Using and Enjoying Biblical Greek

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Using and Enjoying Biblical Greek"

Transcript

1 Using and Enjoying Biblical Greek Reading the New Testament with Fluency and Devotion Rodney A. Whitacre Parsing Practice with Key

2 2015 by Baker Publishing Group Published by Baker Academic a division of Baker Publishing Group P.O. Box 6287, Grand Rapids, MI All rights reserved. 2

3 Contents Introduction 4 Worksheets First and Second Declension Parsing Practice 7 Third Declension Parsing Practice: Patterns Third Declension Parsing Practice: Patterns 5 6 and Adjectives 9 All Nominal Declensions Parsing Practice 10 Present Indicative Parsing Practice 11 Future Indicative Parsing Practice 12 Perfect Indicative Parsing Practice 13 Imperfect Indicative Parsing Practice 14 Aorist Indicative Parsing Practice 15 μι Indicative Parsing Practice 16 Subjunctive Parsing Practice 17 Imperative Verbs Parsing Practice 18 Infinitive Verbs Parsing Practice 19 Participle Verbs Parsing Practice 20 Mixed Verb Parsing Practice 21 Answer Key First and Second Declension Parsing Practice 23 Third Declension Parsing Practice: Patterns Third Declension Parsing Practice: Patterns 5 6 and Adjectives 25 All Nominal Declensions Parsing Practice 26 Present Indicative Parsing Practice 27 Future Indicative Parsing Practice 28 Perfect Indicative Parsing Practice 29 Imperfect Indicative Parsing Practice 30 Aorist Indicative Parsing Practice 31 μι Indicative Parsing Practice 32 Subjunctive Parsing Practice 33 Imperative Verbs Parsing Practice 34 Infinitive Verbs Parsing Practice 35 Participle Verbs Parsing Practice 36 Mixed Verb Parsing Practice 37 3

4 Introduction The following pages contain exercises for practicing the application of the information contained in chapter 3. This exercise is harder than the parsing you do while reading, because the text of the passage often gives help for recognizing the words. But since there are plenty of places where such clues do not exist, it is important to be able to recognize quickly the signals contained in the words themselves. At some points the information on the Sneeze Sheet does not enable you to be precise in your parsing. Instead, it helps you know what valid options exist, which are then nailed down by consulting a lexicon. For example, the gender of some nominals is not precise nor is the lexical form of some of the third declensions. So you should use a lexicon while doing these exercises. Put down the best answer you can and then check the lexicon before looking at the answers provided. Because these words are completely out of context, if you do not know the lexical form you need to think of all the possible options for the parsing. For example, if you see τείχη then you would most likely assume it is a nom.-sg.-fem. noun of the first declension. In actual translation this is not a bad assumption unless there is something in the context to steer you to a different answer. The context may let you know if you should look for an alternative analysis. In the case of τείχη we actually have a nom./acc.- pl.-neut. from τὸ τεῖχος, a pattern 5a third declension. If you saw τὰ τείχη in the passage, the article would enable you to recognize its parsing. So as you do these practice exercises, do not look at the answer until you have consulted the lexicon, unless, of course, the word is one you already know (that is, you have the lexicon information already in your head). The answer sheets give parsing information in the following way: Nominals: Finite Verbs: Participles: Infinitives: case number gender lexical form person number voice Tense mood lexical form case number voice gender Tense mood lexical form Tense voice mood lexical form This particular sequence is based on a way of using the information on the Sneeze Sheet. Nominals. As noted above, the case and number are the most important facts about the form of nominals for how they function in the sentence. These two features are also the clearest from the Sneeze Sheet. So when parsing I try to determine the possible forms of case and number and then go on to gender if it seems important. Finite verbs. If you start parsing a verb by analyzing its ending, then you come up with person, number and voice. The tense and mood are signaled by other features in the word, such as augments, tense signs, and so forth. 4

5 Participles. Here also the ending gives you case, number, voice and (sometimes) gender. Since I start with the ending of the word I put this information down first. Infinitives. Here the ending signals the mood (infinitive) and voice, while other features indicate the tense. However, since the parsing of infinitives includes so few categories I put the tense first. I capitalize the Tense in each case to highlight it, partly to break up the string of information and partly because I find the tense of particular interest. In actual reading, of course, one does such analysis in a less sequential and formal way. But while working on your parsing knowledge and skills, you might consider approaching the analysis along the lines I have just mentioned, unless you have a different approach that works well for you. It is important to note that on the answer sheets I parse by form, not function. So I give mid./pass. for those forms that are used for both of these voices, even though the actual usage in a passage is one or the other. I use this approach also for verbs that do not have an active form in the lexical form. Thus, I would parse λύομαι as a mid./pass. even though in translation or analysis it would be one or the other. But future and aorist forms will be either middle or passive since they do not share a common form in these tenses. Once you look up the word in the lexicon you learn whether it has an active ending in the lexical form. The lexicon sometimes also helps sort out which voice a word has (i.e., mid. or pass.), though often the context of the sentence is necessary for this analysis. Some of the words in the practice exercises assume knowledge of basic irregular principal parts, which I ve listed at the end of chapter 3. Some of the words have more than one answer. The answers are a line below the word to be parsed so you can cover the answers with a piece of paper; as you slide the paper down the next word is visible but not the answer. 5

6 Worksheets 6

7 First and Second Declension Parsing Practice γῇ ἀνομίαν πηγαί θύρας μεμβράνης προφήτου ἵππων φόβοις σταυρούς ξύλον χωρίου δένδρα βιβλίων καρπῷ τόπος βίον πτέρνης 7

8 Third Declension Parsing Practice Patterns 1 4 πίκακι ἀτμίδας δράκουσιν δαιμόνες κυριότητες σωμάτων λέοντος χιτώνων αἵματι βάπτισμα γαστρός ἀρχιτέκτονι βήματα λιβός Σολομῶνος γέροντα φρενάς 8

9 Third Declension Parsing Practice Patterns 5 6 and Adjectives κρίσιν βάθους ὀσφύν ἁλιεῖς πλήρη κτίσεως στάχυες γένει ἱερέα ὑγιοῦς εὐγενεῖς πόλεις γραμματεῦσιν φύσει πάντα χαλκέως πάθη 9

10 All Nominal Declensions Parsing Practice δυναμέως ἀριθμούς μητρί ἑορταίς ὑπακοῆς χρυσός βατράχου ὄφεις λεγιῶνος κλητόν βρώματα μερίδες ἀπαθῆ λόγοι φωσί μέσαις ἀκάθαρτος 10

11 Present Indicative Parsing Practice προσεύχεται βλέπουσιν δίδως διψᾷ κτίζει κελευόμεθα τίθεμαι κάμνῃ ἀσεβοῦνται ἐκφύομεν συμπάσκεις λογεῖται θυμοῖς κουφίζονται θάπτει ζωγρῇ λυμαίνεσθε 11

12 Future Indicative Parsing Practice θηρεύσομεν ὄψεται βλέψω κρινοῦμεν σῴσεις ποιήσει βληθήσεσθε ἀκούσει ἄξουσι ἐλεύσεται σῳθήσῃ λήμψῃ θεραπεύσεσθε πορεύσομαι πέμψετε γενήσεσθε πιστευθησόμεθα 12

13 Perfect Indicative Parsing Practice δεδιώκαμεν πεπίστευκεν τεθεράπευσαι εἰλήφατε πεπόρευται ἐγνώκασι πέποιθας ἠγαπήκατε ἠκολουθήκαμεν σέσῳται βεβλήμεθα πεφανέρωκα πέπαυσαι γεγεννήκασι γεγένηται τετελειώμεθα ᾠκοδόμησθε 13

14 Imperfect Indicative Parsing Practice ἐκάθευδες ἤλπιζον ἦν κατεβαινόμεθα ἑτοιμαζόμαι ἐλάλει ἐχαίρου ἤγον ἐξεπορεύετο ἐδικαίου ἐγίνου ἐδικαιοῦ ἐπιστεύοντο ἐβοήθουν ἐβλεπόμεθα ἠγάπα ἐτηρεῖτε 14

15 Aorist Indicative Parsing Practice ἠκούσασθε ἔβλεψας ἐφάγομεν ἐφοβήθητε ὤφθη ἐπιστεύσαντο ἐγένου εἶπεν ἦλθον ἤχθη κατέβησαν ἀπεστάλης ἀπέστειλας ἐνήψω ἐφίλησεν ἐπαύσασθε ὡδεύθην 15

16 μι Indicative Parsing Practice ἐδώκατε ἵσταμεν ἐτίθεσθε δίδοται ἀφίησι ἵστασαι ἐτίθει δίδοτε ἄφειτο ἔστησε διδόασι ἔθηκαν ἀφήκαμεν ἔδοτο ἀφίεται ἔστην τίθεμαι 16

17 Subjunctive Parsing Practice βάλλῃς διώξητε ἀκούω γενηθῶ λαμβάνωμεν ποιῇ ἔρχηται πιστεύσῃ πιστεύῃ διδῶτε εἴπωσι πεσώμεθα ἐνέχθῃς ἔλθησθε γινώσκῃ 17

18 Imperative Verbs Parsing Practice ἄκουσον διδάσκετε βάλλε πεμψάσθω γραφέτωσαν νίκα ἀγάγετε δοξάζου διδότωσαν φάγε ἐγειράτω θεραπεύθητι βλέψαι λάβεσθε εἰρήσθω βαπτίζετε πεινάτω 18

19 Infinitive Verbs Parsing Practice γράψασθαι ἀρέσκεσθαι ταράσσειν διψᾶν λαβεῖν βλέψαι λυθῆναι δεδιωκέναι τιθέναι θεράπευσαι αἰτήσασθαι ἠγόρασθαι γενήσεσθαι ἄνοιξαι φαγεῖν δείκνυσθαι βλάπτειν 19

20 Participle Verbs Parsing Practice βλέποντος πεπιστευκότες ἀκούσαντος ἀκουόντων ἀκουούσων λάβον βεβληκυίας γενόμενον γίνωσκον θεραπεύσασα βεβαπτισμένου ἐχόμενον γνόντων γραφούσης ἱσταμένῃ σῴσων 20

21 Mixed Verb Parsing Practice λέγεις ἐβλέψαμεν λαμβάνωμεν δοξάζοντος ἐξεβαλόμην ἀποστέλλονται ἠκούσασθε στῆτε εὑρεθήσεσθε αἴρουσα ἐβάπτιζον γινώσκῃ ἠγάπων ἄγειν σέσῳσται διδαχθέντας θεράπευσον 21

22 Answer Key 22

23 First and Second Declension Parsing Practice γῇ ἀνομίαν πηγαί θύρας μεμβράνης προφήτου ἵππων φόβοις σταυρούς ξύλον χωρίου δένδρα βιβλίων καρπῷ τόπος βίον πτέρνης dat. sg. fem. < γῆ acc. sg. fem. < ἀνομία nom. pl. fem. < πηγή gen. sg. fem. < θύρα acc. pl. fem. < θύρα gen. sg. fem. < μεμβράνα gen. sg. masc. < προφήτης gen. pl. masc. < ἵππος dat. pl. masc. < φόβος acc. pl. masc. < σταυρός nom./acc. sg. neut. < ξύλον gen. sg. neut. < χώριον nom./acc. pl. neut. < δένδρον gen. pl. neut. < βιβλίον dat. sg. masc. < καρπός nom. sg. masc. < τόπος acc. sg. masc. < βίος gen. sg. fem. < πτέρνα 23

24 Third Declension Parsing Practice Patterns 1 4 πίκακι ἀτμίδας δράκουσιν δαιμόνες κυριότητες σωμάτων λέοντος χιτώνων αἵματι βάπτισμα γαστρός ἀρχιτέκτονι βήματα λιβός Σολομῶνος γέροντα φρενάς dat. sg. fem. < πίναξ acc. pl. fem. < ἀτμίς dat. pl. masc. < δράκων nom. pl. masc. < δαίμων nom. pl. fem. < κυριότης gen. pl. neut. < σῶμα gen. sg. masc. < λέων gen. pl. masc. < χιτών dat. sg. neut. < αἵμα nom./acc. sg. neut. < βάπτισμα gen. sg. fem. < γαστήρ dat. sg. masc. < ἀρχιτέκτων nom/acc. pl. neut. < βῆμα gen. sg. masc. < λίψ gen. sg. masc. < Σολομών acc. sg. masc. < γέρων acc. pl. fem. < φρήν 24

25 Third Declension Parsing Practice Patterns 5 6 and Adjectives κρίσιν βάθους ὀσφύν ἁλιεῖς πλήρη κτίσεως στάχυες γένει ἱερέα ὑγιοῦς εὐγενεῖς πόλεις γραμματεῦσιν φύσει πάντα χαλκέως πάθη dat. pl. fem. < κρίσις gen. sg. neut. < βάθος acc. sg. fem. < ὀσφύς nom. pl. masc. < ἁλιεύς acc. sg. masc./fem. < πλήρης nom./acc. pl. neut. < πλήρης gen. sg. fem. < κτίσις nom. pl. masc. < στάχυς dat. sg. neut. < γένος acc. sg. masc. < ἱερεύς gen. sg. masc./fem./neut. < ὑγιής nom./acc. pl. masc./fem. < εὐγενής nom./acc. pl. fem. < πόλις dat. pl. masc. < γραμματεύς dat. sg. fem. < φύσις acc. sg. masc. < πᾶς nom./acc. pl. neut. < πᾶς gen. sg. masc. < χαλκεύς nom./acc. pl. neut. < πάθος 25

26 All Nominal Declensions Parsing Practice δυναμέως ἀριθμούς μητρί ἑορταίς ὑπακοῆς χρυσός βατράχου ὄφεις λεγιῶνος κλητόν βρώματα μερίδες ἀπαθῆ λόγοι φωσί μέσαις ἀκάθαρτος gen. sg. fem. < δύναμις acc. pl. masc. < ἀριθμός dat. sg. fem. < μήτηρ dat. pl. fem. < ἑορτή gen. sg. fem. < ὑπακοή nom. sg. masc. < χρυσός gen. sg. masc. < βάτραχος nom./acc. pl. masc. < ὄφις gen. sg. fem. < λεγιών acc. sg. masc. < κλητός, ή, όν nom./acc. sg. neut. < κλητός, ή, όν nom./acc. pl. neut. < βρῶμα nom. pl. fem. < μερίς acc. sg. masc. < ἀπαθής, ές nom./acc. pl. neut. < ἀπαθής, ές nom. pl. masc. < λόγος dat. pl. neut. < φῶς dat. pl. fem. < μέσος, η, ον nom. sg. masc./fem. < ἀκάθαρτος, ον 26

27 Present Indicative Parsing Practice προσεύχεται βλέπουσιν δίδως διψᾷ κτίζει κελευόμεθα τίθεμαι κάμνῃ ἀσεβοῦνται ἐκφύομεν συμπάσκεις ἀπολογεῖται θυμοῖς κουφίζονται θάπτει ζωγρῇ λυμαίνεσθε 3 sg. mid./pass. Pres. ind. < προσεύχομαι 3 pl. act. Pres. ind. < βλέπω 2 sg. act. Pres. ind. < δίδωμι 3 sg. act. Pres. ind. < διψάω 3 sg. act. Pres. ind. < κτίζω 1 pl. mid./pass. Pres. ind. < κελεύω 1 sg. mid./pass. Pres. ind. < τίθημι 2 sg. mid./pass. Pres. ind. < κάμνω 3 pl. mid./pass. Pres. ind. < ἀσεβέω 1 pl. act. Pres. ind. < ἐκφύω 2 sg. act. Pres. ind. < συμπάσκω 3 sg. mid./pass. Pres. ind. < ἀπολογέομαι 2 sg. act. Pres. ind. < θυμόω 3 pl. mid./pass. Pres. ind. < κουφίζω 3 sg. act. Pres. ind. < θάπτω 2 sg. mid./pass. Pres. ind. < ζωγρέω 2 sg. mid./pass. Pres. ind. < λυμαίνω 27

28 Future Indicative Parsing Practice θηρεύσομεν ὄψεται βλέψω κρινοῦμεν σῴσεις ποιήσει βληθήσεσθε ἀκούσει ἄξουσι ἐλεύσεται σῳθήσῃ λήμψῃ θεραπεύσεσθε πορεύσομαι πέμψετε γενήσεσθε πιστευθησόμεθα 1 pl. act. Fut. ind. < θηρεύω 3 sg. mid. Fut. ind. < ὁράω 1 sg. act. Fut. ind. < βλέπω 1 pl. act. Fut. ind. < κρίνω 2 sg. act. Fut. ind. < σῴζω 3 sg. act. Fut. ind. < ποιέω 2 pl. pass. Fut. ind. < βάλλω 3 sg. act. Fut. ind. < ἀκούω 3 pl. act. Fut. ind. < ἄγω 3 sg. mid. Fut. ind. < ἔρχομαι 2 sg. pass. Fut. ind. < σῴζω 2 sg. mid. Fut. ind. < λαμβάνω 2 pl. mid. Fut. ind. < θεραπεύω 1 sg. mid. Fut. ind. < πορεύομαι 2 pl. act. Fut. ind. < πέμπω 2 pl. mid. Fut. ind. < γίνομαι 1 pl. pass. Fut. ind. < πιστεύω 28

29 Perfect Indicative Parsing Practice δεδιώκαμεν πεπίστευκεν τεθεράπευσαι εἰλήφατε πεπόρευται ἐγνώκασι πέποιθας ἠγαπήκατε ἠκολουθήκαμεν σέσῳται βεβλήμεθα πεφανέρωκα πέπαυσαι γεγεννήκασι γεγένηται τετελειώμεθα ᾠκοδόμησθε 1 pl. act. Pf. ind. < διώκω 3 sg. act. Pf. ind. < πιστεύω 2 sg. mid./pass. Pf. ind. < θεραπεύω 2 pl. act. Pf. ind. < λαμβάνω 3 sg. mid./pass. Pf. ind. < πορεύομαι 3 pl. act. Pf. ind. < γινώσκω 2 sg. act. Pf. ind. < πείθω 2 pl. act. Pf. ind. < ἀγαπάω 1 pl. act. Pf. ind. < ἀκολουθέω 3 sg. mid./pass. Pf. ind. < σῴζω 1 pl. mid./pass. Pf. ind. < βάλλω 1 sg. act. Pf. ind. < φανερόω 2 sg. mid./pass. Pf. ind. < παύω 3 pl. act. Pf. ind. < γεννάω 3 sg. mid./pass. Pf. ind. < γίνομαι 1 pl. mid./pass. Pf. ind. < τελειόω 2 pl. mid./pass. Pf. ind. < οἰκοδομέω 29

30 Imperfect Indicative Parsing Practice ἐκάθευδες ἤλπιζον ἦν κατεβαινόμεθα ἑτοιμαζόμαι ἐλάλει ἐχαίρου ἤγον ἐξεπορεύετο ἐδικαίου ἐγίνου ἐδικαιοῦ ἐπιστεύοντο ἐβοήθουν ἐβλεπόμεθα ἠγάπα ἐτηρεῖτε 2 sg. act. Impf. ind. < καθεύδω 1 sg./3. pl. act. Impf. ind. < ἐλπίζω 3 sg. (act.) Impf. ind. < εἰμί 1 pl. mid./pass. Impf. ind. < καταβαίνω 1 sg. mid./pass. Impf. ind. < ἑτοιμάζω 3 sg. act. Impf. ind. < λαλέω 2 sg. mid./pass. Impf. ind. < χαίρω 1 sg./3 pl. act. Impf. ind. < ἄγω 3 sg. mid./pass. Impf. ind. < ἐκπορεύομαι 3 sg. act. Impf. ind. < δικαιόω 2 sg. mid./pass. Impf. ind. < γίνομαι 2 sg. mid./pass. Impf. ind. < δικαιόω 3 pl. mid./pass. Impf. ind. < πιστεύω 1 sg/3. pl. act. Impf. ind. < βοηθέω 1 pl. mid./pass. Impf. ind. < βλέπω 3 sg. act. Impf. ind. < ἀγαπάω 2 pl. act. Impf. ind. < τηρέω 30

31 Aorist Indicative Parsing Practice ἠκούσασθε ἔβλεψας ἐφάγομεν ἐφοβήθητε ὤφθη ἐπιστεύσαντο ἐγένου εἶπεν ἦλθον ἤχθη κατέβησαν ἀπεστάλης ἀπέστειλας ἐνήψω ἐφίλησεν ἐπαύσασθε ὡδεύθην 2 pl. mid. Aor. ind. < ἀκούω 2 sg. act. Aor. ind. < βλέπω 1 pl. act. Aor. ind. < ἐσθίω 2 pl. pass. Aor. ind. < φοβέομαι 3 sg. pass. Aor. ind. < ὁράω 3 pl. mid. Aor. ind. < πιστεύω 2 sg. mid. Aor. ind. < γίνομαι 3 sg. act. Aor. ind. < λέγω 1 sg./3 pl. Aor. ind. < ἔρχομαι 3 sg. pass. Aor. ind. < ἄγω 3 pl. act. Aor. ind. < καταβαίνω 2 sg. pass. Aor. ind. < ἀποστέλλω 2 sg. act. Aor. ind. < ἀποστέλλω 2 sg. mid. Aor. ind. < νήφω 3 sg. act. Aor. ind. < φιλέω 2 pl. mid. Aor. ind. < παύω 1 sg. pass. Aor. ind. < ὁδεύω 31

32 μι Indicative Parsing Practice ἐδώκατε ἵσταμεν ἐτίθεσθε δίδοται ἀφίησι ἵστασαι ἐτίθει δίδοτε ἄφειτο ἔστησε διδόασι ἔθηκαν ἀφήκαμεν ἔδοτο ἀφίεται ἔστην τίθεμαι 2 pl. act. Aor. ind. < δίδωμι 1 pl. act. Pres. ind. < ἵστημι 2 pl. mid. Aor. ind. < τίθημι 3 sg. mid./pass. Pres. ind. < δίδωμι 3 sg. act. Pres. ind. < ἀφίημι 2 sg. mid./pass. Pres. ind. < ἵστημι 3 sg. act. Impf. ind. < τίθημι 2 pl. act. Pres. ind. < δίδωμι 3 sg. mid. Aor. ind. < ἀφίημι 3 sg. act. Aor. ind. < ἵστημι 3 pl. act. Pres. ind. < δίδωμι 3 pl. act. Aor. ind. < τίθημι 1 pl. act. Aor. ind. < ἀφίημι 3 sg. mid. Aor. ind. < δίδωμι 3 sg. mid./pass. Pres. ind. < ἀφίημι 1 sg. act. Aor. ind. < ἵστημι 1 sg. mid./pass. Pres. ind. < τίθημι 32

33 Subjunctive Parsing Practice βάλλῃς διώξητε ἀκούω γενηθῶ λαμβάνωμεν ποιῇ ἔρχηται πιστεύσῃ πιστεύῃ διδῶτε εἴπωσι πεσώμεθα ἐνέχθῃς ἔλθησθε γινώσκῃ 2 sg. act. Pres. subjn. < βάλλω 2 pl. act. Aor. subjn. < διώκω 1 sg. act. Pres. ind./subjn. < ἀκούω 1 sg. pass. Aor. subjn. < γίνομαι 1 pl. act. Pres. subjn. < λαμβάνω 3 sg. act. Pres. subjn. < ποιέω 2 sg. mid./pass. Pres. ind./subjn. < ποιέω 3 sg. mid./pass. Pres. subjn. < ἔρχομαι 3 sg. act. Aor. subjn. < πιστεύω 2 sg. mid. Aor. subjn. < πιστεύω 2 sg. mid. Fut. ind. < πιστεύω 3 sg. act. Pres. subjn. < πιστεύω 2 sg. mid./pass. Pres. ind./subjn. < πιστεύω 2 pl. act. Pres. subjn. < δίδωμι 3 pl. act. Aor. subjn. < λέγω 1 pl. mid. Aor. subjn. < πίπτω 2 sg. pass. Aor. subjn. < φέρω 2 pl. mid. Aor. subjn. < ἔρχομαι 3 sg. act. Pres. subjn. < γινώσκω 2 sg. mid./pass. Pres. ind./subjn. < γινώσκω 33

34 Imperative Verbs Parsing Practice ἄκουσον διδάσκετε βάλλε πεμψάσθω γραφέτωσαν νίκα ἀγάγετε δοξάζου διδότωσαν φάγε ἐγειράτω θεραπεύθητι βλέψαι λάβεσθε εἰρήσθω βαπτίζετε πεινάτω 2 sg. act. Aor. imv. < ἀκούω 2 sp. act. Pres. imv. < διδάσκω 2 sg. act. Pres. imv. < βάλλω 3 sg. mid. Aor. imv. < πέμπω 3 pl. act. Pres. imv. < γράφω 2 sg. act. Pres. imv. < νικάω 2 pl. act. Aor. imv. < ἄγω 2 sg. mid./pass. Pres. imv. < δοξάζω 3 pl. act. Pres. imv. < δίδωμι 2 sg. act. Aor. imv. < ἐσθίω 3 sg. act. Aor. imv. < ἐγείρω 2 sg. pass. Aor. imv. < θεραπεύω 2 sg. mid. Aor. imv. < βλέπω Aor. act. inf. < βλέπω 2 pl. mid. Aor. imv. < λαμβάνω 3 sg. mid./pass. Pf. imv. < λέγω 2 pl. act. Pres. ind./imv. < βαπτίζω 3 sg. act. Pres. imv. < πεινάω 34

35 Infinitive Verbs Parsing Practice γράψασθαι ἀρέσκεσθαι ταράσσειν διψᾶν λαβεῖν βλέψαι λυθῆναι δεδιωκέναι τιθέναι θεράπευσαι αἰτήσασθαι ἠγόρασθαι γενήσεσθαι ἄνοιξαι φαγεῖν δείκνυσθαι βλάπτειν Aor. mid. inf. < γράφω Pres. mid./pass. inf. < ἀρέσκω Pres. act. inf. < ταράσσω Pres. act. inf. < διψάω Aor. act. inf. < λαμβάνω Aor. act. inf. < βλέπω 2 sg. mid. Aor. imv. < βλέπω Aor. pass. inf. < λύω Pf. act. inf. < διώκω Pres. act. inf. < τίθημι Aor. act. inf. < θεραπεύω Aor. mid. inf. < αἰτέω Pf. mid./pass. inf. < ἀγοράζω Fut. mid. ind. < γίνομαι Aor. act. inf. < ἀνοίγω Aor. act. inf. < ἐσθίω Pres. mid./pass. inf. < δείκνυμι Pres. act. inf. < βλάπτω 35

36 Participle Verbs Parsing Practice βλέποντος πεπιστευκότες ἀκούσαντος ἀκουόντων ἀκουούσων λάβον βεβληκυίας γενόμενον γίνωσκον θεραπεύσασα βεβαπτισμένου ἐχόμενον γνόντων γραφούσης ἱσταμένῃ σῴσων gen. sg. act. masc./neut. Pres. ptc. < βλέπω nom. pl. act. masc. Pf. ptc. < πιστεύω gen. sg. act. masc./neut. Aor. ptc. < ἀκούω gen. pl. act. masc./neut. Pres. ptc. < ἀκούω gen. pl. act. fem. Pres. ptc. < ἀκούω nom./acc. sg. act. neut. Aor. ptc. < λαμβάνω gen. sg. act. fem. Pf. ptc. < βάλλω acc. pl. act. fem. Pf. ptc. < βάλλω acc. sg. mid. masc. Aor. ptc. < γίνομαι nom./acc. sg. mid. Aor. ptc. < γίνομαι nom./acc. sg. act. neut. Pres. ptc. < γινώσκω nom. sg. act. fem. Aor. ptc. < θεραπεύω gen. sg. mid./pass. masc./neut. Pf. ptc. < βαπτίζω acc. sg. mid./pass. masc. Pres. ptc. < ἔχω nom./acc. sg. mid./pass. neut. Pres. ptc. < ἔχω gen. pl. act. masc./neut. Aor. ptc. < γινώσκω gen. sg. act. fem. Pres. ptc. < γράφω dat. sg. mid./pass. fem. Pres. ptc. < ἵστημι nom. sg. act. masc. Aor. ptc. < σῴζω 36

37 Mixed Verb Parsing Practice λέγεις ἐβλέψαμεν λαμβάνωμεν δοξάζοντος ἐξεβαλόμην ἀποστέλλονται ἠκούσασθε στῆτε εὑρεθήσεσθε αἴρουσα ἐβάπτιζον γινώσκῃ ἠγάπων ἄγειν σέσῳσται διδαχθέντας θεράπευσον 2 sg. act. Pres. ind. < λέγω 1 pl. act. Aor. ind. < βλέπω 1 pl. act. Pres. subjn. < λαμβάνω gen. sg. act. masc./neut. Pres. ptc. < δοξάζω 1 sg. mid. Aor. ind. < ἐκβάλλω 3 pl. mid./pass. Pres. ind. < ἀποστέλλω 2 pl. mid. Aor. ind. < ἀκούω 2 pl. act. Aor. subjn. < ἵστημι 2 pl. pass. Fut. ind. < εὑρίσκω nom. sg. act. fem. Pres. ptc. < αἴρω 1 sg./3 pl. act. Impf. ind. < βαπτίζω 3 sg. act. Pres. subjn. < γινώσκω 2 sg. mid./pass. Pres. ind./subjn. < γινώσκω 1 sg./3 pl. act. Impf. ind. < ἀγαπάω Pres. act. inf. < ἄγω 3 sg. mid./pass. Pf. ind. < σῴζω acc. pl. pass. masc. Aor. ptc. < διδάσκω 2 sg. act. Aor. imv. < θεραπεύω 37

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

Croy Lesson 10. Kind of action and time of action. and/or Redup. using the verb λύω

Croy Lesson 10. Kind of action and time of action. and/or Redup. using the verb λύω A Lesson 10 Vocabulary Summer Greek Croy Lesson 10 Ω ἄγω αἴρω ἀναβαίνω ἀπέρχοµαι ἀποθνῄσκω ἀποκτείνω καταβαίνω µέλλω ὀφείλω συνάγω ἀπόστολος, ὁ ἱερόν, τό παρά (G,D,A) (+ gen.) from; (+ dat.) beside, with,

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

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων

Croy Lesson 18. First Declension. THIRD Declension. Second Declension. SINGULAR PLURAL NOM -α / -η [-ης]* -αι. GEN -ας / -ης [-ου]* -ων Croy Lesson 18 First Declension SINGULAR PLURAL NOM -α / -η [-ης]* -αι GEN -ας / -ης [-ου]* -ων DAT -ᾳ / -ῃ -αις ACC -αν / -ην -ας VOC -α / -η -αι *Masculine Nouns of First Declension Second Declension

Διαβάστε περισσότερα

d. Case endings (Active follows declension patterns, Middle follows declension patterns)

d. Case endings (Active follows declension patterns, Middle follows declension patterns) Mounce 8 Handout: Aorist-stem PTCs Dr. Phillip Marshall. st Aorist Active and Middle PTC formations: a. Use Aorist Active stem, UN-augmented (not indicative!) b. Tense formative: -σα- c. Participle morpheme:

Διαβάστε περισσότερα

Mounce Handout: Introduction to Participles (PTCs), Present-stem PTCs Dr. Phillip Marshall

Mounce Handout: Introduction to Participles (PTCs), Present-stem PTCs Dr. Phillip Marshall Mounce 26-27 Handout: Introduction to Participles (PTCs), Present-stem PTCs Dr. Phillip Marshall What are PTCs?. Participles are verbal adjectives!! They have verbal characteristics (can be marked in Greek

Διαβάστε περισσότερα

Present Participles. Verbal Adjectives with Present Aspect. A lesson for the Paideia web-app Ian W. Scott, 2015

Present Participles. Verbal Adjectives with Present Aspect. A lesson for the Paideia web-app Ian W. Scott, 2015 Present Participles Verbal Adjectives with Present Aspect A lesson for the Paideia web-app Ian W. Scott, 2015 Participles with Present Aspect Participle = a verbal adjective Allows a whole clause to tell

Διαβάστε περισσότερα

NOM -**- [**] -ες / -εις [-α ] GEN -ος / -ως / -ους -ων. DAT -ι -σι. ACC -α / -ιν [**] -ας / -εις [-α ]

NOM -**- [**] -ες / -εις [-α ] GEN -ος / -ως / -ους -ων. DAT -ι -σι. ACC -α / -ιν [**] -ας / -εις [-α ] Croy Lesson 18 First Declension SINGULAR PLURAL NOM -α / -η [-ης]* -αι GEN -ας / -ης [-ου]* -ων DAT -ᾳ / -ῃ -αις ACC -αν / -ην -ας VOC -α / -η -αι *Masculine Nouns of First Declension Second Declension

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

Croy Lessons Second Declension. First Declension PARTICIPLES. THIRD Declension. -αι -ας. -ον. -οι. -ος. / -ης. -ων. -ου. -αν. / -ον.

Croy Lessons Second Declension. First Declension PARTICIPLES. THIRD Declension. -αι -ας. -ον. -οι. -ος. / -ης. -ων. -ου. -αν. / -ον. Croy Lessons 18-20 Greek Verb Formation Αug Redp STEM Tense Theme Ending PRES ACT -- STEM -- o/ε PRES M/P/D -- STEM -- o/ε IMPF ACT ἐ STEM -- o/ε ΙΜPF M/P ἐ STEM -- o/ε FUT ACT -- STEM σ o/ε FUT M/D --

Διαβάστε περισσότερα

Summer Greek. Greek Verbs - TENSE ASPECT. Greek Verbs. Greek Verbs. Greek Verbs. Greek Verbs. Croy Lesson 9

Summer Greek. Greek Verbs - TENSE ASPECT. Greek Verbs. Greek Verbs. Greek Verbs. Greek Verbs. Croy Lesson 9 A - TENSE ASPECT Summer Greek Croy Lesson 9 Ω KIND of action CONTINUING (ongoing, linear) COMPLETED (with result or ongoing effect) SIMPLE (affirmation of action w/out regard to duration or completion)

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

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

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014

LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV. 18 February 2014 LESSON 14 (ΜΑΘΗΜΑ ΔΕΚΑΤΕΣΣΕΡΑ) REF : 202/057/34-ADV 18 February 2014 Slowly/quietly Clear/clearly Clean Quickly/quick/fast Hurry (in a hurry) Driver Attention/caution/notice/care Dance Σιγά Καθαρά Καθαρός/η/ο

Διαβάστε περισσότερα

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

Summer Greek. Lesson 10 Vocabulary. Greek Verbs using the verb λύω. Greek Verbs. Greek Verbs: Conjugating. Greek Verbs: Conjugating.

Summer Greek. Lesson 10 Vocabulary. Greek Verbs using the verb λύω. Greek Verbs. Greek Verbs: Conjugating. Greek Verbs: Conjugating. A Lesson 10 Vocabulary Summer Greek Croy Lesson 10 Ω ἄγω αἴρω ἀναβαίνω ἀπέρχοµαι ἀποθνῄσκω ἀποκτείνω καταβαίνω µέλλω ὀφείλω συνάγω ἀπόστολος, ὁ ἱερόν, τό παρά (G,D,A) ὑπέρ (G,A) TENSE => KIND of action

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

Croy Lesson 9. => Kind of action and time of action. using the verb λύω

Croy Lesson 9. => Kind of action and time of action. using the verb λύω A - TENSE ASPECT Summer Greek 2009 Croy Lesson 9 Ω KIND of action CONTINUING (ongoing, linear) COMPLETED (with result or ongoing effect) SIMPLE (affirmation of action w/out regard to duration or completion)

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

Croy Lessons GEN GEN. Αug Redp STEM Tense Theme Ending. *Masculine Nouns of First Declension

Croy Lessons GEN GEN. Αug Redp STEM Tense Theme Ending. *Masculine Nouns of First Declension Croy Lessons 18-20 Greek Verb Formation Αug Redp STEM Tense Theme Ending PRES ACT -- STEM -- o/ε PRES M/P/D -- STEM -- o/ε IMPF ACT ἐ STEM -- o/ε ΙΜPF M/P ἐ STEM -- o/ε FUT ACT -- STEM σ o/ε FUT M/D --

Διαβάστε περισσότερα

Croy Lessons PARTICIPLES PARTICIPLES PARTICIPLES PARTICIPLES PARTICIPLES. >> CIRCUMSTANTIAL (ADVERBIAL) Under the circumstance of (UTC )

Croy Lessons PARTICIPLES PARTICIPLES PARTICIPLES PARTICIPLES PARTICIPLES. >> CIRCUMSTANTIAL (ADVERBIAL) Under the circumstance of (UTC ) Croy Lessons 18-20 Greek Verb Formation Αug Redp STEM Tense Theme Ending PRES ACT -- STEM -- o/ε PRES M/P/D -- STEM -- o/ε IMPF ACT ἐ STEM -- o/ε ΙΜPF M/P ἐ STEM -- o/ε FUT ACT -- STEM σ o/ε FUT M/D --

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

Summer Greek. Greek Verbs -TENSE ASPECT. Greek Verbs. Greek Verbs. Greek Verbs. Greek Verbs. Croy Lesson 9. KINDof action.

Summer Greek. Greek Verbs -TENSE ASPECT. Greek Verbs. Greek Verbs. Greek Verbs. Greek Verbs. Croy Lesson 9. KINDof action. A -TENSE ASPECT Summer Greek Croy Lesson 9 Ω KINDof action CONTINUING (ongoing, linear) COMPLETED (with result or ongoing effect) SIMPLE (affirmation of action w/out regard to duration or completion) TIME

Διαβάστε περισσότερα

PERSON PRIMARY. Aorist. Present Future Perfect (Subjunctive) Aorist. Passive. Future SECONDARY. Passive. Imperfect Aorist Pluperfect (Optative)

PERSON PRIMARY. Aorist. Present Future Perfect (Subjunctive) Aorist. Passive. Future SECONDARY. Passive. Imperfect Aorist Pluperfect (Optative) Croy Lesson 8 PERSON Who is acting NUMBER Endings: and S/P Greek Verbs Kind (and with Indic, Time) of action TENSE Imperfect Manner in which action is regarded by subject MOOD Indicative Infinitive Imperative

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

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

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

Non-Indicative Verbs of the LXX, New Testament, Josephus and Philo (in alphabetical order)

Non-Indicative Verbs of the LXX, New Testament, Josephus and Philo (in alphabetical order) Non-Indicative Verbs of the LXX, New Testament, Josephus and Philo (in alphabetical order) v = verb s = subjunctive n = infinitive d = imperative p = present f = future a = aorist x = perfect a = active

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

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

Summer Greek. Lesson 10 Vocabulary. Greek Verbs. Greek Verbs. Greek Verbs: Conjugating. Greek Verbs: Conjugating. Croy Lesson 10

Summer Greek. Lesson 10 Vocabulary. Greek Verbs. Greek Verbs. Greek Verbs: Conjugating. Greek Verbs: Conjugating. Croy Lesson 10 A Lesson 10 Vocabulary Summer Greek Croy Lesson 10 Ω ἄγω αἴρω ἀναβαίνω ἀπέρχοµαι ἀποθνῄσκω ἀποκτείνω καταβαίνω µέλλω ὀφείλω συνάγω ἀπόστολος, ὁ ἱερόν, τό παρά (G,D,A) (+ gen.) from; (+ dat.) beside, with,

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

Croy Lessons Second Declension. First Declension PARTICIPLES. THIRD Declension SINGULAR PLURAL SINGULAR PLURAL. NOM -α / -η [-ης]* -αι

Croy Lessons Second Declension. First Declension PARTICIPLES. THIRD Declension SINGULAR PLURAL SINGULAR PLURAL. NOM -α / -η [-ης]* -αι Croy Lessons 18-20 Greek Verb Formation Αug Redp STEM Tense Theme Ending PRES ACT -- STEM -- o/ε PrimAct PRES M/P/D -- STEM -- o/ε PrimMP IMPF ACT ἐ STEM -- o/ε SecAct ΙΜPF M/P ἐ STEM -- o/ε SecMP FUT

Διαβάστε περισσότερα

GREEK GRAMMAR I Future Active and Middle-Deponent Indicative Tense Dr. Marshall

GREEK GRAMMAR I Future Active and Middle-Deponent Indicative Tense Dr. Marshall GREEK GRAMMAR I Future Active and Middle-Deponent Indicative Tense Dr. Marshall I. Future Active Indicative A. Basics: Stem: The Greek future tense uses the Future Active Stem (sometimes the same as the

Διαβάστε περισσότερα

Concrete Mathematics Exercises from 30 September 2016

Concrete Mathematics Exercises from 30 September 2016 Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)

Διαβάστε περισσότερα

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS

CHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =

Διαβάστε περισσότερα

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

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

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

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

Croy Lesson 9. => Kind of action and time of action. using the verb λύω

Croy Lesson 9. => Kind of action and time of action. using the verb λύω A - TENSE ASPECT Summer Greek Croy Lesson 9 Ω KIND of action CONTINUING (ongoing, linear) COMPLETED (with result or ongoing effect) SIMPLE (affirmation of action w/out regard to duration or completion)

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

Croy Lessons Participles

Croy Lessons Participles A Croy Lessons 1820 Aorist Passive Perfect Ω How is studying functioning? I was studying Greek. >> PERIPHRASTIC (SUPPL.) Studying Greek, I sometimes want to scream. >> (ADV.) VERBAL ADJECTIVES The seminarian

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

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

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

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

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

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

ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ

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

Διαβάστε περισσότερα

Section 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

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

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit

Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ting Zhang Stanford May 11, 2001 Stanford, 5/11/2001 1 Outline Ordinal Classification Ordinal Addition Ordinal Multiplication Ordinal

Διαβάστε περισσότερα

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

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes

Paper Reference. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing. Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Centre No. Candidate No. Paper Reference(s) 1776/04 Edexcel GCSE Modern Greek Paper 4 Writing Thursday 21 May 2009 Afternoon Time: 1 hour 15 minutes Materials required for examination Nil Paper Reference

Διαβάστε περισσότερα

Notes on the Open Economy

Notes on the Open Economy Notes on the Open Econom Ben J. Heijdra Universit of Groningen April 24 Introduction In this note we stud the two-countr model of Table.4 in more detail. restated here for convenience. The model is Table.4.

Διαβάστε περισσότερα

Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz

Solutions to the Schrodinger equation atomic orbitals. Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz Solutions to the Schrodinger equation atomic orbitals Ψ 1 s Ψ 2 s Ψ 2 px Ψ 2 py Ψ 2 pz ybridization Valence Bond Approach to bonding sp 3 (Ψ 2 s + Ψ 2 px + Ψ 2 py + Ψ 2 pz) sp 2 (Ψ 2 s + Ψ 2 px + Ψ 2 py)

Διαβάστε περισσότερα

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect)

Ρηματική άποψη. (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) 15 Ρηματική άποψη (Aspect of the verb) Α. Θέματα και άποψη του ρήματος (Verb stems and aspect) imperfective perfective Verb forms in Modern Greek are based either on the imperfective or the perfective

Διαβάστε περισσότερα

The challenges of non-stable predicates

The challenges of non-stable predicates The challenges of non-stable predicates Consider a non-stable predicate Φ encoding, say, a safety property. We want to determine whether Φ holds for our program. The challenges of non-stable predicates

Διαβάστε περισσότερα

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

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

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

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

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

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

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

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------

Inverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- ----------------- Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin

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

VERBS: memory aids through lesson 9 ACTIVE PRESENT AND IMPERFECT IMPERATIVE

VERBS: memory aids through lesson 9 ACTIVE PRESENT AND IMPERFECT IMPERATIVE Verbs. thr.less9, p1 moods tenses INDICATIVE VERBS: memory aids through lesson 9 ACTIVE PRESENT AND IMPERFECT present present stem + / primary person endings present stem + / ending of infinitive I stop

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

21. δεινός: 23. ἀγορά: 24. πολίτης: 26. δοῦλος: 28. σῶμα: 31. Ἑλλας: 32. παῖς: 34. ὑπέρ: 35. νύξ: 39. μῶρος: 40. ἀνήρ:

21. δεινός: 23. ἀγορά: 24. πολίτης: 26. δοῦλος: 28. σῶμα: 31. Ἑλλας: 32. παῖς: 34. ὑπέρ: 35. νύξ: 39. μῶρος: 40. ἀνήρ: Vocabulary: Give one English meaning and nothing more. 1. ἔτος: 2. τότε: 3. θάνατος: 4. ἐλαύνω: 5. γυνή: 6. ὑπό: 7. λείπω: 8. περί: 9. πόλις: 10. ἄστυ: 11. νομίζω: 12. ἀπάγω: 13. τεῖχος: 14. ὀλίγος: 15.πίπτω:

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

Διαβάστε περισσότερα

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds! MTH U341 urface Integrals, tokes theorem, the divergence theorem To be turned in Wed., Dec. 1. 1. Let be the sphere of radius a, x 2 + y 2 + z 2 a 2. a. Use spherical coordinates (with ρ a) to parametrize.

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

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.

Exercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1. Exercises 0 More exercises are available in Elementary Differential Equations. If you have a problem to solve any of them, feel free to come to office hour. Problem Find a fundamental matrix of the given

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

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

Partial Differential Equations in Biology The boundary element method. March 26, 2013

Partial Differential Equations in Biology The boundary element method. March 26, 2013 The boundary element method March 26, 203 Introduction and notation The problem: u = f in D R d u = ϕ in Γ D u n = g on Γ N, where D = Γ D Γ N, Γ D Γ N = (possibly, Γ D = [Neumann problem] or Γ N = [Dirichlet

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

VBA ΣΤΟ WORD. 1. Συχνά, όταν ήθελα να δώσω ένα φυλλάδιο εργασίας με ασκήσεις στους μαθητές έκανα το εξής: Version 25-7-2015 ΗΜΙΤΕΛΗΣ!!!!

VBA ΣΤΟ WORD. 1. Συχνά, όταν ήθελα να δώσω ένα φυλλάδιο εργασίας με ασκήσεις στους μαθητές έκανα το εξής: Version 25-7-2015 ΗΜΙΤΕΛΗΣ!!!! VBA ΣΤΟ WORD Version 25-7-2015 ΗΜΙΤΕΛΗΣ!!!! Μου παρουσιάστηκαν δύο θέματα. 1. Συχνά, όταν ήθελα να δώσω ένα φυλλάδιο εργασίας με ασκήσεις στους μαθητές έκανα το εξής: Εγραφα σε ένα αρχείο του Word τις

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

Srednicki Chapter 55

Srednicki Chapter 55 Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

Croy Lesson 23. Greek Verbs. Greek Verbs. Greek Verbs. TENSE => KIND of action. VOICE => relation of subject to action

Croy Lesson 23. Greek Verbs. Greek Verbs. Greek Verbs. TENSE => KIND of action. VOICE => relation of subject to action A Croy Lesson 23 TENSE => KIND of action CONTINUING (ongoing, linear) COMPLETED (with result or ongoing effect) SIMPLE (affirmation of action w/out regard to duration or completion) Ω and TIME of action

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

Εγκατάσταση λογισμικού και αναβάθμιση συσκευής Device software installation and software upgrade

Εγκατάσταση λογισμικού και αναβάθμιση συσκευής Device software installation and software upgrade Για να ελέγξετε το λογισμικό που έχει τώρα η συσκευή κάντε κλικ Menu > Options > Device > About Device Versions. Στο πιο κάτω παράδειγμα η συσκευή έχει έκδοση λογισμικού 6.0.0.546 με πλατφόρμα 6.6.0.207.

Διαβάστε περισσότερα

Summer Greek Lesson 3 - Vocabulary

Summer Greek Lesson 3 - Vocabulary A Summer Greek 2006 Ω ἀδελφή, ἡ ἀλήθεια, ἡ βασιλεία, ἡ δόξα, ἡ ἐκκλησία, ἡ ἔχω ζωή, ἡ ἡμέρα, ἡ θάλασσα, ἡ καρδία, ἡ φωνή, ἡ ὥρα, ἡ Parts of Speech NOUN - person, place, thing, quality, idea, or action

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Όλοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα μικρότεροι του 10000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Αν κάπου κάνετε κάποιες υποθέσεις

Διαβάστε περισσότερα

Perfect Participles. A lesson for the Paideia web-app Ian W. Scott, 2015

Perfect Participles. A lesson for the Paideia web-app Ian W. Scott, 2015 Perfect Participles A lesson for the Paideia web-app Ian W. Scott, 2015 Remember the Components of a Participle Stem Tense marker Connecting vowel Voice indicator Case ending Resulting form λυ σ α ντ ος

Διαβάστε περισσότερα

22.1: Root Aorist (Athematic Long-Vowel Aorist)

22.1: Root Aorist (Athematic Long-Vowel Aorist) 22.1: Root Aorist (Athematic Long-Vowel Aorist) A THIRD AORIST? In previous lessons you learned the following types of active aorist conjugations: ἔπαυσα First aorist (Lesson 9). A regular tense that we

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

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

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr

9.09. # 1. Area inside the oval limaçon r = cos θ. To graph, start with θ = 0 so r = 6. Compute dr 9.9 #. Area inside the oval limaçon r = + cos. To graph, start with = so r =. Compute d = sin. Interesting points are where d vanishes, or at =,,, etc. For these values of we compute r:,,, and the values

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

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011

ΚΥΠΡΙΑΚΟΣ ΣΥΝΔΕΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY 21 ος ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ Δεύτερος Γύρος - 30 Μαρτίου 2011 Διάρκεια Διαγωνισμού: 3 ώρες Απαντήστε όλες τις ερωτήσεις Μέγιστο Βάρος (20 Μονάδες) Δίνεται ένα σύνολο από N σφαιρίδια τα οποία δεν έχουν όλα το ίδιο βάρος μεταξύ τους και ένα κουτί που αντέχει μέχρι

Διαβάστε περισσότερα

UNIVERSITY OF CALIFORNIA. EECS 150 Fall ) You are implementing an 4:1 Multiplexer that has the following specifications:

UNIVERSITY OF CALIFORNIA. EECS 150 Fall ) You are implementing an 4:1 Multiplexer that has the following specifications: UNIVERSITY OF CALIFORNIA Department of Electrical Engineering and Computer Sciences EECS 150 Fall 2001 Prof. Subramanian Midterm II 1) You are implementing an 4:1 Multiplexer that has the following specifications:

Διαβάστε περισσότερα

Other Test Constructions: Likelihood Ratio & Bayes Tests

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

Διαβάστε περισσότερα

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

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

Διαβάστε περισσότερα