οιαμθή ηςκ εηπαζδεοηζηχκ ζηδκ 2 Πεξηερόκελα Δονεηήνζμ πζκάηςκ... 4 Δονεηήνζμ δζαβναιιάηςκ... 5 Abstract... 6 Πενίθδρδ... 7 Δζζαβςβή... 8 ΘΔΩΡΗΣΙΚΟ ΜΔΡΟ... 12 Κεθάθαζμ 1: Θεςνδηζηέξ πνμζεββίζεζξ βζα ηδκ ακζζυηδηα ζηδκ εηπαίδεοζδ...

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

The Nottingham eprints service makes this work by researchers of the University of Nottingham available open access under the following conditions.

The Nottingham eprints service makes this work by researchers of the University of Nottingham available open access under the following conditions. Luevorasirikul, Kanokrat (2007) Body image and weight management: young people, internet advertisements and pharmacists. PhD thesis, University of Nottingham. Access from the University of Nottingham repository:

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

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

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

Congruence Classes of Invertible Matrices of Order 3 over F 2

Congruence Classes of Invertible Matrices of Order 3 over F 2 International Journal of Algebra, Vol. 8, 24, no. 5, 239-246 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.2988/ija.24.422 Congruence Classes of Invertible Matrices of Order 3 over F 2 Ligong An and

Διαβάστε περισσότερα

ΔΘΝΙΚΗ ΥΟΛΗ ΓΗΜΟΙΑ ΓΙΟΙΚΗΗ ΚΑ ΔΚΠΑΙΓΔΤΣΙΚΗ ΔΙΡΑ ΣΔΛΙΚΗ ΔΡΓΑΙΑ

ΔΘΝΙΚΗ ΥΟΛΗ ΓΗΜΟΙΑ ΓΙΟΙΚΗΗ ΚΑ ΔΚΠΑΙΓΔΤΣΙΚΗ ΔΙΡΑ ΣΔΛΙΚΗ ΔΡΓΑΙΑ Ε ΔΘΝΙΚΗ ΥΟΛΗ ΓΗΜΟΙΑ ΓΙΟΙΚΗΗ ΚΑ ΔΚΠΑΙΓΔΤΣΙΚΗ ΔΙΡΑ ΣΜΗΜΑ ΓΔΝΙΚΗ ΓΙΟΙΚΗΗ ΣΔΛΙΚΗ ΔΡΓΑΙΑ Θέκα: Η Γηνίθεζε Αιιαγώλ (Change Management) ζην Γεκόζην Σνκέα: Η πεξίπησζε ηεο εθαξκνγήο ηνπ ύγρξνλνπ Γεκνζηνλνκηθνύ

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

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

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

"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