Notes on the Greek New Testament Day 6 January 6 th Matthew 5: Works frequently referenced in these notes on Matthew
|
|
- Παναγιώτης Κορνάρος
- 7 χρόνια πριν
- Προβολές:
Transcript
1 Notes on the Greek New Testament Day 6 January 6 th Matthew 5:27-48 Works frequently referenced in these notes on Matthew Hagner, Donald A Word Biblical Commentary Vols.33a & 33b: Matthew 1-13 & Matthew 14-28, Word Books, Dallas, 1993 & 1995 Morris, Leon The Gospel According to Matthew, Eerdmans, Grand Rapids, 1992 Verse 27 Ἠκούσατε ὅτι ἐρρέθη Οὐ μοιχεύσεις. See verse 21 for opening phrase. Many MSS, including TR, insert τοις ἀρχαιοις after ἐρρεθη, conforming to the pattern of vv 21 and 33. μοιχευω commit adultery Cf. Ex 20:14; Deut 5:18 also Matt 19:18. Verse 28 ἐγὼ δὲ λέγω ὑμῖν ὅτι πᾶς ὁ βλέπων γυναῖκα πρὸς τὸ ἐπιθυμῆσαι αὐτὴν ἤδη ἐμοίχευσεν αὐτὴν ἐν τῇ καρδίᾳ αὐτοῦ. βλεπω see, look γυνη, αικος f woman, wife ἐπιθυμεω long for, desire, lust after ἠδη adv now, already μοιχευω commit adultery Jesus is not saying that there is no difference between the thought and the deed but rather that sin begins in the heart (cf. James 1:14,15 also 2 Pet 2:14). Verses 29, 30 Jesus uses vivid imagery to highlight the importance of dealing with sin in a radical fashion. The eye is the medium through which temptation comes and the hand the instrument through which sin is performed. Verse 29 εἰ δὲ ὁ ὀφθαλμός σου ὁ δεξιὸς σκανδαλίζει σε, ἔξελε αὐτὸν καὶ βάλε ἀπὸ σοῦ, συμφέρει γάρ σοι ἵνα ἀπόληται ἓν τῶν μελῶν σου καὶ μὴ ὅλον τὸ σῶμά σου βληθῇ εἰς γέενναν. δεξιος, α, ον right σκανδαλιζω cause (someone) to sin ἔξελε Verb, 2 aor act imperat ἐξαιρεω pull out βαλλω throw, throw down "This picturesque repudiation of a prized part of the body shows vividly that there is to be no compromise with evil." Morris συμφερω usually impersonal it is better, it is profitable, it is useful ἀπόληται Verb, aor midd subj ἀπολλυμι destroy; midd be lost, perish, die εἱς, μια, ἑν gen ἐνος, μιας, ἑνος one μελος, ους n member, bodily part ὁλος, η, ον whole, all, complete σωμα, τος n body βληθῇ Verb, aor pass subj, 3 s βαλλω γεεννα, ης f see v.22 "The discipleship of the kingdom sometimes requires drastic measures." Hagner. "Better to go limping into heaven than leaping into hell." Bruner. Verse 30 καὶ εἰ ἡ δεξιά σου χεὶρ σκανδαλίζει σε, ἔκκοψον αὐτὴν καὶ βάλε ἀπὸ σοῦ, συμφέρει γάρ σοι ἵνα ἀπόληται ἓν τῶν μελῶν σου καὶ μὴ ὅλον τὸ σῶμά σου εἰς γέενναν ἀπέλθῃ. χειρ, χειρος f hand, power The mention of right hand is probably to signify the most valuable and skilled member. The same thought is thereby applied to the eye in the previous verse. ἐκκοπτω cut off, remove ἀπέλθῃ Verb, aor midd/pass subj, 2 s ἀπερχομαι The majority of MSS have βληθῃ instead of ἀπελθη here assimilating to the ending of the previous verse. Verses 31, 32 Deut 24:1 required a man who divorced his wife to give her a bill of divorce. The OT law was not intended to establish grounds for divorce but to regulate the abuses that might arise from it. However, it was the grounds for divorce that preoccupied Rabbinic discussion in Jesus day.
2 "The school of Shammai took a hard line and saw the meaning of 'some indecency' (Deut 24:1) as adultery, whereas the school of Hillel allowed a much wider range of interpretation, and, for example, permitted a man to divorce his wife if she spoiled his dinner... Against such a background Jesus calls on people to appreciate the true meaning and solemnity of marriage. We should bear in mind that he is laying down great principles that should guide conduct; he is not making laws or giving a precise list of occasions when divorce might take place." Morris Verse 31 Ἐρρέθη δέ Ὃς ἂν ἀπολύσῃ τὴν γυναῖκα αὐτοῦ, δότω αὐτῇ ἀποστάσιον. ἀπολυω release, set free, dismiss, divorce γυνη, αικος f woman, wife δότω Verb, aor act imperat, 3 s διδωμι ἀποστασιον, ου n written notice of divorce Cf Deut 24:1; Matt 19:7,8; Mk 10:4 Verse 32 ἐγὼ δὲ λέγω ὑμῖν ὅτι πᾶς ὁ ἀπολύων τὴν γυναῖκα αὐτοῦ παρεκτὸς λόγου πορνείας ποιεῖ αὐτὴν μοιχευθῆναι, καὶ ὃς ἐὰν ἀπολελυμένην γαμήσῃ μοιχᾶται. παρεκτος prep with gen except, apart from Hagner and others suggest that the exception clause was not part of Jesus' teaching since it weakens the antithesis. It reflects, he argues, the view of Matthew's community. Hagner writes, "The radical character of the righteousness of the kingdom demands a return to the standards of the Garden of Eden. The attitude of Jesus in 19:6 (cf. Mark 10:11, which lacks the exception clause) is absolute; it is indeed so stern that the disciples (who were hardly of a Hillelite persuasion on the subject) wonder who can tolerate such a high standard (19:10-11). Here is the antithesis to Deut 24:1... Moses allowed divorce and remarriage, without designating the remarried as adulterers because of the hardness of the hearts of the people. If, as we shall argue in the explanation of the parallel passage in chap. 19, followers of Jesus, recipients of the kingdom, are still not in this new era rid of their hard hearts, divorce and remarriage will continue to occur among them, just as it did among the people of God in the OT (see further comment on 19:3-12). Matthew's own insertion of the exception clauses, modifying the absolute teaching of Jesus, is just such an admission in the church of his day. Still, however, it is worth adding that conceding the hard realities of our continuing fallenness and the reality of forgiveness for those who fail must not allow us to weaken our commitment to continue to strive after the ideal." πορνεια, ας f sexual immorality μοιχαομαι commit adultery "The word rendered fornication strictly denotes sexual intercourse between unmarried people, and some have seen that meaning here. On this view, Jesus is saying that if two people get married and it is subsequently found that prior to the marriage one of them had committed fornication, then the marriage may be dissolved. But that seems to be confining the meaning in a way that is not common in the New Testament; the word is used for all sorts of sexual sins. It is much more likely that in this passage it signifies adultery." Morris. ὁς ἐαν see v.19 "The husband who divorces his wife causes her to commit adultery because in the culture of that day, unlike ours, a single woman could hardly survive on her own, except through prostitution. She was therefore bound to take another husband and so be made into an adulteress." Hagner. ἀπολελυμένην Verb, perf pass ptc, f acc s ἀπολυω γαμήσῃ Verb, aor act subj, 3 s γαμεω marry
3 "Among the Jews a man was not held to have committed adultery by engaging in sexual acts outside marriage unless his partner was herself a married woman. But Jesus does not distinguish between the man and the woman; either may commit adultery. It seems to have been a Christian idea that a man could commit adultery; others regarded sexual adventures as a normal part of life for a man. Jesus lays down the highest standards for both sexes. Divorce might happen, but it was not meant to be. Marriage is for life." Morris. Verses The Mosaic law expressly commanded swearing in the name of God (Deut 6:13; 10:20). Jesus "was interested in the fact that people seemed very ready to swear oaths. He regarded it as important that what his disciples said could always be relied on; it should not be necessary for them to back up their statements with oaths. This is in striking contrast to a good deal of Judaism, in which oaths evidently played a large part in life. The Mishnah has a complete tractate on oaths (Shebu'ot), dividing them into classes, giving examples of valid and invalid oaths etc." Morris Such traditions were concerned with the question of when a person might legitimately break their word. Verse 33 Πάλιν ἠκούσατε ὅτι ἐρρέθη τοῖς ἀρχαίοις Οὐκ ἐπιορκήσεις, ἀποδώσεις δὲ τῷ κυρίῳ τοὺς ὅρκους σου. παλιν again, once more (see v.21 for opening phrase) ἐπιορκεω break an oath, swear falsely ἀποδιδωμι give, render, give back, fulfil ὁρκος, ου m oath, vow Cf. Ex 20:7; Lev 19:12; Num 30:2; Deut 23: Verse 34 ἐγὼ δὲ λέγω ὑμῖν μὴ ὀμόσαι ὅλως μήτε ἐν τῷ οὐρανῷ, ὅτι θρόνος ἐστὶν τοῦ θεοῦ ὀμόσαι Verb, aor act infin ὀμνυω and ὀμνυμι swear, vow, make an oath ὁλως adv at all "He is not forbidding the taking of an oath in a law court or the like. The law said, "you shall... swear by his name" (Deut 6:13; 10:20), and Jesus himself responded when the High Priest put him on oath (26:63,64). He is saying in the strongest terms that those who follow him must speak the truth. They must never take the line that only when an oath is sworn need they be truthful." Morris. μητε and not; μητε... μητε neither... nor οὐρανος, ου m heaven θρονος, ου m throne Jews thought that only oaths taken in the name of God were absolutely binding and that by swearing 'by heaven' the oath might later be broken. Verse 35 μήτε ἐν τῇ γῇ, ὅτι ὑποπόδιόν ἐστιν τῶν ποδῶν αὐτοῦ μήτε εἰς Ἱεροσόλυμα, ὅτι πόλις ἐστὶν τοῦ μεγάλου βασιλέως γη, γης f earth ὑποποδιον, ου n footstool πους, ποδος m foot πολις, εως f city, town μεγας, μεγαλη, μεγα large, great βασιλευς, εως m king Verse 36 μήτε ἐν τῇ κεφαλῇ σου ὀμόσῃς, ὅτι οὐ δύνασαι μίαν τρίχα λευκὴν ποιῆσαι ἢ μέλαιναν. κεφαλη, ης f head ὀμόσῃς Verb, aor act subj, 2 s ὀμνυω δυναμαι can, be able to, be capable of εἱς, μια, ἑν gen ἐνος, μιας, ἑνος one τρίχα Noun, acc s θριξ, τριχος f hair λευκος, η, ον white, shining ποιῆσαι Verb, aor act infin ποιεω ἠ or μελας, αινα, αν gen ανος, αινης, ανος black Verse 37 ἔστω δὲ ὁ λόγος ὑμῶν ναὶ ναί, οὒ οὔ τὸ δὲ περισσὸν τούτων ἐκ τοῦ πονηροῦ ἐστιν. ἔστω Verb, pres act imperat, 3s εἰμι ναι yes, yes indeed, certainly Cf. James 5:12 περισσος, η, ον more πονηρος, α, ον evil, bad, wicked του πονηρου is ambiguous (as in 5:37; 6:13; 13:38). Lenski and Hagner think it is a reference to the 'evil one', i.e. the devil. "With the dawn of the new era comes a wholly new standard of righteousness, one in which a yes is really a yes and a no is really a no. It is a mistake, however, to take a biblicist approach to this passage that would disallow Christians from taking an oath, say in a court of justice. The issue is nothing less than and nothing more than truthfulness." Hagner.
4 Verses "Jesus is, of course, still dealing with great principles, not laying down rules. We must not think that he held that his followers should never right wrongs, for example, nor that he felt that they must give to every beggar who approaches them. Were this so, all Christians would live under tyranny and in a state of destitution. But the principle that we are to refrain from asserting our own rights and that we should put the needs of others before our own runs through all of life and marks the difference between the servant of God and the worldling." Morris. Verse 38 Ἠκούσατε ὅτι ἐρρέθη Ὀφθαλμὸν ἀντὶ ὀφθαλμοῦ καὶ ὀδόντα ἀντὶ ὀδόντος. (see v.21 for opening phrase) ἀντι prep with gen for, in place of ὀδους, ὀδοντος m tooth "This well known principle is found in Ex 21:24; Deut 19:21 and Lev 24:20 and also in the ancient code of Hammurabi. In its original intention the old Hebrew law was restrictive rather than permissive: it was designed to limit revenge and retaliation by fixing an exact compensation for injury. By this humane measure, the law of blood revenge (which could involve the destruction of a whole family in a feud) was greatly limited." Hill. Green says that in Jesus' day only the Saducees followed this rule literally, the Pharisees usually substituted fines. Verse 39 ἐγὼ δὲ λέγω ὑμῖν μὴ ἀντιστῆναι τῷ πονηρῷ ἀλλʼ ὅστις σε ῥαπίζει εἰς τὴν δεξιὰν σιαγόνα, στρέψον αὐτῷ καὶ τὴν ἄλλην ἀνθιστημι resist, oppose, withstand πονηρος, α, ον evil, bad, wicked Here, obviously, a human aggressor. "Jesus is referring to private retaliation, not to public order." Morris. ὁστις, ἡτις, ὁ τι who, which, whoever ῥαπιζω hit, strike δεξιος, α, ον right σιαγων, ονος f cheek Suggests insult rather than violence. στρέψον Verb, aor act imperat, 2 s στρεφω turn, turn around ἀλλος, η, ο another, other This injunction is not to be taken literally but asserts that disciples of Jesus are not to behave according to the principles of strict retaliation in asserting legal rights (cf. John 18:22,23 for the example of Jesus and Acts 23:22-25 for Paul see also Rom 12:18-21). Verse 40 καὶ τῷ θέλοντί σοι κριθῆναι καὶ τὸν χιτῶνά σου λαβεῖν, ἄφες αὐτῷ καὶ τὸ ἱμάτιον θελω wish, will κριθῆναι Verb, pres pass infin κρινω judge χιτων, ωνος m tunic, shirt (generally of garment worn next to the skin) λαβεῖν Verb, aor act infin λαμβανω ἀφιημι allow, let go ἱματιον, ου n garment, robe, cloak The ἱματιον was the outer cloak, used also for sleeping in at night. Cf. Ex 22:26-27, Deut 24:13 which forbids a plaintiff from claiming this outer garment. Cf. 1 Cor 6:7 for Paul's similar attitude. Verse 41 καὶ ὅστις σε ἀγγαρεύσει μίλιον ἕν, ὕπαγε μετʼ αὐτοῦ δύο. ἀγγαρευω force, press into service Used in Mt 27:32; Mk 15:21 of the soldiers forcing Simon of Cyrene to carry Jesus' cross. The verb is used of any compulsory requisition or conscription. μιλιον, ου n mile (of the Roman mile which was 8 σταδια or about 1618 yards) εἱς, μια, ἑν gen ἐνος, μιας, ἑνος one ὑπαγω go, go one's way, depart δυο gen & acc δυο dat δυσιν two "The first mile renders to Caesar the things that are Caesar's; the second mile, by meeting oppression with kindness, renders to God the things that are God's." Manson. Verse 42 τῷ αἰτοῦντί σε δός, καὶ τὸν θέλοντα ἀπὸ σοῦ δανίσασθαι μὴ ἀποστραφῇς. αἰτεω ask, request, demand δός Verb, aor act imperat, 2 s διδωμι θελω see v.40 δανίσασθαι Verb, aor midd infin δανειζω lend; midd borrow ἀποστραφῇς Verb, aor pass subj, 2 s ἀποστρεφω turn away Cf Psalm 37:21 and other portions of this psalm concerning the conduct and consequent reward (land in Ps 37) of the righteous.
5 Verses Postscript "The disciple does not insist on personal rights. Furthermore, the true disciple does more than is expected. He or she is free from society's low standards of expectation, being subject only to the will of the Father. The conduct of the disciple is filled with surprise for those who experience it. This element of surprise relates closely to and reflects the grace that is central to the gospel. It is the unworthy who have experienced the good things of the kingdom; and as they have experienced the surprise of unexpected grace, so they act in a similar manner toward the undeserving among them (cf. Luke 6:34-35)... Kingdom ethics demands not mechanical compliance to rules but a lifestyle governed by the free grace of God." Hagner. Verse 43 Ἠκούσατε ὅτι ἐρρέθη Ἀγαπήσεις τὸν πλησίον σου καὶ μισήσεις τὸν ἐχθρόν σου. (See v.21 for opening phrase) ἀγαπήσεις Verb, fut act indic, 2 s ἀγαπαω love, show love for πλησιον i) prep with gen near; ii) ὁ π. neighbour, fellow man. μισεω hate, despise, be indifferent to ἐχθρος, α, ον enemy, one hated This latter phrase does not, of course, come from the OT. Some think that it reflects the instruction of the Qumran Manual of Discipline which advises the community "to love everyone whom God has elected, and to hate everyone whom God has rejected... to hate the sons of darkness." Hagner comments, "Clearly, neither Jesus' listeners not Matthew's readers would have been surprised by the added words, since the traditional interpretation had become regularly associated with the text. The 'neighbour' meant fellow Jew; the 'enemy' meant Gentile." Jesus rejects all restriction of the command. Cf. Lk. 10: Verse 44 ἐγὼ δὲ λέγω ὑμῖν, ἀγαπᾶτε τοὺς ἐχθροὺς ὑμῶν καὶ προσεύχεσθε ὑπὲρ τῶν διωκόντων ὑμᾶς ἀγαπαω love, show love for ἐχθρος, α, ον enemy, one hated The majority of MSS (D L W Θ f 13 TR lat sy (p),h ) insert the after ἐχθρους (with occasional slight modifications), εὐλογειτε τοις καταρωμενους ὑμας, καλως ποιειτε τοις μισουσιν ὑμας, and after προσεύχεσθε the words ἐπηρεαζοντων ὑμας και. This material is obviously borrowed from the parallel in Luke 6: The shorter text is supported by א B et al. προσευχομαι pray διωκω persecute, seek after Love, as always in the OT and NT is not mere sentiment and emotion, it involves action. Verse 45 ὅπως γένησθε υἱοὶ τοῦ πατρὸς ὑμῶν τοῦ ἐν οὐρανοῖς, ὅτι τὸν ἥλιον αὐτοῦ ἀνατέλλει ἐπὶ πονηροὺς καὶ ἀγαθοὺς καὶ βρέχει ἐπὶ δικαίους καὶ ἀδίκους. ὁπως (or ὁπως ἀν) that, in order that γένησθε Verb, aor midd depo subj, 2 pl γινομαι Our love is to reflect the quality of God's love. Where would we be if God had loved only those who love him? He loved us while we were enemies (v.44). ἡλιος, ου m the sun ἀνατελλω rise, dawn, shine πονηρος, α, ον evil, bad, wicked ἀγαθος, η, ον good, useful, fitting βρεχω rain, send rain δικαιος, α, ον righteous ἀδικος, ον evil, sinful, unjust "The different words for 'good' (ἀγαθους, 'good,' and δικαιους, 'just') represent stylistic variations, as does the chiastic order of the nouns. The 'bad' are, from the context, analogous to the 'enemies' of God. To love one's enemies is, then, to treat them as God treats those who have rebelled against him." Hagner. Verse 46 ἐὰν γὰρ ἀγαπήσητε τοὺς ἀγαπῶντας ὑμᾶς, τίνα μισθὸν ἔχετε; οὐχὶ καὶ οἱ τελῶναι τὸ αὐτὸ ποιοῦσιν; ἐαν if μισθος, ου m pay, reward, gain οὐχι (emphatic form of οὐ) not, no; used in questions expecting an affirmative answer. τελωνης, ου m tax collector
6 Verse 47 καὶ ἐὰν ἀσπάσησθε τοὺς ἀδελφοὺς ὑμῶν μόνον, τί περισσὸν ποιεῖτε; οὐχὶ καὶ οἱ ἐθνικοὶ τὸ αὐτὸ ποιοῦσιν; ἀσπάσησθε Verb, aor midd dep subj, 2 pl ἀσπαζομαι greet, welcome The salutation is more than a gesture of greeting, it expresses a desire for the peace and welfare of the other. μονον adv only, alone περισσος, η, ον more ἐθνικος, η, ον pagan, heathen, Gentile Many MSS, including the TR, read τελωναι rather than ἐθνικοι. Verse 48 Ἔσεσθε οὖν ὑμεῖς τέλειοι ὡς ὁ πατὴρ ὑμῶν ὁ οὐράνιος τέλειός ἐστιν. Cf. Lk 6:36. ἔσεσθε Verb, fut indic, 2 pl εἰμι τελειος, α, ον complete, perfect, mature Many MSS, including TR, have the slightly more emphatic ὡσπερ rather than ὡς πατηρ, πατρος m father οὐρανιος, ον heavenly, in heaven, from heaven "This call does not differ from that in the OT: 'Be holy for I, the Lord God am holy.' (Lev 19:2; cf. 1 Pet 1:16). The LXX even uses the same word (τελειος, translating מ ים (תּ at one point (Deut 18:13): 'Be perfect before the Lord your God.' The perfection here is the fulfillment of the Mosaic law... but now according to its definitive interpretation by the Messiah who brings the kingdom. Love for God and one's neighbour (and particularly, love for one's enemies) will be described by Matthew as the commandments upon which thus all the law and the prophets depend (22:40). For Matthew, to be τελειος means to fulfill the law through the manifestation of an unrestricted love (including even enemies) that is the reflection of God's love. This unrestricted love preeminently embodies ethical perfection. This perfection, and nothing less, is that to which Jesus calls his disciples." Hagner.
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
Notes on the Greek New Testament Week 134 Matthew 5:21-48
Notes on the Greek New Testament Week 134 Matthew 5:21-48 Day 666: Matthew 5:21-26 Verses 21-48 The contrasts drawn by Jesus in these verses are not, as some argue, contrasts between Old Testament teaching
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
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
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
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.
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
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
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
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,
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
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
ΑΓΓΛΙΚΑ ΙΙΙ. Ενότητα 12b: The Little Prince. Ζωή Κανταρίδου Τμήμα Εφαρμοσμένης Πληροφορικής
Ενότητα 12b: The Little Prince Τμήμα Εφαρμοσμένης Πληροφορικής Άδειες Χρήσης Το παρόν εκπαιδευτικό υλικό υπόκειται σε άδειες χρήσης Creative Commons. Για εκπαιδευτικό υλικό, όπως εικόνες, που υπόκειται
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.
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
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
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
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.
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
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
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
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
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
LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV. 10 December 2013
LESSON 6 (ΜΑΘΗΜΑ ΕΞΙ) REF : 201/045/26-ADV 10 December 2013 I get up/i stand up I wash myself I shave myself I comb myself I dress myself Once (one time) Twice (two times) Three times Salary/wage/pay Alone/only
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
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
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)
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) =
LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG. 4 March 2014
LESSON 16 (ΜΑΘΗΜΑ ΔΕΚΑΕΞΙ) REF : 102/018/16-BEG 4 March 2014 Family η οικογένεια a/one(fem.) μία a/one(masc.) ένας father ο πατέρας mother η μητέρα man/male/husband ο άντρας letter το γράμμα brother ο
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,
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
Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο
Κατανοώντας και στηρίζοντας τα παιδιά που πενθούν στο σχολικό πλαίσιο Δρ. Παναγιώτης Πεντάρης - University of Greenwich - Association for the Study of Death and Society (ASDS) Περιεχόµενα Εννοιολογικές
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
Writing for A class. Describe yourself Topic 1: Write your name, your nationality, your hobby, your pet. Write where you live.
Topic 1: Describe yourself Write your name, your nationality, your hobby, your pet. Write where you live. Χρησιμοποίησε το and. WRITE your paragraph in 40-60 words... 1 Topic 2: Describe your room Χρησιμοποίησε
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
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
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
I haven t fully accepted the idea of growing older
I haven t fully accepted the idea of growing older 1 Peter Authorship Questions Πέτρος ἀπόστολος Ἰησοῦ Χριστοῦ ἐκλεκτοῖς παρεπιδήμοις διασπορᾶς Πόντου, Γαλατίας, Καππαδοκίας, Ἀσίας 1 Peter Authorship
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.
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
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
Οδηγίες Αγοράς Ηλεκτρονικού Βιβλίου Instructions for Buying an ebook
Οδηγίες Αγοράς Ηλεκτρονικού Βιβλίου Instructions for Buying an ebook Βήμα 1: Step 1: Βρείτε το βιβλίο που θα θέλατε να αγοράσετε και πατήστε Add to Cart, για να το προσθέσετε στο καλάθι σας. Αυτόματα θα
LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26. 18 November 2014
LESSON 26 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΕΞΙ) REF : 102/030/26 18 November 2014 But Weekend I love The song I sing I smile I laugh Greek (thing) Greek(people) Greek (man) αλλά (το) Σαββατοκύριακο αγαπώ (το) τραγούδι τραγουδώ
LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28. 2 December 2014
LESSON 28 (ΜΑΘΗΜΑ ΕΙΚΟΣΙ ΟΚΤΩ) REF : 201/033/28 2 December 2014 Place/Seat Right (noun) I am right I am not right It matters It does not matter The same (singular) The same (Plural) Η θέση Το δίκιο Έχω
2 Thessalonians 3. Greek
Book Chapter Verse Interlinear English Word # in 2 Thess Greek # of letters # of words Numeric value 140301 00548 ΤΟ 2 370 140301 finally 00549 ΛΟΙΠΟΝ 6 310 140301 pray 00550 ΠΡΟΣΕΥΧΕΣΘΕ 11 1674 140301
If You Build It, They May Come Parable of the Tower Builder
If You Build It, They May Come Parable of the Mark Vitalis Hoffman www.crossmarks.com Τίς γὰρ ἐξ ὑµῶν θέλων πύργον οἰκοδοµῆσαι οὐχὶ πρῶτον καθίσας ψηφίζει τὴν δαπάνην, εἰ ἔχει εἰς ἀπαρτισµόν; doesn't first
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
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
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
WEEK 21. The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1
WEEK 21 The Feast of Firstfruits, the Feast of Pentecost, and the Feast of Tabernacles OUTLINE DAY 1 I. The Feast of Firstfruits signifies the resurrected Christ as the firstfruits for our enjoyment as
ΦωτίστεΤονΚόσμο. ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ Νοεμβρίου Δεκεμβρίου 2017
ΦωτίστεΤονΚόσμο ΠΡΩΤΟΒΟΥΛΙΑ ΧΡΙΣΤΟΥΓΕΝΝΩΝ 2017 24 Νοεμβρίου -- 25 Δεκεμβρίου 2017 ΘΕΜΑ «Καθώς ακολουθούμε το παράδειγμα του Σωτήρος και ζούμε όπως ζούσε Εκείνος και όπως δίδασκε, αυτό το φως θα καίει μέσα
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
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
Relationships & Reconciliation. Engaging the World Series The Lord s Prayer
Relationships & Reconciliation Engaging the World Series The Lord s Prayer ZGM Vision Every Life for Jesus 11 Jan 2015 ZGM Mission We are a Spirit-led Community That Exalts Christ, By Equipping Disciples
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
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
ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ
ΟΙ ΑΞΙΕΣ ΤΗΣ ΖΩΗΣ THE VALUES OF LIFE Η ΥΠΕΥΘΥΝΟΤΗΤΑ..THE RESPONSIBILITY ΔΗΜΗΤΡΑ ΚΩΝΣΤΑΝΤΙΝΟΥ ΜΑΘΗΜΑΤΑ ΥΠΕΥΘΥΝΟΤΗΤΑΣ/ LESSONS ABOUT RESPONSIBILITY Μάθημα 1: Νιώθω υπερήφανος όταν.../ I feel proud when.
Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951)
1 Verklarte Nacht, Op.4 (Εξαϋλωμένη Νύχτα, Έργο 4) Arnold Schoenberg (1874-1951) Αναγνώσματα από το βιβλίο Η Απόλαυση της Μουσικής (Machlis, Forney), για τους μαθητές που θα μελετήσουν το έργο: «Ο Σαίνμπεργκ
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
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
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
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
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)
FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17
FINAL TEST B TERM-JUNIOR B STARTING STEPS IN GRAMMAR UNITS 8-17 Name: Surname: Date: Class: 1. Write these words in the correct order. /Γράψε αυτέσ τισ λέξεισ ςτη ςωςτή ςειρά. 1) playing / his / not /
1 John 5. LGNT - September 6, 2019 Page 1. Book Chapter Verse. Word # 1 John Greek. # of words. Numeric value. Interlinear English.
Book Chapter Verse Interlinear English Word # 1 John Greek # of letters # of words Numeric value 230501 everyone 01709 ΠΑΣ 3 281 230501 01710 Ο 1 70 230501 believing 01711 ΠΙΣΤΕΥΩΝ 8 1845 230501 that 01712
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
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
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
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
TMA4115 Matematikk 3
TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet
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
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
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
Στην παθητική φωνή η έμφαση δίνεται στην πράξη όχι στο ποιος την διέπραξε.
THE PASSIVE VOICE ΠΑΘΗΤΙΚΗ ΦΩΝΗ Στην παθητική φωνή η έμφαση δίνεται στην πράξη όχι στο ποιος την διέπραξε. Είναι επίσης πιθανό είτε κάποιος να αγνοεί το άτομο που έκανε κάτι (το ποιητικό αίτιο agent) είτε
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
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
13:31 38 Intro to farewell discourse. Jesus is going
South Central Gospel Partnership Day Conference THESE THINGS I HAVE SAID TO YOU John 14-16 If running a discipleship group/course, what topics would you want to cover? Purpose clauses in John 14-16 ταῦτα
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
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
1 JOHN 4:1--5:12 The New Testament Eyewitnesses The Son
70 The Spirit Agreement that Jesus is the Son is the Revelation of the Spirit Apostles which is the Apostolic witness Children Thus those who believe the Apostles are children Witnesses to The Love of
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
Door Hinge replacement (Rear Left Door)
Door Hinge replacement (Rear Left Door) We will continue the previous article by replacing the hinges of the rear left hand side door. I will use again the same procedure and means I employed during the
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)
BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN. Fairly true If I decide to learn something hard, I can.
BECAUSE WE REALLY WANT TO KNOW WHAT YOU THINK ABOUT SCHOOL AND YOUR GARDEN Name GRADE Science Teacher A. What do I think about School? bit I try hard to do well in school. I look forward to coming to school.
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
ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ
Ανοικτά Ακαδημαϊκά Μαθήματα στο ΤΕΙ Ιονίων Νήσων ΕΠΙΧΕΙΡΗΣΙΑΚΗ ΑΛΛΗΛΟΓΡΑΦΙΑ ΚΑΙ ΕΠΙΚΟΙΝΩΝΙΑ ΣΤΗΝ ΑΓΓΛΙΚΗ ΓΛΩΣΣΑ Ενότητα 9: Inversion Το περιεχόμενο του μαθήματος διατίθεται με άδεια Creative Commons εκτός
«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE
«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE We would like to invite you to participate in GAMIAN- Europe research project. You should only participate if you want to and choosing
Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get)
Νόμος περί Αναπηριών 2006 (Disability Act 2006) Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get) Greek Νόμος περί Αναπηριών
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,
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
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
Lecture 2. Soundness and completeness of propositional logic
Lecture 2 Soundness and completeness of propositional logic February 9, 2004 1 Overview Review of natural deduction. Soundness and completeness. Semantics of propositional formulas. Soundness proof. Completeness
2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, EVALUATION REPORT
2nd Training Workshop of scientists- practitioners in the juvenile judicial system Volos, 26-6-2016 Can anyone hear me? The participation of juveniles in juvenile justice. EVALUATION REPORT 80 professionals
[1] P Q. Fig. 3.1
1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One
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»
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
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
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