Chapter 5. IMPLICITATION

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Chapter 5. IMPLICITATION"

Transcript

1 Chapter 5. IMPLICITATION 5.1 Introduction The analysis of LXX Isaiah would be less complicated if we were able to outline a consistent and uniform translation method which was applied by its translator. But in fact, the opposite appears to be true. The Greek Isaiah is typified by contrasting translation tendencies. Just as chapter 2 and 3 have described two such contrary patterns, the present chapter will also discuss a feature that seems to be discrepant from the one analysed in the previous section. While chapter 4 has shown that many pluses in the Greek Isaiah can be explained by the translator s inclination towards making his text more explicit, the present chapter will deal with his penchant for implicitation. Implicitation is a term used in translation studies to indicate that an element which in the source text is stated explicitly, is made implicit in the translation. 1 This technique may have been employed by the translator because he considered some information provided by the Hebrew text as redundant, since it could also have been derived from the context, or was supposed to have been familiar to the readers. Besides, he may have used implicitation so as to strengthen the textual coherence. If, for instance, a proper name instead of being repeated, is replaced by a pronoun, this makes a stronger link to the clause in which the name itself is mentioned. 2 Implicitation often entails the replacement of one word or phrase by another, but in some cases it accounts for a minus. Such minuses, as found in LXX Isaiah, will be listed below. They will be grouped according to the following division: - Implicitation through the omission of an attribute. - Implicitation through the omission of the governing noun in a genitival construction..יחד and כל - Omission of - Implicitation of the subject. - Implicitation through the omission of an object. Sometimes the omission of details that may have seemed insignificant in the eyes of the translator, has led to the generalisation of the text (e.g. the palm of his hand becomes his hand ). As it is not always easy to draw a line between implicitation and generalisation, 1 Like explicitation, the term implicitation was first introduced by Vinay and Darbelnet (Vinay and Darbelnet, Stylistique comparée du francais, 10). They define this technique as: Procédé qui consiste à laisser au contexte ou à la situation le soin de préciser certains détails explicites dans LD [source language]. For the application of the term on the Septuagint, see van der Louw, Transformations, Van der Louw defines implicitation as follows: An implicitation is a transformation whereby elements that are explicit in the source text are made implicit in the target text. This transformation is close to omission, the difference being that the information explicit in the source text is not deleted altogether, but recedes into the background while leaving traces in the target text, thus becoming implicit (op.cit. p.71). ואבוס עמים באפי 2 See van Peursen, Language and Interpretation, An example can be found in Isa 63:6 / καὶ κατεπάτησα αὐτοὺς τῇ ὀργῇ µου; while in the MT v.6 repeats the people mentioned in v.3, in LXX Isa a pronoun replaces the noun, just as in the previous verses, which makes the internal connection between these verses stronger. For two cases in which the implicitation of the subject strengthens the cohesion of the text, see 33:24 and 49:23 in section below.

2 CHAPTER FIVE these two phenomena will not be strictly differentiated, but will be treated alongside each other in the present chapter. 5.2 Implicitation through the omission of an attribute Attributes, which modify the noun to which they are syntactically subordinate, can often be omitted without significantly changing the content of the text. They may consist of: - an attributive pronoun, which in Hebrew is formed by a nominal suffix (i.e. a suffix joined to a substantive noun); - the governed noun in a genitival (construct state) construction; - an apposition The omission of a nominal suffix In Greek it is not necessary to use an attributive ( possessive ) pronoun in order to denote the possessor, object, subject, or the whole of something or someone when this entity or being is made obvious by the immediate context. Particularly when attached to body parts, the attributive pronoun is regularly omitted; see for instance 1:15, where ובפרשכם כפיכם becomes ὅταν τὰς χεῖρας ἐκτείνητε πρός µε (for more examples, see section 9.5). When in such situations the translation does not represent the Hebrew suffix, this has rather been motivated by the translator s concern for using stylistically correct Greek than by his deliberation to make information implicit. However, when the translator chose not to render a suffix because he wanted to remove or reduce the emphasis on the idea that something was in a genitive relationship to something else, or because he intended to generalise a notion by leaving out the specifying genitive pronoun, this might be considered as implicitation or generalisation. See the following examples: 13:21 בתיהםםםם אחים ומלאו καὶ ἐµπλησθήσονται αἱ οἰκίαι ἤχου 3 14:32 ובה יחסו עניי עממממו καὶ δι αὐτοῦ σωθήσονται οἱ ταπεινοὶ τοῦ λαοῦ. 24:23 כי מלך צבאות בהר ὅτι βασιλεύσει κύριος ἐν Σιων καὶ ἐν Ιερουσαληµ זקניוווו כבוד ציון ובירושלם ונגד καὶ ἐνώπιον τῶν πρεσβυτέρων ρων δοξασθήσεται. 26:19 מתיך יחיו ἀναστήσονται οἱ νεκροί, נבלתי יקומון καὶ ἐγερθήσονται οἱ ἱ ἐν ἐ τοῖς ς µνηµείοις 4 40:16 ולבנון אין די בער καῦσιν, ὁ δὲ Λίβανος οὐχ ἱκανὸς εἰς וחיתו אין די עולה καὶ πάντα τὰ τετράποδα οὐχ ἱκανὰ εἰς ὁλοκάρπωσιν 49:11 ושמתי כל הררררי לדרך καὶ θήσω πᾶν ὄρος εἰς ὁδὸν ומסלתי ירמון καὶ πᾶσαν τρίβον εἰς βόσκηµα αὐτοῖς. 5 3 In the Hebrew the suffix in בתיהם probably refers to the רעים of v.20. LXX Isa may with αἱ οἰκίαι refer to all houses of the city referred to in the text (i.e. Babylon). 4 The omission of the genitive pronoun may have been influenced by v.14 where מתים appears in a similar phrasing, but without a suffix: מתים בל יחיו / οἱ δὲ νεκροὶ ζωὴν οὐ µὴ ἴδωσιν. 5 Perhaps also under the influence of ובכל שפיים מרעיתם v.9 / καὶ ἐν πάσαις ταῖς τρίβοις ἡ νοµὴ αὐτῶν. 112

3 IMPLICITATION The omission of the governed noun in a genitival relationship In a genitival relationship between words which in Hebrew is expressed in a construct state conjunction the second noun (the governed noun) qualifying the first one (the governing noun), has occasionally not been represented in LXX Isaiah. In most of these cases the qualifying noun is pleonastic. Perhaps the translator left it out because he thought it redundant: 10:13 עשיתי ידי בכחחחח 17:6 פריה בסעפיה 23:3 תבואתה יאור קציר 29:23 ידדדדי מעשה 30:29 לבב ושמחת 30:30 אשששש אוכלה ולהב 34:6 אילים כליות מחלבבבב 58:11 מי םים מ וכמוצא Τῇ ἰσχύι ποιήσω ἐπὶ τῶν κλάδων αὐτῶν α ὡς ἀµητο µητοῦ εἰσφεροµένου τὰ ἔργα µου καὶ ὡσεὶ εὐφραινοµένους καὶ φλογὸς κατεσθιούσης καὶ ἀπὸ στέατος τράγων καὶ κριῶν καὶ ὡς πηγὴ For the omission of the governed noun in a genitival relationship when this noun is synonymous to the governing noun, see section 3.2.2a The omission of an apposition Also appositions may primarily have been deleted in order to avoid redundancy. a. The omission of a divine name As we have seen in chapter 4, LXX Isaiah regularly offers κύριος ὁ θεός where the MT only has either אלהים or. However, the converse situation also occurs, appositionally used designations for God being absent in the Greek translation. Indeed, in nearly all cases where the Hebrew presents the combinations,,האדון or,יה LXX Isaiah displays merely one divine name. These compound Hebrew titles are mostly represented in the translation by: - κύριος: 7:7 כה אמר 10:16 צבאות האדון לכן ישלח 10:24 צבאות לכן כה אמר 12:2 כי עזי וזמרת יהההה 19:4 צבאות האדון נאם 22:5 צבאות בגיא חזיון ל 22:12 צבאות ויקרא 22:15 צבאות כה אמר 28:16 לכן כה אמר צבאות 28:22 שמעתי מאת τάδε λέγει κύριος σαβαωθ ἀλλὰ ἀποστελεῖ κύριος σαβαωθ 6 Διὰ τοῦτο τάδε λέγει κύριος σαβαωθ 7 διότι ἡ δόξα µου καὶ ἡ αἴνεσίς µου κύριος τάδε λέγει κύριος σαβαωθ. παρὰ κυρίου σαβαωθ ἐν φάραγγι Σιων καὶ ἐκάλεσε κύριος σαβαωθ Τάδε λέγει κύριος σαβαωθ διὰ τοῦτο οὕτως λέγει κύριος 8 ἤκουσα παρὰ κυρίου σαβαωθ equally is missing in some Hebrew manuscripts (but not in the Qumran documents of Isaiah). According האדון 6 to Wildberger (Jesaja, 1:405) it was originally absent. 7 Wildberger (Jesaja, 1:417) thinks that the LXX translator has not read in his Vorlage. אדוני 8 In 1QIsa a ). (see section לכן כה אמר superscript: appears as אדוני 113

4 CHAPTER FIVE קדוש ישראל 30:15 כה אמר 40:10 בחזק יבוא הנה 48:16 שלחני ועתה 49:22 כה אמר 50:4 נתן לי לשון למודים 50:5 פתח לי אזן 50:7 יעזר לי ו 50:9 יעזר לי הן 52:4 כי כה אמר 56:8 נאם 61:1 עלי רוח 61:11 יצמיח צדקה כן 65:13 לכן כה אמר 65:15 והמיתך οὕτως λέγει κύριος ὁ ἅγιος τοῦ Ισραηλ 9 ἰδοὺ κύριος µετὰ ἰσχύος ἔρχεται καὶ νῦν κύριος ἀπέσταλκέ µε Οὕτως λέγει κύριος 10 Κύριος δίδωσί µοι γλῶσσαν παιδείας καὶ ἡ παιδεία κυρίου ἀνοίγει µου τὰ ὦτα καὶ κύριος βοηθός µου ἐγενήθη ἰδοὺ κύριος βοηθεῖ µοι οὕτως λέγει κύριος εἶπε κύριος Πνεῦµα κυρίου ἐπ ἐµέ οὕτως ἀνατελεῖ κύριος δικαιοσύνην Διὰ τοῦτο τάδε λέγει κύριος ὑµᾶς δὲ ἀνελεῖ κύριος. - ὁ θεός: 10:23 כי כלה ונחרצה ὅτι λόγον συντετµηµένον ποιήσει ὁ θεὸς צבאות עשה בקרב כל הארץ ὅλῃ. ἐν τῇ οἰκουµένῃ 25:8 דמעה ומחה καὶ πάλιν ἀφεῖλεν ὁ θεὸς πᾶν δάκρυον 26:4 צור עולמים כי ביהההה ὁ θεὸς ὁ µέγας ὁ αἰώνιος The translator probably did not translate because he was unable to think of an apt Greek counterpart. He could have rendered the word by δεσπότης, yet only uses that title three 11 :האדון times, where the Hebrew in all three places displays 1:24 צבאות האדון לכן נאם διὰ τοῦτο τάδε λέγει ὁ δεσπότης κύριος σαβαωθ 3:1 צבאות מסיר האדון Ἰδοὺ δὴ ὁ δεσπότης κύριος σαβαωθ ἀφελεῖ 10:33 צבאות מסעף האדון הנה ἰδοὺ γὰρ ὁ δεσπότης κύριος σαβαωθ συνταράσσει The combination אלהים (+ suffix) has mostly received a literal rendering as κύριος ὁ θεός. Still, in the following places אלהיך is represented by a mere ὁ θεός σου: 41:13 אלהיך כי אני ὅτι ἐγὼ ὁ θεός σου 48:17 אלהיך אני Ἐγώ εἰµι ὁ θεός σου 51:15 אלהיך ואנכי ὅτι ἐγὼ ὁ θεός σου למען אלהיך ולקדוש ישראל 55:5 ἕνεκεν τοῦ θεοῦ σου τοῦ ἁγίου Ισραηλ Also the noun צבאות ( hosts ), which can be joined as an apposition to the divine name, 12 has now and again no equivalent in LXX Isaiah. Often this can be attributed to the translator s aspiration to assimilate clauses to related ones in the surrounding text or to similar formulations elsewhere in Scripture: כי כה אמר 9 1QIsa a reads אדוני.( (see section קדוש ישראל 10 In 1QIsa a likewise is missing: כיא כוה אמר (see section ). 11 In 10:16 and 19:4 the translator has omitted,האדון though (see above). 12 On צבאות being an apposition rather than the governed noun in a construct state conjunction, see Jouön 131o. 114

5 IMPLICITATION 8:13 אתו תקדישו צבאות את (13)9:12 לא דרשו צבאות ואת (19)9:18 צבאות בעברת עשה 10:23 צבאות כי כלה ונחרצה 10:26 שוט צבאות ועורר עליו 19:17 צבאות מפני עצת אשר הוא יועץ עליו 19:18 צבאות ל ונשבעות 19:20 צבאות ל והיה לאות ולעד 24:23 בהר ציון צבאות כי מלך 31:5 על ירושלם צבאות כן יגן κύριον αὐτὸν ἁγιάσατε 13 καὶ τὸν κύριον οὐκ ἐξεζήτησαν. 14 διὰ θυµὸν ὀργῆς κυρίου ὅτι λόγον συντετµηµένον ποιήσει ὁ θεὸς 15 καὶ ἐπεγερεῖ ὁ θεὸς ἐπ αὐτοὺς 16 διὰ τὴν βουλήν, ἣν βεβούλευται κύριος ἐπ αὐτήν. 17 καὶ ὀµνύουσαι τῷ ὀνόµατι κυρίου 18 καὶ ἔσται εἰς σηµεῖον εἰς τὸν αἰῶνα κυρίῳ 19 ὅτι βασιλεύσει κύριος ἐν Σιων 20 οὕτως ὑπερασπιεῖ κύριος ὑπὲρ Ιερουσαληµ b. The omission of other appositions Some other examples of appositions missing a counterpart: 8:2 את אוריה הכהן τὸν Ουρίαν 20:2 ישעיהו בן אמוץ Ησαίαν 24:23 בהר ציון ἐν Σιων 37:4 מלך אשור ו βασιλεὺς Ἀσσυρίων 37:5 עבדי המלך חזקיהו οἱ παῖδες τοῦ βασιλέως 37:37 סנחריב מלך אשור βασιλεὺς Ἀσσυρίων 5.3 The omission of the governing noun in a genitival relationship Also when the translator did not render the first (governing) noun in a genitival relationship, this was probably mostly because that noun was not vital to the message of the text and hence could be left out without significantly changing the content. may have been removed in assimilation to the phrase κύριος αὐτός / αὐτὸς κύριος, which occurs in צבאות 13 LXX Isa 3:14; 7:14; and 63:9, and elsewhere in the LXX e.g. in Deut 10:9; 18:2; and Ps 104:7,21; 151:3. 14 Possibly in harmonisation with ואת לא דרשו Jer 10:21 / καὶ τὸν κύριον οὐκ ἐξεζήτησαν; cf. section The omission of צבאות in 10:23 and 26 is likely connected to the translation of by ὁ θεός, which on its own is rarely followed by σαβαωθ in the LXX (see only Isa 44:6 and 1 Esd 9:46). The use of θεός instead of κύριος may be due to the appearance of the same title in v.20 (LXX) and v.21, or in assimilation to similar statements announcing what God will do in the future, which likewise use a mere ὁ θεός; see e.g. 7:17 ἀλλὰ ἐπάξει ὁ θεὸς ἐπὶ σὲ ἡµέρας, αἳ οὔπω ἥκασιν; 24:21 καὶ ἐπάξει ὁ θεὸς ἐπὶ τὸν κόσµον τοῦ οὐρανοῦ τὴν χεῖρα (see further e.g. 3:17; 4:2; 6:12; 14:3; 23:17; 25:10; and 30:30). 16 See the previous footnote. According to Wildberger (Jesaja, 1:417) צבאות possibly has to be deleted. 17 Perhaps צבאות was omitted because in the ensuing section 19:17 22 κύριος without σαβαωθ appears no less then twelve times, usually at the end of the clause; see section c. 18 Maybe in harmonisation with הנשבעים בשם Isa 48:1 / οἱ ὀµνύοντες τῷ ὀνόµατι κυρίου θεοῦ Ισραηλ. Furthermore, parallel to κύριος in the preceding and following verses (cf. 19:17 and footnote above). 19 Parallel to κύριος in the preceding and following verses (cf. 19:17 and footnote above). 20 Possibly relying on Mic 4:7 καὶ βασιλεύσει κύριος ἐπ αὐτοὺς ἐν ὄρει Σιων. 115

6 CHAPTER FIVE The omitted governing noun consists of the name for a body part The omitted governing noun relatively often is the name of a body part, which is used either in a literal sense (see e.g. 1:6; 25:11; 30:6; 34:16; 40:5; and 62:2 below) or in a metaphorical sense (see e.g. 11:15; 14:21; 24:18; 27:6; and 30:17 below). Concerning metaphorically used body parts, the translator may have opted not to represent them because he wanted to make his text more concrete. In the case of literally used ones the omission is probably largely the result of the translator s inclination to shorten or simplify his text. Perhaps he considered it unnecessary to be very specific. Furthermore, he may have avoided rendering parts of the body governing a (pro)noun in order not to produce Hebraistic language (in analogy to his frequent rendition of compound prepositional expressions containing the name of a body part by a simple preposition [e.g. מפני becomes ἀπό]) 21. Nevertheless, on the whole the nontranslation of body parts occurs only sporadically: Most commonly they did receive a rendering, both the ones used in a literal and those used in a metaphorical way. Some instances of the omission of body parts in a genitive construction are as follows: 1:6 ועד ראש מכףףףף רגל ἀπὸ ποδῶν ἕως κεφαλῆς 11:15 יםםםם מצרים לשון והחרים את καὶ ἐρηµώσει κύριος τὴν θάλασσαν Αἰγύπτου 24:18 הפחד הנס מקוווול ὁ φεύγων τὸν φόβον 22 25:11 ידיו ארבות עם ἐφ ἃ τὰς ς χεῖρας ἐπέβαλε 30:6 עירים על כתף ישאו οἳ ἔφερον ἐπ ὄνων גמלים ועל דבשת καὶ καµήλων ההר 30:17 על ראש עד אם נותרתם כתרן ἕως ἂν καταλειφθῆτε ὡς ἱστὸς ἐπ ὄρους 37:14 ויקח חזקיהו את הספרים καὶ ἔλαβεν Εζεκιας τὸ βιβλίον המלאכים מידדדד παρὰ τῶν ἀγγέλων Both times the phrase פני תבל occurs in Isaiah פני has no equivalent in the LXX, most probably so as to escape a Hebraistic translation: 14:21 ערים פני תבל ומלאו 27:6 תנובה פני תבל ומלאו καὶ ἐµπλήσωσι τὴν γῆν πολέµων καὶ ἐµπλησθήσεται ἡ οἰκουµένη τοῦ καρποῦ αὐτοῦ A comparable move is the rendering by a mere pronoun where the Hebrew offers a pronoun governed by a body part, see e.g.: 10:27 שכמך יסור סבלו מעל ἀφαιρεθήσεται ὁ φόβος αὐτοῦ ἀπὸ σοῦ שכמו 22:22 על שכמ ונתתי מפתח בית דוד καὶ δώσω τὴν δόξαν Δαυιδ αὐτῷ כי השלכת אחרי גווווך כל חטאי 38:17 καὶ ἀπέρριψας ὀπίσω µου πάσας τὰς ἁµαρτίας µου. Also the few examples of the omission of body parts belonging to God can be clarified in the light of what has been discussed above. These minuses are sometimes explained as an attempt by the translator to avoid anthropomorphism: 23 בהר הזה 25:10 ידדדד ὅτι ἀνάπαυσιν δώσει ὁ כי תנוח θεὸς ἐπὶ τὸ ὄρος τοῦτο 21 See section The contrary has happened in 38:5, where one finds a word for voice as a plus: שמעתי את תפלתך / Ἤκουσα τῆς φωνῆς τῆς προσευχῆς σου. 23 See section

7 IMPLICITATION בראתו ילדיו מעשה ידדדדי בקרבו 29:23 ἀλλ ὅταν ἴδωσιν τὰ τέκνα αὐτῶν τὰ ἔργα µου 30:2 ופי לא שאלו ἐµὲ δὲ οὐκ ἐπηρώτησαν 34:16 הו אוא צוה ה כי פיייי κύριος ἐνετείλατο αὐτοῖς 37:29 אזני באזנ ושאננך עלה καὶ ἡ πικρία σου ἀνέβη πρός µε 40:5 דבר כי פיייי ὅτι κύριος ἐλάλησε. 62:2 יקבנו אשר פיייי ὃ ὁ κύριος ὀνοµάσει αὐτό The omitted governing noun consists of a word other than a body part When preceding geographical names, ארץ has in LXX Isaiah generally received a rendering as γῆ or χώρα. However, on several occasions a translation of ארץ is missing: 19:18 בארץ מצרים ἐν Αἰγύπτῳ 27:13 בארץ מצרים ἐν Αἰγύπτῳ 34:6 בארץ אדום ἐν τῇ Ιδουµαίᾳ 24 37:38 ארץ אררט εἰς Ἀρµενίαν Some additional examples of the omission of a governing noun: 2:17 תי האדם גבהות ושח 6:4 הספים אמות וינעו העליונה 7:3 הברכה תעלת אל קצה 10:12 לבב פרי גדל על פרי אפקד 10:20 תית יעקב בי ופליטת ב 14:14 עב על במתי אעלה 14:19 אבני בור אל אבני יורדי 14:30 דלים בכורי ורעו 17:14 והנה בלהה ערב לעתתתת 21:17 מספר קשת ושאר גבורי בני קדר 22:22 תית דוד בי ונתתי מפתח ב על שכמו 24:4 עםםםם הארץ אמללו מרום 30:2 פרעה במעוז לעוז מצרים ולחסות בצלללל 30:3 לכלמה בצלללל מצרים והחסות 30:6 וצוקה צרה בארץ 30:30 ברד ואבן נפץ וזרם 40:12 הארץ עפר וכל בשלש 40:14 משפט בארח וילמדהו 48:1 יצאו יהודה וממיייי 52:1 תפארתך בגדי לבשי καὶ ταπεινωθήσεται πᾶς ἄνθρωπος καὶ ἐπήρθη τὸ ὑπέρθυρον πρὸς τὴν κολυµβήθραν τῆς ἄνω ὁδοῦ ἐπάξει ἐπὶ τὸν νοῦν τὸν µέγαν καὶ οἱ σωθέντες τοῦ Ιακωβ ἀναβήσοµαι ἐπάνω τῶν νεφελῶν καταβαινόντων εἰς ᾅδου δου. 25 καὶ βοσκηθήσονται πτωχοὶ δι αὐτοῦ πρὸς ἑσπέραν ἔσται πένθος καὶ τὸ κατάλοιπον τῶν τοξευµάτων τῶν ἰσχυρῶν υἱῶν Κηδαρ καὶ δώσω τὴν δόξαν Δαυιδ αὐτῷ ἐπένθησαν οἱ ὑψηλοὶ τῆς ς γῆς. γ 26 τοῦ βοηθηθῆναι ὑπὸ Φαραω καὶ σκεπασθῆναι ὑπὸ Αἰγυπτίων γυπτίων. καὶ τοῖς πεποιθόσιν ἐπ Αἴγυπτον ὄνειδος. Ἐν τῇ θλίψει καὶ τῇ στενοχωρίᾳ καὶ ὡς ὕδωρ καὶ χάλαζα συγκαταφεροµένη βίᾳ. καὶ πᾶσαν τὴν γῆν γ δρακί; ἢ τίς ἔδειξεν αὐτῷ κρίσιν ιν; καὶ οἱ ἐξ Ιουδα ἐξελθόντες καὶ ἔνδυσαι τὴν δόξαν σου Βοσορ. may have been left out in parallelism to the preceding phrase ὅτι θυσία κυρίῳ ἐν ארץ 24 אבני 25 1QIsa a has אבני written supralinearly: יורדו א [ל] בור (see section ). עמ 26 In 1QIsa a ). (see section אמלל מרום הארצ hand: has been added by a later עמ 117

8 CHAPTER FIVE,כלללל 5.4 The omission of יחד רבבבב and The translator gives the impression of having been quite flexible in using or not using expressions in the sense of all and together. Whereas the previous chapter listed plenty of examples of his addition of such words, the next pages will demonstrate that he equally often has omitted Hebrew lexemes bearing these connotations. Representations of כל and יחד are absent in LXX Isaiah so regularly, that this cannot simply be attributed to a different Vorlage. Probably their frequent omission is due to the fact that in most cases the meaning of these words is logically inherent in the text in which they appear. For this reason the translator may have thought their lexical presence not absolutely necessary. כל 1:23 שריך סוררים וחברי גנבים κλεπτῶν, οἱ ἄρχοντές σου ἀπειθοῦσι, κοινωνοὶ כלו אהב שחד ἀγαπῶντες δῶρα כי הנה האדון צבאות מסיר 3:1 Ἰδοὺ δὴ ὁ δεσπότης κύριος σαβαωθ ἀφελεῖ מירושלם ומיהודה משען ומשענה ἀπὸ τῆς Ιουδαίας καὶ ἀπὸ Ιερουσαληµ ἰσχύοντα כל משען לחם וכל משען מים καὶ ἰσχύουσαν, ἰσχὺν ἄρτου καὶ ἰσχὺν ὕδατος 5:28 אשר חציו שנונים ὧν τὰ βέλη ὀξεῖά ἐστι וכל קשתתיו דרכות καὶ τὰ τόξα αὐτῶν ἐντεταµένα 8:7 את מלך אשור ואת כל כבודו τὸν βασιλέα τῶν Ἀσσυρίων καὶ τὴν δόξαν αὐτοῦ 8:9 והאזינו כל מרחקי ארץ ἐπακούσατε ἕως ἐσχάτου τῆς γῆς 13:15 כל הנמצא ידקר ἡττηθήσεται, ὃς γὰρ ἂν ἁλῷ, וכל הנספה יפול בחרב πεσοῦνται καὶ οἵτινες συνηγµένοι εἰσί, µαχαίρᾳ כל מלכי גוים כלם שכבו בכבוד 14:18 πάντες οἱ βασιλεῖς τῶν ἐθνῶν ἐκοιµήθησαν ἐν τιµῇ 27 21:16 וכלה כל כבוד קדר ἐκλείψει ἡ δόξα τῶν υἱῶν Κηδαρ 28 22:3 כל נמצאיך אסרו יחדו καὶ οἱ ἁλόντες σκληρῶς δεδεµένοι εἰσί 24:10 סגר כל בית מבוא εἰσελθεῖν. 29 κλείσει οἰκίαν τοῦ µὴ 27:9 וזה כל פרי καὶ τοῦτό ἐστιν ἡ εὐλογία αὐτοῦ 29:20 ונכרתו כל שקדי און καὶ ἐξωλεθρεύθησαν οἱ ἀνοµοῦντες ἐπὶ κακίᾳ 30:18 אשרי כל חוכי לו αὐτῷ. µακάριοι οἱ ἐµµένοντες ἐν 33:20 וכל חבליו בל ינתקו διαρραγῶσιν. οὐδὲ τὰ σχοινία αὐτῆς οὐ µὴ 34:1 תבל וכל צאצאיה αὐτῇ. ἡ οἰκουµένη καὶ ὁ λαὸς ὁ ἐν 34:2 כי קצף ל על כל הגוים διότι θυµὸς κυρίου ἐπὶ πάντα τὰ ἔθνη וחמה על כל צבאם καὶ ὀργὴ ἐπὶ τὸν ἀριθµὸν αὐτῶν 34:12 וכל שריה οἱ γὰρ βασιλεῖς αὐτῆς καὶ οἱ ἄρχοντες αὐτῆς יהיו אפס ἀπώλειαν. καὶ οἱ µεγιστᾶνες αὐτῆς ἔσονται εἰς 36:1 עלה סנחריב מלך אשור ἀνέβη Σενναχηριµ βασιλεὺς Ἀσσυρίων על כל ערי יהודה הבצרות ἐπὶ τὰς πόλεις τῆς Ιουδαίας τὰς ὀχυρὰς 30 37:17 ושמע את כל דברי סנחריב καὶ ἰδὲ τοὺς λόγους, οὓς ἀπέστειλε Σενναχηριµ In 1QIsa a כלם is missing correspondingly: מלכי גואים שכבו בכבוד.כול Probably it was left out for the sake of condensation (see section ). 28 Cf. 1QIsa a כבוד קדר.יכלה The lack of representation of כל might be caused by an error of haplography (cf. sections 11.1 and ). πόλις. / ἠρηµώθη πᾶσα נשברה קרית תהו clause: may have been transposed to the previous כל 29 In the parallel text 4 Kgdms 18:13 a Greek.(על כל ( haplography might have become lost on account of כל 30 equivalent for כל likewise is missing. 118

9 IMPLICITATION 38:13 כארי כן ישבר כל עצמותי οὕτως τὰ ὀστᾶ µου συνέτριψεν 40:2 כי לקחה מיד כפלים ὅτι ἐδέξατο ἐκ χειρὸς κυρίου διπλᾶ בכל חטאתיה αὐτῆς. τὰ ἁµαρτήµατα 45:22 פנו אלי והושעו σωθήσεσθε, ἐπιστράφητε πρός µε καὶ כל אפסי ארץ γῆς οἱ ἀπ ἐσχάτου τῆς 53:6 ו הפגיע בו את עון כלנו ἡµῶν. 32 καὶ κύριος παρέδωκεν αὐτὸν ταῖς ἁµαρτίαις 55:1 הוי כל צמא לכו למים Οἱ διψῶντες, πορεύεσθε ἐφ ὕδωρ 56:2 ושמר ידו מעשות כל רע ἀδίκηµα. καὶ διατηρῶν τὰς χεῖρας αὐτοῦ µὴ ποιεῖν הנחמים באלים תחת כל עץ רענן 57:5 οἱ παρακαλοῦντες ἐπὶ τὰ εἴδωλα ὑπὸ δένδρα δασέα 59:8 נתיבותיהם עקשו להם διεστραµµέναι, αἱ γὰρ τρίβοι αὐτῶν כל דרך בה לא ידע שלום εἰρήνην. 33 ἃς διοδεύουσι, καὶ οὐκ οἴδασιν 59:11 נהמה כדבים כלנו ὡς ἄρκος וכיונים הגה נהגה πορεύσονται 34 καὶ ὡς περιστερὰ ἅµα 60:4 כלם נקבצו σου 35 συνηγµένα τὰ τέκνα 60:14 והלכו אליך שחוח בני מעניך καὶ πορεύσονται πρὸς σὲ δεδοικότες υἱοὶ והשתחוו על כפות רגליך כל מנאציך ταπεινωσάντων σε καὶ παροξυνάντων σε 62:2 וראו גוים צדקך καὶ ὄψονται ἔθνη τὴν δικαιοσύνην σου וכל מלכים כבודך καὶ βασιλεῖς τὴν δόξαν σου In a large proportion of these cases an extra motivation for the omission of כל may have been the amelioration of parallelism, given that in a parallel phrase or clause a word corresponding to כל is absent: see 1:23; 3:1; 5:28; 8:7; 21:16; 22:3; 29:20; 33:20; 34:1,12; 40:2; 53:6; 56:2; 57:5; 59:11; 60:14; and 62:2. יחדו / יחד 22:3 כל קציניך נדדו יחד πεφεύγασι, πάντες οἱ ἄρχοντές σου מקשת אסרו כל נמצאיך אסרו יחדו καὶ οἱ ἁλόντες σκληρῶς δεδεµένοι εἰσί 27:4 אציתנה יחד πάντα, ὅσα συνέταξε. κατακέκαυµαι 36 40:5 וראו כל בשר יחדו θεοῦ 37 καὶ ὄψεται πᾶσα σὰρξ τὸ σωτήριον τοῦ 41:19 אתן במדבר ארז שטה והדס θήσω εἰς τὴν ἄνυδρον γῆν κέδρον καὶ πύξον ועץ שמן אשים בערבה ברוש καὶ µυρσίνην תדהר ותאשור יחדו καὶ κυπάρισσον καὶ λεύκην 43:26 הזכירני נשפטה יחד κριθῶµεν σὺ δὲ µνήσθητι καὶ 45:16 בושו וגם נכלמו αἰσχυνθήσονται καὶ ἐντραπήσονται 31 Possibly in assimilation to v.4: τοὺς λόγους Ραψακου, οὓς ἀπέστειλε βασιλεὺς Ἀσσυρίων (see section ). 32 Perhaps in parallelism to the first two lines of v.5: αὐτὸς δὲ ἐτραυµατίσθη διὰ τὰς ἀνοµίας ἡµῶν καὶ µεµαλάκισται διὰ τὰς ἁµαρτίας ἡµῶν. 33 LXX Isa has likely perceived דרך בה as a relative clause modifying כל ( all [roads] on which they walk ), whereas in the MT כל דרך בה forms the subject of the next clause: דרך בה לא ידע שלום no כל one who walks in them knows peace. ἅµα. could be represented by כל Maybe כל has been moved to the next sentence: בניך מרחוק יבאו / ἰδοὺ ἥκασι πάντες οἱ υἱοί σου µακρόθεν. 36 Possibly יחד is rendered by πάντα. For an analysis of this translation, cf. section 2.7a. 37 According to Ziegler (Untersuchungen, 150) the Vorlage of the LXX read ישועת,את the more original form יחדו mistakenly having been copied as. It is also thinkable, however, that the translator himself has.יחדו for read 119

10 CHAPTER FIVE πάντες οἱ ἀντικείµενοι αὐτῷ 38 כלם יחדו In four of the seven cases in which a rendering of יחד or יחדו ( together ) is missing, in the same clause the synonymous כל appears (see 22:3[2x]; 40:5; and 45:16). Apparently, the combination of these two expressions was regarded as superfluous by the translator. רב The noun רב ( abundance ) lacks a Greek counterpart in the following two verses: 47:9 שכול ואלמן כתמם באו עליך χηρεία καὶ ἀτεκνία ἥξει ἐξαίφνης ἐπὶ σὲ ברב כשפיך ἐν τῇ φαρµακείᾳ σου 47:13 נלאית ברב עצתיך σου κεκοπίακας ἐν ταῖς βουλαῖς 5.5 Implicitation of the subject The omission of a pronominal subject When in Hebrew an independent personal pronoun functions as a subject in a nominal clause, and is placed at the end of that clause (which means that it is not intended to give prominence to the subject), 39 LXX Isaiah generally reproduces this pronoun by a form of εἰµί. See e.g.: 41:9 אתה עבדי Παῖς µου εἶ 41:10 אל תירא כי עמך אני µὴ φοβοῦ, µετὰ σοῦ γάρ εἰµι µι 41:23 אתם ונדעה כי אלהים καὶ γνωσόµεθα ὅτι θεοί ἐστε στε 43:2 אני אתך µετὰ σοῦ εἰµι 43:5 אני אל תירא כי אתך µὴ φοβοῦ, ὅτι µετὰ σοῦ εἰµι µι 44:5 אני ל Τοῦ θεοῦ εἰµι 48:4 אתה מדעתי כי קשה γινώσκω ἐγὼ ὅτι σκληρὸς εἶ If the independent pronoun in nominal clauses does have an emphatic function, in which case it usually precedes the predicate, 40 LXX Isaiah often renders it in a double way : by means of a form of εἰµί in combination with a Greek independent pronoun. See e.g.: 8:13 הו אוא מוראכם וה καὶ αὐτὸς ἔσται σου φόβος. 37:20 לבדך אתה כי µόνος. ὅτι σὺ εἶ ὁ θεὸς 42:17 אלהינו אתם Ὑµε µεῖς ἐστε θεοὶ ἡµῶν. 43:1 אתה לי ἐµὸς εἶ σύ. 44:8 עדי ואתם µάρτυρες ὑµε µεῖς ἐστε 45:22 אל אני כי ἐγώ εἰµι ὁ θεός 46:9 אל אנכי כי ὅτι ἐγώ εἰµι ὁ θεός 48:12 ראשון אני ἐγώ εἰµι πρῶτος 48:17 אלהיך אני Ἐγώ εἰµι ὁ θεός σου 56:3 עץ יבש אני הן Ἐγώ εἰµιε ξύλον ξηρόν. כל הנחרים בך 41:11 (cf. and on those grounds translated as οἱ ἀντικείµενοι נחרים might have been linked to יחדו 38 / πάντες οἱ ἀντικείµενοί σοι). 39 Cf. Joüon 154fa. 40 Cf. Joüon 154fa. 120

11 IMPLICITATION ילדי פשע 57:4 אתם οὐχ ὑµε הלוא µεῖς ἐστε τέκνα ἀπωλείας In expressions in which the Hebrew employs the independent pronoun together with a predicative participle in order to indicate the person who forms the subject of this participle, 41 this construction is mostly reproduced into Greek by means a finite verb form without an independent pronoun. See e.g.: 5:5 עשה לכרמי אני את אשר τί ποιήσω τῷ ἀµπελῶνί µου 21:8 עמד תמיד יומם אנכי Ἔστην διὰ παντὸς ἡµέρας 29:11 הוא חתום כי ἐσφράγισται γάρ. 37:10 בוטח בו אתה אשר ἐφ ᾧ πεποιθὼς εἶ ἐπ αὐτῷ 48:13 אני אליהם קרא καλέσω αὐτούς Independent pronouns preceding finite verbal forms with the purpose of giving special prominence to the subject of these verbs, 42 are virtually always represented in LXX Isaiah. Only incidentally do they not have a match in the Greek, namely in the following cases: 10:14 וכאסף ביצים עזבות καὶ ὡς καταλελειµµένα ᾠὰ אספתי אני כל הארץ ἀρῶ 34:16 קבצן הו אוא ה ורוחו καὶ τὸ πνεῦµα αὐτοῦ συνήγαγεν αὐτάς τάς. 37:11 שמעת אתה הנה ἢ οὐκ ἤκουσας 37:25 ושתיתי מים קרתי אני καὶ ἔθηκα γέφυραν 38:17 נפשי חשקת ואתה εἵλου γάρ µου τὴν ψυχήν 38:19 יודך הו אוא ה חי חי οἱ ζῶντως εὐλογήσουσί σε 43:12 והושעתי הגדתי אנכי ἀνήγγειλα καὶ ἔσωσα In nearly all of the instances offered (10:14; 34:16; 37:25; 38:17; 43:12) the omission of the independent pronoun could be brought about by the translator s levelling the clause to a parallel one in which (in the Greek) an independent pronoun does not appear either The omission of a nominal subject Subjects have repeatedly been omitted in LXX Isaiah because in the translation their function is adopted by an identical or synonymous subject in a neighbouring clause ( distributive rendering, see section 3.6.2b). Under other circumstances, Hebrew nominal subjects are in LXX Isaiah only rarely transformed into subjects that are implied in the verb: וקרוב לבוא עתה וימיה לא ימשכו 13:22 χρονιεῖ. 43 ταχὺ ἔρχεται καὶ οὐ 16:10 יין ביקבים לא ידרך הדרך καὶ οὐ µὴ πατήσουσιν οἶνον εἰς τὰ ὑπολήνια 44 16:14 ועתה דבר לאמר καὶ νῦν λέγω 45 28:21 כי כהר פרצים יקום ὥσπερ ὄρος ἀσεβῶν ἀναστήσεται 46 33:24 ובל יאמר שכן καὶ οὐ µὴ εἴπῃ 41 Cf. Joüon 154fd. 42 Cf. Joüon 146a. 43 Cf. Hab 2:3 (see section ). 44 Cf. sections 3.5 and LXX Isa has changed indirect speech into direct speech, probably because an introduction of direct speech has already occurred (Τοῦτο τὸ ῥῆµα, ὃ ἐλάλησε κύριος ἐπὶ Μωαβ, ὁπότε καὶ ἐλάλησε). following. and rendered by καὶ ἔσται at the beginning of the clause יהיה has probably been read as

12 CHAPTER FIVE 49:23 אשר לא יבשו קוי αἰσχυνθήσῃ. καὶ οὐκ 61:1 רוח עלי יען Πνεῦµα κυρίου ἐπ ἐµέ, οὗ εἵνεκεν משח אתי µε 47 ἔχρισέ In some of these examples, the omission entails that whereas the Hebrew starts with a new subject, the Greek continues with the subject of the preceding clause. Through this continuation the cohesion of the text is strengthened (see 16:10; 33:24; and 49:23) Implicitation by the omission of an object Just as was the case with other sentence elements, objects 49 were probably also mostly omitted because their information was seen as redundant (see e.g. 9:3[4]; 25:10; 26:20,21; 28:4; 30:14,33; 31:7; 33:12; 36:21; 40:20; 44:5; and 54:1 below). Furthermore they may have been deleted in order to circumvent a certain suggestion in the text (e.g. 37:28 29 and 59:13), or to give a broader validity to the words (e.g. 8:11 and 40:17). Lastly, they may sometimes have been omitted for the sake of parallelism (e.g. 44:7; 46:11; and 48:15) The omission of a pronominal object 8:11 כי כה אמר אלי Οὕτως λέγει κύριος 9:3(4) שבט הנגש בו τὴν γὰρ ῥάβδον τῶν ἀπαιτούντων החתת כיום מדין Μαδιαµ. διεσκέδασε κύριος ὡς τῇ ἡµέρᾳ τῇ ἐπὶ 25:10 ונדוש מואב תחתיו καὶ καταπατηθήσεται ἡ Μωαβῖτις 26:20 וסגר דלתיך בעדך ἀπόκλεισον τὴν θύραν σου 26:21 כי הנה יצא ממקומו ἰδοὺ γὰρ κύριος ἀπὸ τοῦ ἁγίου ἐπάγει τὴν לפקד עון ישב הארץ עליו ὀργὴν ἐπὶ τοὺς ἐνοικοῦντας ἐπὶ τῆς γῆς 30:33 נשמת כנחל גפרית בערה בה καιοµένη. ὁ θυµὸς κυρίου ὡς φάραγξ ὑπὸ θείου 31:7 אשר עשו לכם ידיכם חטא αὐτῶν. ἃ ἐποίησαν αἱ χεῖρες 36:7 וכי תאמר אלי אל אלהינו εἰ δὲ λέγετε Ἐπὶ κύριον τὸν θεὸν ἡµῶν בטחנו πεποίθαµεν 50 36:21 לא תענהו ἀποκριθῆναι. µηδένα ואת התרגזך אלי יען התרגזך אלי 37:28 29 ὁ δὲ θυµός σου, ὃν ἐθυµώθης 51 40:17 כל הגוים כאין נגדו καὶ πάντα τὰ ἔθνη ὡς οὐδέν εἰσι מאפס ותהו נחשבו לו ἐλογίσθησαν. καὶ εἰς οὐθὲν 40:20 חרש חכם יבקש לו להכין פסל καὶ σοφῶς ζητεῖ πῶς στήσει αὐτοῦ εἰκόνα לא ימוט σαλεύηται. καὶ ἵνα µὴ 44:7 יקרא ויגידה ויערכה לי στήτω καλεσάτω καὶ ἑτοιµασάτω µοι 46:11 אף דברתי אף אביאנה ἤγαγον, ἐλάλησα καὶ יצרתי אף אעשנה ἔκτισα καὶ ἐποίησα 48:15 אני אני דברתי אף קראתיו ἐγὼ ἐλάλησα, ἐγὼ ἐκάλεσα Presumably omitted in order to avoid repetition. 48 See van Peursen, Language and Interpretation, The term object includes direct, indirect, and prepositional objects. 50 According to Goshen-Gottstein (HUB Isa, 151) אלי is omitted mistakenly, due to haplography אל).(אלי Yet, the translator may also have left it out deliberately, because he thought it superfluous. 51 Perhaps anger directed towards God was offensive in the eyes of the translator; cf. section

13 IMPLICITATION Object suffixes are occasionally not represented when a reference to the object also occurs elsewhere in the same sentence (either in a different or in the same syntactical function): - As object to a another phrase: 53 27:11 על כן לא ירחמנוווו עשהוווו διὰ τοῦτο οὐ µὴ οἰκτιρήσῃ ὁ ποιήσας αὐτούς τούς, ויצרו לא יחננוווו οὐδὲ ὁ πλάσας αὐτο τοὺς οὐ µὴ ἐλεήσῃ. 37:11 אתה שמעת אשר עשו מלכי אשור ἢ οὐκ ἤκουσας ἃ ἐποίησαν βασιλεῖς Ἀσσυρίων להחרימם לכל הארצות πᾶσαν τὴν τ γῆν γ ὡς ἀπώλεσαν; 49:10 כי מרחמם ינהגם ἀλλὰ ὁ ἐλεῶν αὐτο τοὺς παρακαλέσει 55:6 בהמצאו קראהוווו ἐπικαλέσασθε 54 καὶ ἐν τῷ εὑρίσκειν αὐτὸν 56:2 מחללו שבת שמר καὶ φυλάσσων τὰ σάββατα µὴ βεβηλοῦν 56:6 שבת כל שמר καὶ πάντας τοὺς φυλασσοµένους τὰ σάββατά מחללו µου µὴ βεβηλοῦν 58:7 וכסיתו ערם כי תראה ἐὰν ἴδῃς γυµνόν, περίβαλε 62:9 כי מאספיוווו יאכלהוווו ἀλλ ἢ οἱ συνάγοντες φάγονται αὐτὰ 62:9 ומקבציוווו ישתהוווו καὶ οἱ συνάγοντες πίονται αὐτὰ - As an object in casus pendens, located at the beginning of the clause and later resumed by way of a retrospective pronoun: 55 13:17 לא יחפצו בוווו וזהב 14:27 ומי ישיבנהההה הנטויה וידו 42:3 לא יכבנהההה כהה ופששששתהההה 59:12 ידענום ועונתינו οὐδὲ χρυσίου χρείαν ἔχουσι. καὶ τὴν χεῖρα τὴν τ ὑψηλ ψηλὴν τίς ἀποστρέψει; καὶ λίνον καπνιζόµενον οὐ σβέσει 56 καὶ τὰ ἀδικήµατα ἀ ἡµῶν ἔγνωµεν - When the object is made explicit in an apposition at the end of the sentence (a figure called epergesis). In the Greek the words of the apposition are integrated within the sentence: 15:7 הערבים ופקדתם על נחל ἐπάξω γὰρ ἐπὶ τὴν φάραγγα Ἄραβας 23:9 לחלל צבאות יעצה κύριος σαβαωθ ἐβουλεύσατο παραλῦσαι כל צבי גאון πᾶσαν τὴν τ ὕβριν τῶν τ ἐνδόξων 41:12 תבקשם ולא תמצאם ζητήσεις αὐτοὺς καὶ οὐ µὴ εὕρῃς מצתך אנשי τοὺς ἀνθρώπους, οἳ ο παροινήσουσιν εἰς ε ς σέ 52 Cf 1QIsa a : אני אני דברתי אפ קראתי (see section ). 53 Cf. also 8:16. דרשו בהמצאו קראהו בהיותו קרוב :קראהו and בהמצאו 54 In the MT the sentence division lies in between Seek the LORD while he may be found, call upon him while he is near. 55 Cf. Joüon 156. For an example in which such a construction has been maintained in LXX Isa, see e.g. 1:7 אתה / τὴν χώραν ὑµῶν ἐνώπιον ὑµῶν ἀλλότριοι κατεσθίουσιν αὐτήν אדמתכם לנגדכם זרים אכלים For an וחרבות e.g. 5:17 example in which both MT Isa and LXX Isa do not resume the object after a casus pendens, see φάγονται. / καὶ τὰς ἐρήµους τῶν ἀπειληµµένων ἄρνες מחים גרים יאכלו 56 1QIsa a displays ופשתה כהה לוא יכבה (see section ). :הערבים as a pf. cons. 1 st sg., with a suffix in the 3 rd masc. pl. pointing to ופקדתם 57 LXX Isa seems to have read For I will bring them to the valley, namely the Arabs. In the MT, by contrast, הערבים is a genitive attribute to,נחל while ופקדתם is vocalised as a noun phrase meaning their possessions ק דּ ת ם).(וּפ The latter is the subject of a clause governed by the verb phrase על נחל הערבים ישאום :ישאום and ופקדתם their possessions they carry away over the Wadi of the Willows. The rendering of ישאום forms a separate clause in the LXX: καὶ λήµψονται αὐτήν and they will take her. 123

14 CHAPTER FIVE 63:11 רעי צאנו את איה המעלם מים ὁ ἀναβιβάσας ἐκ τῆς γῆς τὸν ποιµένα τῶν τ προβάτων 58 - In another syntactical function, for instance as a subject or as an object complement: 24:9 לשתיוווו שכר ימר πικρὸν ἐγένετο τὸ σικερα τοῖς πίνουσιν. 46:6 ויעשהוווו אלללל ἐποίησαν χειροποίητα The omission of a nominal object 30:10 לא תחזו לנו נכחות Μὴ λαλεῖτε ἡµῖν 30:14 לחתות אש מיקוד ולחשף ἐν ᾧ πῦρ ἀρεῖς καὶ ἐν ᾧ ἀποσυριεῖς מים מגבא µικρόν. ὕδωρ 31:7 אשר עשו לכם ידיכם חטא αὐτῶν. ἃ ἐποίησαν αἱ χεῖρες 33:12 והיו עמים משרפות שיד קוצים καὶ ἔσονται ἔθνη κατακεκαυµένα ὡς ἄκανθα כסוחים באש יצתו κατακεκαυµένη. ἐν ἀγρῷ ἐρριµµένη καὶ 38:21 ישאו דבלת תאנים וימרחו Λαβὲ παλάθην ἐκ σύκων καὶ τρῖψον על השחין καὶ κατάπλασαι 44:5 וזה יכתב ידו ל καὶ ἕτερος ἐπιγράψει Τοῦ θεοῦ εἰµι 54:1 פצחי רנה וצהלי ῥῆξον καὶ βόησον 59:13 פשע וכחש ב ונסוג ἠσεβήσαµεν καὶ ἐψευσάµεθα καὶ ἀπέστηµεν מאחר אלהינו ἡµῶν 59 ἀπὸ ὄπισθεν τοῦ θεοῦ Elsewhere, the omission of objects bears on the application of distributive rendering. See for examples section 3.6.2a. 5.7 Implicitation without the occurrence of a minus Implicitation is only now and then achieved by way of an omission. In other places it is done through the substitution of words, in particular of a noun by a pronoun. Three examples to illustrate this are: 14:22 שם ושאר לבבל והכרתי ונין ונכד 52:9 גאל ירושלם עמו כי נחם 63:6 באפי עמים ואבוס καὶ ἀπολῶ αὐτῶν ὄνοµα καὶ κατάλειµµα καὶ σπέρµα ὅτι ἠλέησε κύριος αὐτὴν καὶ ἐρρύσατο Ιερουσαληµ. καὶ κατεπάτησα αὐτο τοὺς τῇ ὀργῇ µου 5.8 Conclusion Even though the Isaiah translator was particularly apt to make his text more explicit and to add interpretative glosses to it, some instances of implicitation can also be encountered in his כל translation. He has regularly left out words that are already implied by the context (such as and,(יחד or information he may have supposed to be familiar to his readers. Now and then he has omitted specifying details that do not really influence the message and content of the text ו 58 1QIsa a gives איה המעלה מים את רוע צ א(ו)נו (see section.( Possibly the translator regarded the idea of lying to God himself as too offensive. 124

15 IMPLICITATION (e.g. specifications of body parts). By removing such superfluous words, he may have wished to create a text that was more concise in character. 60 Nevertheless, the avoidance of redundancy on its own does not provide a sufficient explanation for many of the translator s omissions mentioned in this chapter. It does not answer the question of why in some cases he has made elements implicit, whereas in plenty of other cases he has rather made his text more explicit, sometimes even by adding the same words that in other verses he had discarded (such as words in the sense of all ). One solution for this paradox is that the translator was quite willing either to add or omit (seemingly) insignificant elements if this could serve other purposes, such as the amelioration of parallelism, the assimilation of an expression to a related one nearby, or the strengthening of the coherence of his discourse. The possibility also exists that he occasionaly deleted or inserted small words just because this favoured the rhythm of his text. Finally, he may sometimes have employed the implicitation of textual elements with the aim of extending or generalising a notion of the text, or in order to reduce the emphasis on or sometimes even to remove certain suggestions (see e.g. 37:29 and 59:13). This is were implicitation begins to touch on exegesis. In this twilight zone it could be used as a technique that on the one hand allowed the translator to remain close to the literal wording of Scripture, but which on the other hand gave him some room for a broader or slightly different interpretation of the source text. Without doubt this chapter has included some minuses that have not actually been caused by the application of implicitation, but by the fact that the translator had a source text in front of him that sometimes differed from the MT. Still, because the omission of redundant words closely accords with the translator s penchant for condensation, this favours the attribution of implicitating minuses to the translator himself. 60 Despite the translator s aim for conciseness, implicitation in LXX Isa hardly ever leads to ellipsis, i.e. the omission of syntactically required elements. See section 7.4a. 125

16 CHAPTER FIVE 126

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

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

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

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

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

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

Διαβάστε περισσότερα

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

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

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

C.S. 430 Assignment 6, Sample Solutions

C.S. 430 Assignment 6, Sample Solutions C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα

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

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

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

εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016

εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016 εἶμι, φημί, Indirect Discourse Intensive Classical Greek Prof. Kristina Chew June 28, 2016 Conditional Relative Clauses relative clauses referring to an indefinite person or thing (whoever, whatever, anyone,

Διαβάστε περισσότερα

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

Λέξεις, φράσεις και προτάσεις

Λέξεις, φράσεις και προτάσεις 1 Λέξεις, φράσεις και προτάσεις (Words, phrases and clauses) The Greek language, like all human languages, has a Lexicon and a Grammar that are used to create sentences. The Lexicon consists of the words

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

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

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

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

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

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 7: More about gerunds Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

Διαβάστε περισσότερα

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

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

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

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

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

The 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

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

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

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

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

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

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

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

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

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

5. Choice under Uncertainty

5. Choice under Uncertainty 5. Choice under Uncertainty Daisuke Oyama Microeconomics I May 23, 2018 Formulations von Neumann-Morgenstern (1944/1947) X: Set of prizes Π: Set of probability distributions on X : Preference relation

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

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

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

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

Lesson Seven: ADULTERY Matthew 5:27-30

Lesson Seven: ADULTERY Matthew 5:27-30 Lesson Seven: ADULTERY Matthew 5:27-30 LESSON OBJECTIVE: The student demonstrates understanding of the historical and literary meaning of Matthew 5:27-30 and related texts. LESSON INDICATORS: Upon successful

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

ΑΓΓΛΙΚΑ IV. Ενότητα 6: Analysis of Greece: Your Strategic Partner in Southeast Europe. Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών

ΑΓΓΛΙΚΑ IV. Ενότητα 6: Analysis of Greece: Your Strategic Partner in Southeast Europe. Ιφιγένεια Μαχίλη Τμήμα Οικονομικών Επιστημών Ενότητα 6: Analysis of Greece: Your Strategic Partner in Southeast Europe Ιφιγένεια Μαχίλη Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό,

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

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

Galatia SIL Keyboard Information

Galatia SIL Keyboard Information Galatia SIL Keyboard Information Keyboard ssignments The main purpose of the keyboards is to provide a wide range of keying options, so many characters can be entered in multiple ways. If you are typing

Διαβάστε περισσότερα

On a four-dimensional hyperbolic manifold with finite volume

On a four-dimensional hyperbolic manifold with finite volume BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Numbers 2(72) 3(73), 2013, Pages 80 89 ISSN 1024 7696 On a four-dimensional hyperbolic manifold with finite volume I.S.Gutsul Abstract. In

Διαβάστε περισσότερα

LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS

LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS LECTURE 2 CONTEXT FREE GRAMMARS CONTENTS 1. Developing a grammar fragment...1 2. A formalism that is too strong and too weak at the same time...3 3. References...4 1. Developing a grammar fragment 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

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

Summer Greek. Lesson 3. NOUNS GENDER (does not refer to fe/male) masculine feminine neuter NUMBER singular plural. NOUNS -Case.

Summer Greek. Lesson 3. NOUNS GENDER (does not refer to fe/male) masculine feminine neuter NUMBER singular plural. NOUNS -Case. A Summer Greek Lesson 3 Ω Parts of Speech NOUN- person, place, thing, quality, idea, or action ARTICLE Indefinite = a / an ; Definite = the ADJECTIVE- describes a noun (includes in/definite articles) PRONOUN-word

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

Problem Set 3: Solutions

Problem Set 3: Solutions CMPSCI 69GG Applied Information Theory Fall 006 Problem Set 3: Solutions. [Cover and Thomas 7.] a Define the following notation, C I p xx; Y max X; Y C I p xx; Ỹ max I X; Ỹ We would like to show that C

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 11: The Unreal Past Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons

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 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

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

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

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

Passive and Middle Voices. A lesson for the Paideia web-app Ian W. Scott, 2015

Passive and Middle Voices. A lesson for the Paideia web-app Ian W. Scott, 2015 Passive and Middle Voices A lesson for the Paideia web-app Ian W. Scott, 2015 The Passive Voice So far all of our Greek verbs have been in the active voice Subject performs the verbal action "Clare is

Διαβάστε περισσότερα

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας»

ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. ΘΕΜΑ: «ιερεύνηση της σχέσης µεταξύ φωνηµικής επίγνωσης και ορθογραφικής δεξιότητας σε παιδιά προσχολικής ηλικίας» ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΙΓΑΙΟΥ ΣΧΟΛΗ ΑΝΘΡΩΠΙΣΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΕΠΙΣΤΗΜΩΝ ΤΗΣ ΠΡΟΣΧΟΛΙΚΗΣ ΑΓΩΓΗΣ ΚΑΙ ΤΟΥ ΕΚΠΑΙ ΕΥΤΙΚΟΥ ΣΧΕ ΙΑΣΜΟΥ «ΠΑΙ ΙΚΟ ΒΙΒΛΙΟ ΚΑΙ ΠΑΙ ΑΓΩΓΙΚΟ ΥΛΙΚΟ» ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ που εκπονήθηκε για τη

Διαβάστε περισσότερα

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

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

Subject - Students love Greek.

Subject - Students love Greek. A Summer Greek 2009 Ω Parts of Speech NOUN - person, place, thing, quality, idea, or action ARTICLE Indefinite = a / an ; Definite = the ADJECTIVE - describes a noun (includes in/definite articles) VERB

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

Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς

Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς Review 4n.1: Vowel stems of the third declension: πόλις, πρέσβυς We review side by side a model of stems ending in ι: πόλις, πόλεως, ἡ = city-state and a masculine model of stems ending in υ: πρέσβυς,

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

Lesson Five: LAW AND THE GOSPEL Matthew 5:17-20 LESSON OBJECTIVE:

Lesson Five: LAW AND THE GOSPEL Matthew 5:17-20 LESSON OBJECTIVE: Lesson Five: LAW AND THE GOSPEL Matthew 5:17-20 LESSON OBJECTIVE: The student demonstrates understanding of the historical and literary meaning of Matthew 5:17-20 and related texts. LESSON INDICATORS:

Διαβάστε περισσότερα

1999 MODERN GREEK 2 UNIT Z

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

Διαβάστε περισσότερα

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

Modern Greek Extension

Modern Greek Extension Centre Number 2017 HIGHER SCHOOL CERTIFICATE EXAMINATION Student Number Modern Greek Extension Written Examination General Instructions Reading time 10 minutes Working time 1 hour and 50 minutes Write

Διαβάστε περισσότερα

Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in

Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in Nowhere-zero flows Let be a digraph, Abelian group. A Γ-circulation in is a mapping : such that, where, and : tail in X, head in : tail in X, head in A nowhere-zero Γ-flow is a Γ-circulation such that

Διαβάστε περισσότερα

SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions

SCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions SCHOOL OF MATHEMATICAL SCIENCES GLMA Linear Mathematics 00- Examination Solutions. (a) i. ( + 5i)( i) = (6 + 5) + (5 )i = + i. Real part is, imaginary part is. (b) ii. + 5i i ( + 5i)( + i) = ( i)( + i)

Διαβάστε περισσότερα

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS

CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS CHAPTER 48 APPLICATIONS OF MATRICES AND DETERMINANTS EXERCISE 01 Page 545 1. Use matrices to solve: 3x + 4y x + 5y + 7 3x + 4y x + 5y 7 Hence, 3 4 x 0 5 y 7 The inverse of 3 4 5 is: 1 5 4 1 5 4 15 8 3

Διαβάστε περισσότερα

LESSON TEN: THE ADJECTIVE. Memorization of vocabulary ten

LESSON TEN: THE ADJECTIVE. Memorization of vocabulary ten LESSON TEN: THE ADJECTIVE Memorization of vocabulary ten ἀγαθος good ἁγιος holy, set apart ἀλλα but (the regular contrasting particle, with δε used at times) ἀληθεια truth ἀληθινος true/genuine αὐτος he

Διαβάστε περισσότερα

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

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

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

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

F-TF Sum and Difference angle

F-TF Sum and Difference angle F-TF Sum and Difference angle formulas Alignments to Content Standards: F-TF.C.9 Task In this task, you will show how all of the sum and difference angle formulas can be derived from a single formula when

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

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O

Mean bond enthalpy Standard enthalpy of formation Bond N H N N N N H O O O Q1. (a) Explain the meaning of the terms mean bond enthalpy and standard enthalpy of formation. Mean bond enthalpy... Standard enthalpy of formation... (5) (b) Some mean bond enthalpies are given below.

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

forms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with

forms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with Week 03: C lassification of S econd- Order L inear Equations In last week s lectures we have illustrated how to obtain the general solutions of first order PDEs using the method of characteristics. We

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

Croy Lessons Participles

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

Διαβάστε περισσότερα

About these lecture notes. Simply Typed λ-calculus. Types

About these lecture notes. Simply Typed λ-calculus. Types About these lecture notes Simply Typed λ-calculus Akim Demaille akim@lrde.epita.fr EPITA École Pour l Informatique et les Techniques Avancées Many of these slides are largely inspired from Andrew D. Ker

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

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

6.3 Forecasting ARMA processes

6.3 Forecasting ARMA processes 122 CHAPTER 6. ARMA MODELS 6.3 Forecasting ARMA processes The purpose of forecasting is to predict future values of a TS based on the data collected to the present. In this section we will discuss a linear

Διαβάστε περισσότερα

Uniform Convergence of Fourier Series Michael Taylor

Uniform Convergence of Fourier Series Michael Taylor Uniform Convergence of Fourier Series Michael Taylor Given f L 1 T 1 ), we consider the partial sums of the Fourier series of f: N 1) S N fθ) = ˆfk)e ikθ. k= N A calculation gives the Dirichlet formula

Διαβάστε περισσότερα

Herodian and the Greek language: rules of thumb for accenting Greek enclitics. Stephanie Roussou (a joint project with Philomen Probert)

Herodian and the Greek language: rules of thumb for accenting Greek enclitics. Stephanie Roussou (a joint project with Philomen Probert) Herodian and the Greek language: rules of thumb for accenting Greek enclitics Stephanie Roussou (a joint project with Philomen Probert) What are enclitics? Enclitics are small words forming close-knit

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

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

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